Design of an Interaction Region at C0 in the Tevatron

February 4, 2004

Table of Contents

[1 Introduction 5](#__RefHeading___Toc63699057)

[2 Accelerator Physics 6](#__RefHeading___Toc63699058)

[2.1 Lattice 6](#lattice)

[2.1.1 Injection 9](#injection)

[2.1.2 C0 Collisions 10](#c0-collisions)

[2.1.3 B0/D0 Collisions 13](#b0d0-collisions)

[2.2 Helix 14](#helix)

[2.2.1 Injection Helix 15](#injection-helix)

[2.2.2 C0 Collision Helix 16](#c0-collision-helix)

[2.2.3 B0/D0 Collision Helix 18](#b0d0-collision-helix)

[2.3 Orbit Correction and Physical Aperture
20](#orbit-correction-and-physical-aperture)

[2.4 Higher Order Correction 22](#higher-order-correction)

[2.4.1 Quadrupole Misalignment 22](#quadrupole-misalignment)

[2.4.2 Feeddown Circuits 24](#feeddown-circuits)

[2.5 Dynamic Aperture Calculations 26](#dynamic-aperture-calculations)

[2.5.1 Single Beam 27](#single-beam)

[2.5.2 Beam-beam 30](#beam-beam)

[2.6 Beam Halo Calculations and Collimators
33](#beam-halo-calculations-and-collimators)

[2.7 Emittance Growth Calculations 33](#emittance-growth-calculations)

[3 LHC Style Quadrupoles 34](#__RefHeading___Toc63699076)

[3.1 Overview and Conceptual Design 34](#overview-and-conceptual-design)

[3.2 Magnet Coils and Mechanical Description
37](#magnet-coils-and-mechanical-description)

[3.3 Field Quality 42](#field-quality)

[3.3.1 Iron Yoke Optimization 43](#iron-yoke-optimization)

[3.3.2 Magnet transfer function 44](#magnet-transfer-function)

[3.3.3 Field Harmonics 45](#field-harmonics)

[3.4 Quench Protection, Electrical Specifications, and Bus
48](#quench-protection-electrical-specifications-and-bus)

[3.4.1 Inductance, resistance and stored energy
48](#inductance-resistance-and-stored-energy)

[3.4.2 Voltage taps and heaters 48](#voltage-taps-and-heaters)

[3.4.3 Quench Detection and Protection
49](#quench-detection-and-protection)

[3.4.4 Bus 49](#bus)

[3.5 Cryostat Requirements 49](#cryostat-requirements)

[3.6 Cryogenic Specifications 52](#cryogenic-specifications)

[3.7 Design Changes, R&D, and Infrastructure Needs
53](#design-changes-rd-and-infrastructure-needs)

[4 New Spools 56](#__RefHeading___Toc63699091)

[4.1 Overview and Conceptual Design
56](#overview-and-conceptual-design-1)

[4.2 Corrector Design 57](#corrector-design)

[4.2.1 56" (1420mm) spool 58](#mm-spool)

[4.2.2 72" (1830mm) spool 62](#mm-spool-1)

[4.3 Dimensional Specifications 64](#dimensional-specifications)

[4.4 Cryogenic Specifications 67](#cryogenic-specifications-1)

[4.4.1 Item 67](#item)

[4.5 Quench Protection 67](#quench-protection)

[4.6 Connections and Interfacing 67](#connections-and-interfacing)

[4.7 Measurements and R&D to Date 69](#measurements-and-rd-to-date)

[4.7.1 HTS Leads 69](#hts-leads)

[4.7.2 Flat Coil Corrector Design 70](#flat-coil-corrector-design)

[5 Power Supplies 72](#__RefHeading___Toc63699104)

[5.1 High Current Power Supply Layout
72](#high-current-power-supply-layout)

[5.2 Buswork 73](#buswork)

[5.3 Electrical Specifications 73](#electrical-specifications)

[5.4 AC Power and LCW Requirements 74](#ac-power-and-lcw-requirements)

[5.5 Corrector Power Supply Configuration
74](#corrector-power-supply-configuration)

[5.6 B4 and C1 QPM Modifications 75](#b4-and-c1-qpm-modifications)

[5.7 Electrostatic Separator Power Supplies
75](#electrostatic-separator-power-supplies)

[6 Cryogenic Systems 76](#__RefHeading___Toc63699112)

[6.1 Heat Load 76](#heat-load)

[6.2 Cryogenic Capacity Limitation 77](#cryogenic-capacity-limitation)

[6.3 Layout 78](#layout)

[6.4 Cryogenic Controls Modifications
78](#cryogenic-controls-modifications)

[7 Vacuum Systems 80](#__RefHeading___Toc63699117)

[7.1 Layout 80](#layout-1)

[7.2 Requirements for Cryogenic Vacuum
80](#requirements-for-cryogenic-vacuum)

[7.3 Requirements for Warm Vacuum 80](#requirements-for-warm-vacuum)

[8 Controls 81](#__RefHeading___Toc63699121)

[8.1 Integration with Current Tevatron Systems
81](#integration-with-current-tevatron-systems)

[8.2 Low Beta QPM System 81](#low-beta-qpm-system)

[8.3 Controls Modifications 82](#controls-modifications)

[9 Beam Instrumentation 84](#__RefHeading___Toc63699125)

[9.1 Synchrotron Light Monitor 84](#synchrotron-light-monitor)

[9.2 Instrumentation between B4 and C1
84](#instrumentation-between-b4-and-c1)

[9.3 Instrumentation Software Modifications
85](#instrumentation-software-modifications)

[10 Commissioning 86](#__RefHeading___Toc63699129)

[10.1 Operational Scenarios 86](#operational-scenarios)

[10.2 Commissioning Plan 87](#commissioning-plan)

[11 Conversion of C0 to a Normal Straight Section
88](#__RefHeading___Toc63699132)

[11.1 Overview 88](#overview)

[11.1.1 Motivation 88](#motivation)

[11.1.2 Scope of Change 89](#scope-of-change)

[11.1.3 Tevatron Beam Optics Considerations
91](#tevatron-beam-optics-considerations)

[11.2 Installation Plan 92](#installation-plan)

[11.2.1 Tunnel modifications 94](#tunnel-modifications)

[11.2.2 LCW modifications 94](#lcw-modifications)

[11.2.3 Controls, PS, and QPM modifications
96](#controls-ps-and-qpm-modifications)

[11.3 Recommissioning Plan 96](#recommissioning-plan)

[12 Installation, Integration, Schedule, and Cost
98](#__RefHeading___Toc63699142)

[12.1 Tunnel installation 98](#tunnel-installation)

[12.1.1 Magnetic Element Installation
98](#magnetic-element-installation)

[12.1.2 Electrostatic Separators 99](#electrostatic-separators)

[12.1.3 Q1 and P Spool Removal from A4/B1
100](#q1-and-p-spool-removal-from-a4b1)

[12.1.4 Beam Collimators and Shielding
101](#beam-collimators-and-shielding)

[12.2 Interfacing with civil construction project
101](#interfacing-with-civil-construction-project)

[12.3 Interfacing with Detector Installation
101](#interfacing-with-detector-installation)

[12.4 Schedule and Cost 102](#schedule-and-cost)

[13 Appendices 103](#__RefHeading___Toc63699151)

[13.1 Table of beamline elements between B43 and C17
103](#table-of-beamline-elements-between-b43-and-c17)

[13.2 Alternative Corrector Approach -- "Flat Coil Array" Design
107](#alternative-corrector-approach-flat-coil-array-design)

[13.2.1 Corrector Magnetic Design 109](#corrector-magnetic-design)

[13.2.2 Corrector Type-A 109](#corrector-type-a)

[13.2.3 Corrector Type B 114](#corrector-type-b)

[13.2.4 Corrector Type C 115](#corrector-type-c)

[13.2.5 Mechanical Design Concepts 118](#mechanical-design-concepts)

[13.2.6 Electrical Circuits, Currents and Power Supplies
118](#electrical-circuits-currents-and-power-supplies)

[13.3 Preliminary Test Plan for H Spool with HTS Current Leads
120](#preliminary-test-plan-for-h-spool-with-hts-current-leads)

1.  []{#__RefHeading___Toc63699057 .anchor}Introduction

The C0 Interaction Region (IR) project provides a solution for creating
high luminosity proton-antiproton collisions at the C0 region of the
Tevatron for the BTeV experiment. The two largest technical components
are modified LHC-style quadrupoles and newly designed corrector magnet
packages (spools). This project takes full advantage of the Tevatron
luminosity upgrades of the Run II Collider Program to obtain the highest
luminosity possible for BTeV. It is designed to allow continued
operation of the CDF and D0 experiments concurrently with the BTeV
experiment. It makes use of proven existing Tevatron infrastructure to
the fullest extent possible without compromising design goals.
Modifications to the Tevatron are almost entirely restricted to the
region from B43 to C17 (445 meters) and the 3 service buildings above.

The lattice design is robust. It utilizes asymmetric quadrupole triplets
on either side of the IR to produce a 35 cm \* at C0 ̶ the same design
\* as B0 and D0. Additional quadrupoles, some new and some reused from
the Tevatron Low Beta Project, match to the Run II lattice at all
energies and at all steps of the transition from injection to the low
beta lattice. The C0 insertion itself introduces exactly one unit of
tune to both horizontal and vertical planes, so that the Tevatron
fractional tunes remain unchanged. This design minimizes the impact on
Tevatron operation. Corrector magnet packages are designed to give
excellent orbit control and coupling correction to provide added
insurance against magnet misalignments and imperfections. The power
supply configuration is versatile enough to tune out any foreseeable
magnet errors. This lattice design is optimized for 36 x 36 bunch
operation but does not preclude 132 nsec operation.

The LHC IR quadrupole produced by the Fermilab Technical Division is a
well tested and proven magnet. A modification of this design provides a
cost-effective and timely solution for the C0 IR project. The
modifications are restricted to the cryostat and end enclosures of the
magnet ̶ the cold mass remains the same as the original LHC design.

The unique demands of the C0 IR and the antiquity of the original
Tevatron spools preclude the use of these spools in this project. New
spools will be designed and fabricated. The baseline design uses a
standard nested cos(n) coil package to produce dipole, quadrupole, and
sextupole fields. In addition, these spools contain the high current
leads for the low beta quadrupoles. Limitations in the helium liquifying
capacity of the Tevatron cryogenic system necessitate the use of high
temperature superconductor for these leads.

The scope of this project also encompasses the construction and
installation of new power supplies, new cryogenic elements in the
Tevatron tunnel, modifications to low conductivity water systems, vacuum
systems, beam collimation systems, controls infrastructure, software,
instrumentation, and operational procedures ̶ all the things necessary
to make a high energy accelerator function.

Read on......

2.  []{#__RefHeading___Toc63699058 .anchor}Accelerator Physics

## Lattice

Every facet of successful Tevatron collider operations is tied
intimately to specific details of the optical lattice functions in the
ring. As examples, the locations of beam collimators, separators for
helix generation, and the feeddown circuits are all determined largely
by the distribution of betatron phase advance. So as not to disrupt
these nominal Run II operating parameters it is essential that a new C0
Interaction Region (IR) insertion meld seamlessly with this existing
Tevatron lattice. This implies the need to create an entirely localized
insertion one which is transparent to the rest of the machine. This
constraint has important design implications, the most notable of which
are pointed out below:

• An IR design similar to that employed at B0 & D0 is unacceptable as a
C0 candidate. The addition of such a (single) low- region to the machine
would raise the tune by a half-integer in each plane, moving them far
from the standard operating point and directly onto the 21.0 integer
resonance. The nominal (fractional) tunes can be retained by adding 2
low-\'s locally in each plane, thereby boosting the machine tunes by a
full integer.

• The B0 & D0 IR\'s are not optically-isolated entities. Progression
through the B0/D0 low- squeeze involves adjusting, not only the main IR
quadrupoles, but also the tune quad strings distributed around the ring.
The result is that lattice functions at any point in the ring, and the
phase advances across any section of the ring, are not fixed quantities,
but vary through the squeeze sequence. For the operational mode of
B0/D0-only collisions, the C0 insertion must be sufficiently flexible to
track these changing matching conditions.

• With collisions only at B0 & D0 the unit of tune added by the C0
insert ensures that the incoming & outgoing helices are automatically
matched into the Run II values. To maintain this match with collisions
at all 3 IP\'s, however, would require additional separators in the
short B0 C0 & C0 D0 arcs. There is no space available for more
separators, so high luminosity collisions can only be created at B0 &
D0, or just C0, but not all three simultaneously. Furthermore, without
new arc separators the 2 IP collision options, B0 & C0 or D0 & C0, are
also excluded.

Both the series & independent C0 IR quad circuits are illustrated in
Figure 2-1. The specialized IR magnets required fall into 3 gradient
ranges. First, there are LHC-like magnets operating at or below 170 T/m.
This is substantially less than the \>220 T/m LHC design, but the
gradients are limited here by the Tevatron 4.5K cryogenics. Second,
there are high-field 140 T/m Q1 quadrupoles previously installed for
Tevatron collider operation. And third, there are strong (25 T.m/m) quad
correction spools for the final optical match into the arcs.

Composition of the quadrupole circuits is described below, with the
indicated lengths being magnetic lengths.

• The triplets:

Q1 : 96.5\" 170 T/m

Q2 : 173.5\" 170 T/m

Q3 : 96.5\" 170 T/m

![](media/image1.wmf){width="5.230555555555555in"
height="4.079861111111111in"}

**Figure 2-1: Power circuits of the IR quadrupoles.**

Schematic layout of an IR triplet is given in Figure 2-2, showing the
slot lengths & magnetic lengths of the elements, and spaces allocated
for flanges, cryo, coil supports, etc. A special correction package is
installed between the Q2 & Q3 magnets. This contains both vertical &
horizontal BPM\'s, dipole correctors in each plane, plus a trim skew
quad. The dipole correctors are well situated for beam control at the
IP: x y \> 60% max, and the betatron phase advance to the IP is almost
exactly 90o in both planes. Because of the almost zero degrees of phase
advance across the triplet magnets, the trim skew quad is perfectly
located to compensate locally for triplet roll mis-alignments. The final
focus triplets are powered in series, with a small additional power
source added to Q2 for independent gradient variation to complete the
match to the appropriate IP optics.

![](media/image2.wmf){width="5.625694444444444in"
height="1.9027777777777777in"}

**Figure 2-2: Details of the IR triplet**

• B48/C12 & B47/C13:

Q4 : 79\" 170 T/m

Q5 : 54\" 170 T/m

Apart from their magnetic lengths the Q4 & Q5 magnets are the same
design as the triplet quadrupoles, having adequate space at each end of
the cryostat to accommodate the necessary ancillary hardware (see Figure
2-2). These quadrupoles are accompanied by new, short (56.175\") spools,
containing BPM\'s and dipole correctors in each plane. These spools also
serve as the magnet power feeds & transport the main bus.

• B46/B45 & C14/C15:

Q6 : 55.19\" 140 T/m

Q7 : 55.19\" 140 T/m

The four Q6 & Q7 magnets are independently powered. The regular 66\" arc
quads and their spools at the B46, B45, C14 & C15 locations are replaced
with relocated highfield Q1 low-beta quads (defunct in Run II) from CDF
& D0, along with their accompanying P spools. The P spools have BPM\'s
and dipole correctors in each plane, plus a skew quad. These spools also
serve as the magnet power feeds & transport the main bus.

• B43/B44 & C16/C17:

The normal 72\" Tevatron arc spools at these 4 locations are replaced by
72\" spools containing high-field (25 T.m/m) trim quads plus standard
strength horizontal or vertical dipoles and chromaticity sextupoles.

• B38/B42:

The trim quads (7.5 T.m/m) at B38 & B42 are removed from the main tune
quad circuit and powered independently for final optical matching to the
arc.

This design uses non-standard separations between some of the
insertion\'s inner arc quadrupoles. Between the B48 & B47 \[C12 & C13\]
quadrupoles space is reduced by 1 dipole, whereas between B46 & B45
\[C14 & C15\] separation increases by 1 dipole. Extensive simulations
have shown that this configuration contributes markedly to the
robustness of the IR\'s tuning range.

Trim quads are allocated in a lopsided configuration, with 2 more
installed in the upstream end of the insert. In B-sector it is possible
to extend insert elements a good distance back into the arc before
interfering with Run II operation. This is not so in C-sector. The 4
vertical separators at C17 are integral components of Run II operation,
and therefore define the downstream insert boundary.

There are 15 optical constraints the insertion satisfies. The 6 incoming
Twiss parameters are matched at the IP to x\* = y\* \*, x\* = y\* , \*,
\*, and then matched back into the nominal arc values at the downstream
end of the insert (at C17). The fractional Run II phase shifts, x and y,
are preserved across the insert. The final constraint imposed in the
design is that x,max = y,max in the triplets on each side of the IP.
While this last restriction isn\'t really crucial, it is the best
choice, minimizing the consumption of aperture in the low- quads.

Every stage of the C0 low beta squeeze from \* = 3.50 to 0.35 m can
match exactly to any step in the B0/D0 low beta squeeze. Subsequent
sections illustrate these lattice parameters corresponding to the
specific operational conditions:

\(1\) Injection : \*= 3.50 m @ C0 (x\*, y\*) = (1.61,1.74) m @ B0/D0

\(2\) C0 Collisions : \*= 0.35 m @ C0 (x\*, y\*) = (1.61,1.74) m @ B0/D0

\(3\) B0/D0 Collisions : \*= 3.50 m @ C0 \* = 0.35 m @ B0 & D0

All gradient entries in the accompanying tables reflect 1 TeV/c
operations. Highlighted entries indicate those magnets that must change
polarity at some point during the transition between the various
operating modes.

### Injection

In the injection lattice, shown in Figure 2-3, \* = 3.50 m results in a
~max~ of 177 m in the triplets. This is appreciably less than the 240 m
of the B0 & D0 injection lattices and, so, is not anticipated to pose
any aperture problems for Tevatron operations. The corresponding
quadrupole gradients are listed in Table 2-1 (at 1 TeV/c).

![](media/image3.wmf){width="5.122222222222222in"
height="3.7618055555555556in"}

**Figure 2-3: C0 injection optics**

**Table 2-1: C0 IR gradients for 1 TeV/c injection optics.**

+-----------+-----------+-----------+-----------+-----------+-----------+
| INJECTION |           |           |           |           |           |
| OPTICS :  |           |           |           |           |           |
| C0 @ \* = |           |           |           |           |           |
| 3.50m :   |           |           |           |           |           |
| B0/D0 @   |           |           |           |           |           |
| \* =      |           |           |           |           |           |
| 1.65m     |           |           |           |           |           |
| (**1      |           |           |           |           |           |
| TeV/c)**  |           |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
|           | Gradient  | Current   |           | Gradient  | Current   |
|           |           |           |           |           |           |
|           | (T/m)     | \(A\)     |           | (T/m)     | \(A\)     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q1D       | -164.783  | 9267      | Q1F       | 164.783   | 9267      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q2F       | 168.814   | 9493      | Q2D       | -168.814  | 9493      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q3D       | -164.783  | 9267      | Q3F       | 164.783   | 9267      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB48      | 133.019   | 7480      | QC12      | -133.019  | 7480      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB47      | -145.047  | 8157      | QC13      | 145.047   | 8157      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB46      | 117.055   | 4045      | QC14      | -122.786  | 4248      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB45      | -92.551   | 3198      | QC15      | 92.940    | 3211      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB44      | 4.939     |           | TC16      | -25.569   |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB43      | 17.724    |           | TC17      | -10.470   |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB42      | 6.793     |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB39      | 0         |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB38      | 3.013     |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

### C0 Collisions

For collisions at C0, the B0 & D0 optics remain in their injection
configuration, while at C0 \* is squeezed from 3.50 m at injection to
0.35 m Current Tevatron Collider understanding and experience suggests
that the smallest realistic \* attainable is limited by the adverse
impact on the beam by high-order multipoles in the low- quadrupoles and,
therefore, ~max~ in the low beta triplets. In the C0 IR lattice the Q1
magnets at C0 are roughly 15\' farther from the IP than the
corresponding ones at B0 & D0. As a result, ~max~ is considerably larger
at C0 for any given value of \*. With \* = 35 cm, ~max~ has grown to
1660 m (Figure 2-4), which is significantly larger than the ~max~ of
\~1130 m for a \* = 35 cm at the other IP\'s. In addition, the 63 mm
physical aperture of the LHC magnets is also less than the 70 mm of the
B0/D0 triplets. Nonetheless, dynamic aperture studies indicate that this
tighter aperture restriction should not be a limiting factor in
determining the minimum \* attainable.

For C0 collisions, \* at the IP is squeezed to 35 cm the same value as
for B0/D0 collisions. The luminosity at C0 will therefore be identical
to that of B0/D0 at the end of Run II. Anticipated Collider parameters
at the end of Run II are summarized in Table 2-3.

![](media/image4.wmf){width="5.144444444444445in"
height="3.642361111111111in"}

![](media/image5.wmf){width="5.122222222222222in"
height="3.7354166666666666in"}

**Figure 2-4: C0 collision optics B38 C19 (top), and ring-wide
(bottom).**

**Table 2-2: IR gradients for C0 collisions at \* = 35 cm.**

+-----------+-----------+-----------+-----------+-----------+-----------+
| C0        |           |           |           |           |           |
| C         |           |           |           |           |           |
| OLLISIONS |           |           |           |           |           |
| @ \* =    |           |           |           |           |           |
| 0.35 m :  |           |           |           |           |           |
| B0/D0 @   |           |           |           |           |           |
| \* = 1.65 |           |           |           |           |           |
| m (**1    |           |           |           |           |           |
| TeV/c)**  |           |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
|           | Gradient  | Current   |           | Gradient  | Current   |
|           |           |           |           |           |           |
|           | (T/m)     | \(A\)     |           | (T/m)     | \(A\)     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q1D       | -169.228  | 9517      | Q1F       | 169.228   | 9517      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q2F       | 165.397   | 9301      | Q2D       | -165.397  | 9301      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q3D       | -169.228  | 9517      | Q3F       | 169.228   | 9517      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB48      | 169.688   | 9524      | QC12      | -169.688  | 9524      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB47      | -168.875  | 9497      | QC13      | 168.875   | 9497      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB46      | 91.625    | 3166      | QC14      | -101.95   | 3523      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB45      | -66.539   | 2299      | QC15      | 76.322    | 2637      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB44      | 9.528     |           | TC16      | -35.373   |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB43      | -0.819    |           | TC17      | 22.589    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB42      | -0.844    |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB39      | 0         |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB38      | -7.424    |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

**Table 2-3: Collider parameters projected for the end of Run II. The
\'Base\' projection uses conservative performance estimates for Run II
upgrade projects. The \'Design\' parameters include more ambitious, but
realistic, expectations of the upgrades.**

+------------------------+--------------+--------------+--------------+
| C0 COLLISION           |              |              |              |
| PARAMETERS             |              |              |              |
+------------------------+--------------+--------------+--------------+
|                        | BASE         | DESIGN       |              |
|                        |              |              |              |
|                        | PROJECTION   | PROJECTION   |              |
+------------------------+--------------+--------------+--------------+
| protons/bunch          | 250          | 270          | x 109        |
+------------------------+--------------+--------------+--------------+
| pbars/bunch            | 76.4         | 129.6        | x 109        |
+------------------------+--------------+--------------+--------------+
| proton emittance       | 18           | 18           | π µm         |
+------------------------+--------------+--------------+--------------+
| pbar emittance         | 18           | 18           | π µm         |
+------------------------+--------------+--------------+--------------+
| \* at C0 IP            | 0.35         | 0.35         | m            |
+------------------------+--------------+--------------+--------------+
| Bunches                | 36           | 36           |              |
+------------------------+--------------+--------------+--------------+
| Bunch length (rms)     | 0.45         | 0.45         | m            |
+------------------------+--------------+--------------+--------------+
| Hour-Glass Form Factor | 0.70         | 0.70         |              |
+------------------------+--------------+--------------+--------------+
| Proton tune shift      | 0.0005       | 0.0008       |              |
+------------------------+--------------+--------------+--------------+
| Pbar tune shift        | 0.0017       | 0.0018       |              |
+------------------------+--------------+--------------+--------------+
| Initial Luminosity     | 160.5        | 294.0        | x 1030       |
|                        |              |              | cm-2s-1      |
+------------------------+--------------+--------------+--------------+

### B0/D0 Collisions

For collisions at just B0 & D0, the C0 \* is fixed at its injection
value of 3.50 m while at B0 & D0 \* is squeezed from \~1.65 m at
injection to 0.35 m (see Figure 2-5) A comparison of C0 IR gradients
listed in Table 2-4 with the injection values of Table 2-1 demonstrates
the small tuning changes required at C0 to fix \* = 3.50 m while
maintaining the ideal optical match to the nominal Run II squeeze
lattice.

![](media/image6.wmf){width="5.394444444444445in"
height="3.8784722222222223in"}

**Figure 2-5: B0/D0 collision optics**

**Table 2-4: C0 IR gradients for B0/D0 collisions and \* fixed at 3.50 m
at C0.**

+-----------+-----------+-----------+-----------+-----------+-----------+
| B0/D0     |           |           |           |           |           |
| C         |           |           |           |           |           |
| OLLISIONS |           |           |           |           |           |
| @ \* =    |           |           |           |           |           |
| 0.35 m :  |           |           |           |           |           |
| C0 @ \* = |           |           |           |           |           |
| 3.50 m    |           |           |           |           |           |
| (**1      |           |           |           |           |           |
| TeV/c)**  |           |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
|           | Gradient  | Current   |           | Gradient  | Current   |
|           |           |           |           |           |           |
|           | (T/m)     | \(A\)     |           | (T/m)     | \(A\)     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q1D       | -165.998  | 9335      | Q1F       | 165.998   | 9335      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q2F       | 168.619   | 9482      | Q2D       | -168.619  | 9482      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| Q3D       | -165.998  | 9335      | Q3F       | 165.998   | 9335      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB48      | 131.721   | 7407      | QC12      | -131.721  | 7407      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB47      | -144.299  | 8115      | QC13      | 144.299   | 8115      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB46      | 117.055   | 4045      | QC14      | -122.786  | 4248      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| QB45      | -92.551   | 3302      | QC15      | 92.940    | 3211      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB44      | 8.059     |           | TC16      | -15.743   |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB43      | 9.440     |           | TC17      | -8.110    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB42      | 6.252     |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB39      | 0         |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| TB38      | 3.870     |           |           |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

## Helix

With 36x36 bunch operation in the Tevatron there are 72 potential
collision points of the proton and pbar beams. In Run II there are
currently 6 sets of electrostatic separator modules available in both
horizontal and vertical planes to keep the proton and pbar orbits
separated everywhere in the ring except at the B0 & D0 IP\'s during
collisions. One part of the Run II upgrade project is to increase by 6
the number of separator modules in the ring. The optimum sites for these
new separators is still being studied. Another part of the Run II plan
is to enhance the performance of the existing units. The present
separators are run with gradients as high as \~40 kV/cm (\~10.3 µrad
kick at 1 TeV/c) before sparking becomes a problem. This is believed to
be a conservative estimate of the maximum attainable gradient, however,
and that with conditioning as much as a 30% increase should be possible.
The outcome of these separator upgrades will be a better controlled,
smoother helix at injection, where apertures are problematic, and
increased beam separation at collision where the helix is limited by the
available gradients. In view of the uncertainties still associated with
implementing the Run II separator upgrade, however, in the discussions
to follow only the currently installed ring separator configuration is
considered, and the modules are assumed to have the conservative maximum
electric field gradient of 40 kV/cm.

In the BTeV era it is expected that the Tevatron will continue with
36x36 bunch operations. Additional separator modules will then need to
be added to create collisions at the C0 IP. Like the other 2 IR\'s these
will be installed immediately outboard of the C0 IR triplets. At B49
there will be a set of 2 horizontal modules and 1 vertical module, with
the reverse configuration installed at C11.

### Injection Helix

At the injection energy of 150 GeV, separation of the p-pbar orbits is
controlled using a small sub-set of the 12 separators available in the
machine. Separator strength is not an issue at 150 GeV, but the large
beam sizes lead to aperture problems. The horizontal orbits are largely
determined by the B17 separators, and the vertical by the C17
separators. The horizontal B17 gradients in particular are constrained
by the aperture restrictions at the F0 injection Lambertson.

One separator solution from Run II is listed in Table 2-5. Here, only 4
sets of separators are used to create the helix, and the new B49/C11
separators are not used at all. The resulting beam separation around the
ring is shown in Figure 2-6. Outside of the B38 C17 C0 insert the helix
is unchanged from the Run II value, and through the C0 IR region it can
be seen that beam separation is at least as good as throughout the rest
of the ring. The average separation is \~8.

**Table 2-5: Injection Separator gradients at 150 GeV/c.**

  ------------ ------- --------------- ----------- ------- ---------------
  INJECTION                                                
  HELIX : C0 @                                             
  \* = 3.50m :                                             
  B0/D0 @ \* =                                             
  3.50m (**150                                             
  GeV/c)**                                                 

  Horizontal                           Vertical            

               \#      kV/cm                       \#      kV/cm

  A49          1       0.0             A49         2       0.0

  B11          2       -14.800         B11         1       -9.050

  B17          4       25.740                              

  B49          2       0.0             B49         1       0.0

  C11          1       0.0             C11         2       0.0

                                       C17         4       -26.150

  C49          1       0.0             C49         2       0.0

  D11          2       0.0             D11         1       0.0

  D48          1       0.0                                 

                                       A17         1       0.0
  ------------ ------- --------------- ----------- ------- ---------------

![](media/image7.wmf){width="5.479861111111111in"
height="4.180555555555555in"}

**Figure 2-6: Injection helix at 150 GeV/c. N = 20π µm & p/p = 6.E-4.**

### C0 Collision Helix

For collisions at C0 the optics at B0 & D0 remain in their Injection
configuration. In this case, all the separators in the ring become
available for bringing beams together at the C0 IP, while keeping them
separated everywhere else. One possible (minimal) separator solution is
given in Table 2-6. The selection of separators has not been optimized
particularly, other than to ensure adequate beam separation around the
ring. Many more combinations still need to be explored.

Figures 2-7 and 2-8 illustrate the beam separation across the insert
from B38 C21, and also the separation around the ring. With this
separator solution the closest approach through the insert is at the 1st
parasitic crossing, where separation is about 3.7. Although 5 separation
is generally believed to be the minimum acceptable separation in the Run
II collision lattice, dynamic aperture studies indicate that these 1st
parasitic crossings are relatively benign for C0 collisions. Elsewhere
in the ring, separation drops close to 5 in a few spots, but otherwise
the average separation is \~8. Oscillations in the helix could probably
be smoothed further using a larger subset of separators.

**Table 2-6**: C0 collision separator gradients at 1 TeV/c.

  ------------ ------- --------------- ----------- ------- ---------------
  C0                                                       
  COLLISIONS @                                             
  \* = 0.35 m                                              
  : B0/D0 @ \*                                             
  = 1.65 m                                                 
  (**1                                                     
  TeV/c)**                                                 

  Horizontal                           Vertical            

               \#      kV/cm                       \#      kV/cm

  A49          1       0.0             A49         2       25.744

  B11          2       0.0             B11         1       -25.744

  B17          4       18.112                              

  B49          2       -40.000         B49         1       -40.000

  C11          1       40.000          C11         2       40.000

                                       C17         4       -20.355

  C49          1       13.486          C49         2       0.0

  D11          2       -13.486         D11         1       0.0

  D48          1       0.0                                 

                                       A17         1       0.0
  ------------ ------- --------------- ----------- ------- ---------------

![](media/image8.wmf){width="5.0in" height="3.7618055555555556in"}

**Figure 2-7: Beam separation through the C0 IR during C0 collisions. N
= 20π µm & p/p = 1.47E-4.**

![](media/image9.wmf){width="5.531944444444444in" height="4.125in"}

**[F]{.smallcaps}igure 2-8: Ring-wide beam separation during C0only
collisions. N = 20π µm & p/p = 1.47E-4.**

### B0/D0 Collision Helix

With collisions at just B0 & D0, the optics at C0 remain at the
injection value of \* = 3.50 m, and the B49 & C11 separator voltages are
turned up to create horizontal & vertical separation bumps at the C0 IP.
Because the phase advance across the C0 separators is nearly 180o in
each plane, to a very good approximation the C0 bumps cancel away from
the IR region. The settings of the rest of the ring separators remain
essentially unchanged from their nominal Run II B0/D0 collision helix
values (see Table 2-7). The resulting beam separation around the machine
is shown in Figure 2-9 below. Away from the B0 & D0 IP\'s beam
separation is 5 everywhere, with an average separation of \~8.5.

![](media/image10.wmf){width="5.479861111111111in"
height="3.9583333333333335in"}

**Figure 2-9 Separation during B0 & D0 collisions. N = 20π µm & p/p =
1.47E-4.**

**Table 2-7: Separator gradients for B0/D0 collisions at 1 TeV/c.**

  ------------ ------- --------------- ----------- ------- ---------------
  B0/D0                                                    
  COLLISIONS @                                             
  \* = 0.35 m                                              
  : C0 @ \* =                                              
  3.50 m (**1                                              
  TeV/c)**                                                 

  Horizontal                           Vertical            

               \#      kV/cm                       \#      kV/cm

  A49          1       40.000          A49         2       -33.287

  B11          2       40.000          B11         1       40.000

  B17          4       -18.864                             

  B49          2       40.000          B49         1       40.000

  C11          1       40.000          C11         2       40.000

                                       C17         4       -19.180

  C49          1       37.197          C49         2       33.414

  D11          2       -34.509         D11         1       40.000

  D48          1       -5.162                              

                                       A17         1       1.736
  ------------ ------- --------------- ----------- ------- ---------------

## Orbit Correction and Physical Aperture

From Table 2-8, dipole corrector bumps can be calculated for controlling
position and angle at the IP. Tables 2-9 and 2-10 give the correct kick
ratios for 2 efficient position bumps and 2 angle bumps in each plane.
Other choices of magnet combinations are possible. The dipole correctors
have integrated fields of 0.48 T.m. At 1 TeV/c this translates into a
maximum kick angle of 144 µrad. Solutions (a) use the triplet spool
package correctors, while solutions (b) use only arc correctors.

**Table 2-8**: C0 IR correctors and lattice functions.

+-----+-----+--------------------+------+------+------+------+------+
| C0  |     |                    |      |      |      |      |      |
| IR  |     |                    |      |      |      |      |      |
| C   |     |                    |      |      |      |      |      |
| ORR |     |                    |      |      |      |      |      |
| ECT |     |                    |      |      |      |      |      |
| ION |     |                    |      |      |      |      |      |
| SP  |     |                    |      |      |      |      |      |
| OOL |     |                    |      |      |      |      |      |
| PA  |     |                    |      |      |      |      |      |
| CKA |     |                    |      |      |      |      |      |
| GES |     |                    |      |      |      |      |      |
+-----+-----+--------------------+------+------+------+------+------+
| S   | Sp  | Elements           | x    | x    | x    | y    | y    |
| ite | ool |                    |      |      |      |      |      |
|     |     |                    | \    | (2π) | \    | \    | (2π) |
|     | T   |                    | (m\) |      | (m\) | (m\) |      |
|     | ype |                    |      |      |      |      |      |
+-----+-----+--------------------+------+------+------+------+------+
| B38 | TSE | HD, QTF, SxF       | 90.4 | 0    | 3.66 | 29.6 | 0    |
|     |     |                    |      | .005 |      |      | .018 |
+-----+-----+--------------------+------+------+------+------+------+
| B39 | TSB | VD, QTD, SxD       | 33.2 | 0    | 3.00 | 87.2 | 0    |
|     |     |                    |      | .104 |      |      | .110 |
+-----+-----+--------------------+------+------+------+------+------+
| B42 | TSC | HD, QTF, SxF       | 1    | 0    | 5.87 | 30.0 | 0    |
|     |     |                    | 03.6 | .182 |      |      | .217 |
+-----+-----+--------------------+------+------+------+------+------+
| B43 | X1  | VD, QT, SxD        | 29.8 | 0    | 3.57 | 1    | 0    |
|     |     |                    |      | .278 |      | 00.2 | .301 |
+-----+-----+--------------------+------+------+------+------+------+
| B44 | X1  | HD, QT, SxF        | 84.6 | 0    | 5.54 | 32.3 | 0    |
|     |     |                    |      | .371 |      |      | .395 |
+-----+-----+--------------------+------+------+------+------+------+
| B45 | TSP | H&VD, SQ, H&VBPM   | 23.1 | 0    | 2.22 | 1    | 0    |
|     |     |                    |      | .491 |      | 02.7 | .476 |
+-----+-----+--------------------+------+------+------+------+------+
| B46 | TSP | H&VD, SQ, H&VBPM   | 92.9 | 0    | 1.48 | 66.6 | 0    |
|     |     |                    |      | .622 |      |      | .552 |
+-----+-----+--------------------+------+------+------+------+------+
| B47 | X2  | H&VD, H&VBPM       | 33.4 | 0    | 0.32 | 2    | 0    |
|     |     |                    |      | .723 |      | 10.6 | .588 |
+-----+-----+--------------------+------+------+------+------+------+
| B48 | X2  | H&VD, H&VBPM       | 1    | 0    | 0.43 | 1.70 | 0    |
|     |     |                    | 23.8 | .767 |      |      | .777 |
+-----+-----+--------------------+------+------+------+------+------+
| B49 | TSH | H&VD, SQ, VBPM     | 1    | 1    | 0.00 | 8    | 1    |
|     |     |                    | 60.7 | .240 |      | 75.0 | .047 |
+-----+-----+--------------------+------+------+------+------+------+
| C0  | X3  | H&VD, SQ, H&VBPM   | 10   | 1    | 0.00 | 10   | 1    |
| U   |     |                    | 42\. | .247 |      | 17\. | .049 |
+-----+-----+--------------------+------+------+------+------+------+
| C   |     |                    | 0.35 | 1    | 0.00 | 0.35 | 1    |
| 0\* |     |                    |      | .494 |      |      | .297 |
+-----+-----+--------------------+------+------+------+------+------+
| C0  | X3  | H&VD, SQ, H&VBPM   | 10   | 1    | 0.00 | 10   | 1    |
| D   |     |                    | 17\. | .742 |      | 42\. | .545 |
+-----+-----+--------------------+------+------+------+------+------+
| C12 | X2  | H&VD, H&VBPM       | 17.3 | 1    | 0.43 | 95.4 | 2    |
|     |     |                    |      | .778 |      |      | .018 |
+-----+-----+--------------------+------+------+------+------+------+
| C13 | X2  | H&VD, H&VBPM       | 2    | 2    | 2.53 | 30.6 | 2    |
|     |     |                    | 53.4 | .207 |      |      | .087 |
+-----+-----+--------------------+------+------+------+------+------+
| C14 | TSP | H&VD, SQ, H&VBPM   | 59.9 | 2    | 1.03 | 95.7 | 2    |
|     |     |                    |      | .247 |      |      | .171 |
+-----+-----+--------------------+------+------+------+------+------+
| C15 | TSP | H&VD, SQ, H&VBPM   | 99.0 | 2    | 1.88 | 17.0 | 2    |
|     |     |                    |      | .320 |      |      | .356 |
+-----+-----+--------------------+------+------+------+------+------+
| C16 | X1  | VD, QT, SxD        | 20.6 | 2    | 2.08 | 1    | 2    |
|     |     |                    |      | .447 |      | 04.1 | .474 |
+-----+-----+--------------------+------+------+------+------+------+
| C17 | X1  | HD, QT, SxF        | 90.1 | 2    | 5.32 | 29.7 | 2    |
|     |     |                    |      | .558 |      |      | .571 |
+-----+-----+--------------------+------+------+------+------+------+

HBPM & VBPM - position monitors

HD & VD - trim dipoles 0.48 T.m

QTF & QTD - tune quads 7.5 T.m/m

SxF & SxD - chromaticity sextupoles 450 T.m/m\^2

QT - strong trim quads 25 T.m/m

SQ - skew quadrupole 7.5 T.m/m

**Table 2-9: Relative dipole kick strengths to vary the beam positions
(x\*, y\*) at the IP while fixing the angles (x\'\*, y\'\* ) Positions
(x\*, y\*) are in mm and is corrector kick angle in mrad of the
strongest corrector.**

+---------+------+----------+----------+------+----------+----------+
|         | X\*  |          |          | Y\*  |          |          |
|         | POSI |          |          | POSI |          |          |
|         | TION |          |          | TION |          |          |
|         | BUMP |          |          | BUMP |          |          |
|         |      |          |          |      |          |          |
|         | COEF |          |          | COEF |          |          |
|         | FICI |          |          | FICI |          |          |
|         | ENTS |          |          | ENTS |          |          |
+---------+------+----------+----------+------+----------+----------+
|         |      | \(a\)    | \(b\)    |      | \(a\)    | \(b\)    |
+---------+------+----------+----------+------+----------+----------+
| B45     |      |          |          |      | -0.0706  | -0.0052  |
+---------+------+----------+----------+------+----------+----------+
| B46     |      | -0.0861  | +0.5043  |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| B47     |      |          |          |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| B48     |      |          |          |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| B49     |      |          | +1.0     |      |          | -0.3881  |
+---------+------+----------+----------+------+----------+----------+
| C0U     |      | +0.9882  |          |      | +1.0     |          |
+---------+------+----------+----------+------+----------+----------+
| C0      | X\*  | 19.1     | 7.3      | Y\*  | 18.4     | 6.8      |
|         | =    |          |          | =    |          |          |
+---------+------+----------+----------+------+----------+----------+
| C0D     |      | +1.0     |          |      | +0.9043  |          |
+---------+------+----------+----------+------+----------+----------+
| C12     |      |          |          |      |          | +1.0     |
+---------+------+----------+----------+------+----------+----------+
| C13     |      |          | -0.5461  |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| C14     |      |          |          |      | -0.0818  | +0.2622  |
+---------+------+----------+----------+------+----------+----------+
| C15     |      | -0.0686  | -0.4359  |      |          |          |
+---------+------+----------+----------+------+----------+----------+

For position control at the IP the solutions (a), using the triplet
correctors, are most effective. With corr \> 1000 m for \* = 0.35 m, and
with almost exactly 90o of phase between the correctors and the IP, the
beam position can be adjusted by as much as 2.75 mm. This is nearly 3
times the control possible at the B0/D0 IR\'s. Furthermore, because
there is nearly 180o of phase separating the upstream & downstream
packages the cancellation between the triplet corrector kicks is
excellent, with very little orbit distortion leaking into the arcs for
final elimination. The position bumps (b) use only arc spool packages.
These would be useful either to supplement the triplet corrector
solution, or to provide the IP position control in the event that the
triplet dipoles are being used primarily to compensate for triplet quad
mis-alignments. In any case, with the much smaller -functions in the
arc, solutions (b) are comparable to the orbit control at B0 & D0. At
full corrector field the beam positions at the IP can be shifted by 1.0
mm with solutions (b).

**Table 2-10: Relative dipole kick strengths to vary the angles (x\'\*,
y\'\*) at the IP while fixing the beam positions (x\*, y\* ). Angles
(x\'\*, y\'\*) are in µrad and is corrector kick angle in µrad of the
strongest corrector**.

+---------+------+----------+----------+------+----------+----------+
|         | X    |          |          | Y    |          |          |
|         | \'\* |          |          | \'\* |          |          |
|         | A    |          |          | A    |          |          |
|         | NGLE |          |          | NGLE |          |          |
|         | BUMP |          |          | BUMP |          |          |
|         |      |          |          |      |          |          |
|         | COEF |          |          | COEF |          |          |
|         | FICI |          |          | FICI |          |          |
|         | ENTS |          |          | ENTS |          |          |
+---------+------+----------+----------+------+----------+----------+
|         |      | \(c\)    | \(d\)    |      | \(c\)    | \(d\)    |
+---------+------+----------+----------+------+----------+----------+
| B45     |      |          |          |      | +1.0     | +1.0     |
+---------+------+----------+----------+------+----------+----------+
| B46     |      | -0.6812  | +0.8620  |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| B47     |      |          |          |      |          | -0.6505  |
+---------+------+----------+----------+------+----------+----------+
| B48     |      |          | -0.5443  |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| B49     |      |          |          |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| C0U     |      | -0.1467  |          |      | +0.3003  |          |
+---------+------+----------+----------+------+----------+----------+
| C0      | X\   | 7.8      | 11.2     | Y\   | 7.6      | 11.4     |
|         | '\*= |          |          | '\*= |          |          |
+---------+------+----------+----------+------+----------+----------+
| C0D     |      | +0.2772  |          |      | -0.1336  |          |
+---------+------+----------+----------+------+----------+----------+
| C12     |      |          |          |      |          | +0.6029  |
+---------+------+----------+----------+------+----------+----------+
| C13     |      |          | +0.5708  |      |          |          |
+---------+------+----------+----------+------+----------+----------+
| C14     |      |          |          |      | +0.6419  | -0.8284  |
+---------+------+----------+----------+------+----------+----------+
| C15     |      | +1.0     | +1.0     |      |          |          |
+---------+------+----------+----------+------+----------+----------+

For angle control at the IP there is no overpowering reason to prefer
one of solutions (c) or (d) over the other. In either case the IP angle
must be generated out in the arcs and the level of angle control
possible at the IP is limited by the aperture in the low beta triplet
quadrupoles rather than the available field strengths of the correction
dipoles. For a 20π µm beam at 1 TeV, and ~max~ = 1660 m in the triplets,
the 1 beam width is \~2.5 mm. The quadrupole physical aperture has a
radius of only 31.5 mm. In an extremely optimistic scenario which
imagines the beam orbit can be displaced by as much as 25 mm in the
triplet quadrupoles, the corresponding angle control at the IP is 1.04
mrad.

## Higher Order Correction

### Quadrupole Misalignment

The effects of misaligned quadrupoles other than the triplet quadrupoles
are straightforward to correct using the arc correction spools between
B38 and C17 listed in Table 2-8. The following discussion therefore is
limited to the triplets.

Two types of misalignment are particularly harmful transverse
misalignments, which deliver kicks to the beam, and roll of the
quadrupoles about the longitudinal axis, leading to coupling of the two
transverse planes. The beam optics are not as sensitive to other
misalignments, such as displacement of the magnets along their
longitudinal axis. Transverse misalignments can be corrected using the
position bumps described in the preceding section. With maximum
integrated fields of 0.48 T.m, the triplet spool correction dipoles can
compensate for systematic transverse displacements of the triplet by 0.5
mm, and random transverse errors of 0.25 mm.

Rolls of the triplet quadrupoles introduce coupling that degrades
luminosity. Although this coupling can be corrected globally with
distributed skew quadrupoles, reduction in luminosity is unavoidable
unless there are skew correction elements located physically at the
triplets. Table 2-11 lists the locations of skew quadrupoles, and their
contributions to the real & imaginary components of the coupling
coefficient. Because there is essentially zero phase advance across the
triplets it can be seen that the triplet skew quad elements at C0U & C0D
are ideally situated to correct for roll errors of the triplet magnets.

**Table 2-11: Skew quadrupole locations and their real & imaginary
coupling components. The midpoint optics values of the Q1, Q2, and Q3 IR
magnets are also given.**

+-----------+--------+--------+-----------+--------------+--------------+
| SKEW QUAD |        |        |           |              |              |
| C         |        |        |           |              |              |
| ORRECTORS |        |        |           |              |              |
| FOR       |        |        |           |              |              |
| TRIPLET   |        |        |           |              |              |
| ROLL      |        |        |           |              |              |
| MIS-A     |        |        |           |              |              |
| LIGNMENTS |        |        |           |              |              |
+-----------+--------+--------+-----------+--------------+--------------+
| Spool     | x      | y      | 2π (µx -  | $$\sqrt{\b   | $$\sqrt{\b   |
|           |        |        | µy)       | eta x\beta y | eta x\beta y |
|           | \(m\)  | \(m\)  |           | } \cdot \tex | } \cdot \tex |
|           |        |        | (deg)     | t{cos}(Dm)$$ | t{sin}(Dm)$$ |
|           |        |        |           |              |              |
|           |        |        |           | \(m\)        | \(m\)        |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKB45   | 23.1   | 102.7  | 5.4       | 48.49        | 4.58         |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKB46   | 92.9   | 66.6   | 25.2      | 71.17        | 33.49        |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKB49   | 160.7  | 875.0  | 69.5      | 131.32       | 351.24       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q3D       | 570.0  | 1593\. | 70.9      | 311.75       | 900.28       |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKC0U   | 1042\. | 1017\. | 71.3      | 330.05       | 975.08       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q2F       | 1660\. | 467.9  | 70.9      | 288.44       | 832.96       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q1D       | 619.5  | 538.0  | 70.9      | 188.90       | 545.50       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q1F       | 538.0  | 619.5  | 70.6      | 191.75       | 544.50       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q2D       | 467.9  | 1660\. | 71.3      | 282.62       | 834.95       |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKC0D   | 1017\. | 1042\. | 70.9      | 336.84       | 972.75       |
+-----------+--------+--------+-----------+--------------+--------------+
| Q3F       | 1593\. | 570.0  | 71.3      | 305.46       | 902.43       |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKC14   | 59.9   | 95.7   | 27.4      | 67.22        | 34.84        |
+-----------+--------+--------+-----------+--------------+--------------+
| PACKC15   | 99.0   | 17.0   | -13.0     | 39.97        | -9.23        |
+-----------+--------+--------+-----------+--------------+--------------+

To estimate the integrated skew gradient of the triplets, 1000 random
cases have been studied with all six quadrupoles rolled independently.
With uniformly distributed rolls between , the real and imaginary parts
of the integrated skew gradients (when multiplied by
$\sqrt{\beta_{x}\beta_{y}}$) are 980 and 2835 T.m, respectively (with in
mrad). The maximum integrated field of the C0U & C0D skew quadrupoles is
7.5 T.m/m, so that the triplet correctors are capable of compensating
*locally* for random roll angles as large as 2.5 mrad. For larger roll
mis-alignments the B49 corrector is useful for global compensation, and
the B45, B46, and C14, C15 correctors can be used to fine tune
cancellation of the real coupling component.

### Feeddown Circuits

The Tevatron sextupole and skew sextupole circuits are used to adjust
the tunes and coupling of the protons and pbars independently during
collider operation. In particular, these circuits can adjust the
difference in horizontal & vertical tunes, and sine and cosine
components of the coupling between the proton and pbar helices. The 7
feeddown families and their functionality in Run II are listed in Table
2-12. Four of the families are used for the injection helix and another
set of four is used for the B0/D0 collision helix. (The S1 family is
shared.) The family elements are given in Table 2-13.

**Table 2-12: Feeddown circuits and their functionality: x, y are the
differential tunes; C*sq*, S*sq* are the cosine and sine components of
the differential coupling.**

+--------------------+------------------------+------------------------+
| Circuit            | Injection              | Collision              |
|                    |                        |                        |
|                    | Helix                  | Helix                  |
+--------------------+------------------------+------------------------+
| S1                 | ![](med                | C*sq*                  |
|                    | ia/image11.emf){width= |                        |
|                    | "0.3055555555555556in" |                        |
|                    | height="0.25in"}x      |                        |
+--------------------+------------------------+------------------------+
| S2                 | ![](med                |                        |
|                    | ia/image12.emf){width= |                        |
|                    | "0.3194444444444444in" |                        |
|                    | height="0              |                        |
|                    | .2638888888888889in"}y |                        |
+--------------------+------------------------+------------------------+
| S3                 | C*sq*                  |                        |
+--------------------+------------------------+------------------------+
| S4                 |                        | ![](med                |
|                    |                        | ia/image11.emf){width= |
|                    |                        | "0.3055555555555556in" |
|                    |                        | height="0.25in"}x      |
+--------------------+------------------------+------------------------+
| S5                 |                        | ![](med                |
|                    |                        | ia/image12.emf){width= |
|                    |                        | "0.3194444444444444in" |
|                    |                        | height="0              |
|                    |                        | .2638888888888889in"}y |
+--------------------+------------------------+------------------------+
| S6                 | ![](med                |                        |
|                    | ia/image13.emf){width= |                        |
|                    | "0.3611111111111111in" |                        |
|                    | height="0.263          |                        |
|                    | 8888888888889in"}S*sq* |                        |
+--------------------+------------------------+------------------------+
| S7                 |                        | S*sq*                  |
+--------------------+------------------------+------------------------+

**Table 2-13**: Locations, magnet elements, and polarities of the 7
feeddown family members.

+-----------+------+-------+-----+-----------+-------+-------+-------+
| Circuit   | Pola | M     | Sp  | Circuit   | Pol   | M     | Spool |
|           | rity | agnet | ool |           | arity | agnet |       |
| Name      |      |       |     | Name      |       |       | type  |
|           |      | loc   | t   |           |       | loc   |       |
|           |      | ation | ype |           |       | ation |       |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1B1A   | \-   | B19   | E   | C:S3A2A   | \+    | A17   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1B3A   | \+   | B38   | E   |           | \-    | A24   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1C2A   | \+   | C24   | E   | C:S3D2A   | \-    | D19   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | C32   | G   |           | \+    | D26   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1E2A   | \+   | E24   | E   | C:S3D4A   | \+    | D38   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | E28   | E   |           | \-    | D46   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1F2A   | \+   | F19   | E   | C:S3E1A   | \-    | E17   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | F26   | G   |           | \+    | E22   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S1F3A   | \+   | F34   | E   | C:S3E3A   | \-    | E32   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | F38   | E   |           | \+    | E36   | C     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2A1A   | \-   | A14   | D   | C:S4C2A   | \+    | C19   | E     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2A3A   | \+   | A33   | D   |           | \-    | C26   | G     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2B4A   | \-   | B43   | D   | C:S4C2B   | \+    | C22   | G     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \+   | B47   | D   |           | \-    | C28   | E     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2C3A   | \+   | C27   | D   | C:S4F2A   | \+    | F24   | E     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | C33   | D   |           | \-    | F28   | E     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2D2A   | \-   | D23   | D   | C:S5A2A   | \+    | A18   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \+   | D27   | D   | C:S5A3A   | \-    | A37   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2F1A   | \+   | F12   | D   | C:S5D3A   | \-    | D33   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           | \-   | F16   | D   |           | \+    | D37   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2F2A   | \+   | F23   | D   | C:S5F1A   | \-    | F14   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
| C:S2F4A   | \-   | F43   | D   | C:S5F3A   | \+    | F33   | D     |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           |      |       |     | C:S6A4A   | \+    | A46   | T:SF  |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           |      |       |     | C:S6C4A   | \-    | C46   | T:SF  |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           |      |       |     | C:S7B1A   | \+    | B14   | T:SD  |
+-----------+------+-------+-----+-----------+-------+-------+-------+
|           |      |       |     | C:S7D1A   | \+    | D14   | T:SD  |
+-----------+------+-------+-----+-----------+-------+-------+-------+

• Spool types TSC & TSD contain skew sextupoles \-- all others contain
normal sextupoles.

When the beams travel off-axis through the sextupoles, they see feeddown
normal and skew quadrupoles, the effects of which depend on the
orientation of the helix, and the polarity and tilt angle of the magnet.
Installation of the C0 interaction region will eliminate the 2 skew
sextupoles at B43 and B47 from the S2 family. The S2 family is used for
adjusting the differential vertical tune, and is used only with the
injection helix. Two possibilities are currently being explored to
compensate for the missing elements: (i) Since there will still be 10 S2
elements distributed in the ring, it might be acceptable simply to
increase the S2 circuit current by \~20%; (ii) It should be possible to
move these 2 elements to other locations in the ring which have the
appropriate helix orientation & lattice functions. Example replacement
sites are listed in Table 2-13 below.

**[Table 2-13: Possible locations in the ring where the B43 & B47 skew
sextupole S2 circuit elements could be relocated.]{.underline}**

+---------+---------+---------+---------+---------+---------+---------+
| Site    | Spool   | x       | y       | µx µy   | Xo      | Yo      |
|         |         |         |         |         |         |         |
|         |         | \(m\)   | \(m\)   | (deg o) | \(mm\)  | \(mm\)  |
+---------+---------+---------+---------+---------+---------+---------+
| B43     | TSD     | 32.7    | 95.4    | 26.6    | -0.50   | -5.20   |
+---------+---------+---------+---------+---------+---------+---------+
| D43     | TSD     | 33.1    | 94.9    | 30.8    | +0.66   | +5.76   |
+---------+---------+---------+---------+---------+---------+---------+
| E43     | TSF     | 33.2    | 93.9    | 29.2    | -0.67   | -5.86   |
+---------+---------+---------+---------+---------+---------+---------+
|         |         |         |         |         |         |         |
+---------+---------+---------+---------+---------+---------+---------+
| B47     | TSD     | 30.5    | 89.8    | 28.1    | +3.62   | +4.02   |
+---------+---------+---------+---------+---------+---------+---------+
| E27     | TSFR    | 30.7    | 93.2    | 28.1    | +3.73   | +6.39   |
+---------+---------+---------+---------+---------+---------+---------+
| E47     | TSFR    | 30.5    | 92.8    | 25.5    | -4.08   | -6.01   |
+---------+---------+---------+---------+---------+---------+---------+

##  {#section .unnumbered}

## Dynamic Aperture Calculations

Realistic tune footprint and dynamic aperture calculations require the
inclusion of lattice nonlinearities. The studies described below include
the B0/D0 IR triplet quadrupole multipoles, chromatic sextupoles, and
the multipoles of the C0 LHC triplet magnets. The LHC multipoles are
listed in Table 2-14. All calculations correspond to the top energy of
980 GeV for C0 collisions at \* = 35 cm on the collision helix.

Table 2-14: LHC quadrupole magnetic nonlinearities included in dynamic
aperture studies.

  ----------- ----------- ----------- ----------- ----------- -----------
  LHC                                                         
  HARMONICS @                                                 
  11922 A                                                     

              Average     Sigma                   Average     Sigma

  b3          0.31        0.47        a3          -0.57       0.65

  b4          0.02        0.48        a4          0.30        0.39

  b5          -0.03       0.13        a5          -0.38       0.18

  b6          -0.02       0.45        a6          -0.04       0.11

  b7          -0.01       0.03        a7          0.01        0.03

  b8          0.00        0.02        a8          0.01        0.03

  b9          0.03        0.01        a9          -0.02       0.03

  b10         0.01        0.02        a10         -0.03       0.02
  ----------- ----------- ----------- ----------- ----------- -----------

\- LHC harmonics reported in \"units\" at a reference radius of 17 mm.

\- Harmonics are a weighted average over body + end fields for 6
magnets.

\- All data taken at 215 T/m.

### Single Beam

The single beam tune footprint can be a good measure of the impact of
the machine nonlinearities on the beam. Figures 2-10a,b show the tune
footprint extending to amplitudes of 6 in each plane. Without the C0
triplet magnet errors the horizontal tune spread is twice the vertical
spread at (x, y) = (8E-5, 4E-5). The inclusion of the C0 IR errors does
not greatly affect the tune spreads; (x, y) = (8E-5, 6E-5), but it can
be seen that the shape of the distribution is appreciably altered. For
comparison, the corresponding tune footprint in the current Run II
Tevatron lattice with B0/D0 collisions is shown in Figure 2-11. The Run
II B0/D0 lattice tune spread is approximately 6E-4 in both planes a
factor of 10 or more broader than in the C0 collision lattice.

![](media/image14.wmf){width="5.417361111111111in"
height="3.8465277777777778in"}

**Figure 2-10a: Single beam tune footprint, in the absence of C0 IR
quadrupole errors. The base tunes are (.585, .575).**

![](media/image15.wmf){width="5.490277777777778in"
height="3.8465277777777778in"}

**Figure 2-10b: Single beam tune footprint, with the C0 multipole errors
of Table 2-14 also included. The base tunes are (.585, .575).**

![](media/image16.wmf){width="5.290277777777778in"
height="3.654166666666667in"}

**Figure 2-11: Tune footprint of a single beam in the current Run II
lattice, with collisions at B0 & D0.**

The dynamic aperture is calculated by launching particles at several
angles in x y space. In the following calculations 13 launch points were
taken, spaced apart by 7.5o from 0o (horizontal) to 90o (vertical). The
radial dynamic aperture at each angle is then calculated to be the
largest stable amplitude below which all amplitudes are stable. A
comparison of the single beam dynamic aperture with the dynamic aperture
including beam-beam forces indicates the relative importance of
beam-beam effects.

Figure 2-12 shows the calculated single beam dynamic aperture for C0
collisions averaged over 5 seeds for the magnetic multipoles. The
maximum separation launched was 25. The average dynamc aperture is 24
well beyond the physical aperture of the low quads. From Figure 2-13 it
can be seen that this C0 collision lattice average dynamic aperture is
nearly twice as large as the single beam dynamic aperture calculated for
Run II B0/D0 collisions. In that case, also calculated for p/p = 3E-4,
the average dynamic aperture is just 12.3

![](media/image17.wmf){width="5.563194444444444in"
height="3.8465277777777778in"}

**Figure 2-12: Single beam dynamic aperture for C0 collisions with N =
20π µm & p/p = 3E-4.**

![](media/image18.wmf){width="5.354861111111111in" height="3.75in"}

**Figure 2-13: Current Run II B0/D0 collision lattice. Single beam
dynamic aperture with N = 20π µm & p/p = 3E-4**

### Beam-beam

With 36x36 operation there are 71 long-range interactions between the
separated proton and pbar bunches in addition to the head-on collision
at the C0 IP. The long-range interactions are more complex than the
head-on collisions. In addition to changing the tunes, these parasitic
interactions also change the orbits, coupling, and chromaticity.

The tune footprint for pbar bunch #6 is shown in Figure 2-14., including
the beam-beam forces in addition to the magnetic nonlinearities
discussed earlier. The tune spread has grown by about 2 orders of
magnitude compared to the single beam analysis, to (x, y) = (8E-3,
9E-3). This spread is still a factor of 3 or more less than the
corresponding footprint for the Run II B0/D0 collision lattice, as given
in Figure 2-15. In the Run II lattice the spread is approximately equal
in both planes at = 2.3E-3. In both of these cases most of the
contribution comes, not from the head-on collisions, but from the 1st
parasitic crossings on each side of the IP. While the beam separation at
the C0 first parasitics is \~3.7, or about half the separations at B0 &
D0\'s nearest misses in Run II, this is compensated to a large extent by
there being only one IP and two nearest miss points, as compared to the
two IP\'s and four nearest misses of Run II.

![](media/image19.wmf){width="5.248611111111111in"
height="3.6805555555555554in"}

**Figure 2-14: Tune footprint of pbar bunch #6 including beam-beam
effects for the head-on collision plus the 71 long-range interactions in
the C0 collision lattice.**

![](media/image20.wmf){width="5.248611111111111in"
height="3.6805555555555554in"}

**Figure 2-15: Current Run II B0/D0 collision lattice. Beam-beam effects
are included for the 2 head-on collisions plus the 70 long-range
interactions.**

Figure 2-16 shows the dynamic aperture including beam-beam effects for
C0 collisions, averaged over the magnetic multipoles generated by 5
seeds. The average dynamic aperture is 14, indicating that beam-beam
effects reduce the aperture of the machine by a substantial 10. However,
this analysis also suggests that the minimum dynamic aperture of 12
should exceed the physical aperture set by the primary collimators,
which are typically placed at \~6 By comparison with Figure 2-17 it can
be seen that the average dynamic aperture in the C0 collision lattice is
roughly twice as large as the 8average calculated for Run II B0/D0
collisions, and, furthermore, the C0 *minimum* dynamic aperture of 12
even significantly exceeds the *maximum* 9dynamic aperture of the Run II
lattice.

![](media/image21.wmf){width="5.490277777777778in"
height="3.8465277777777778in"}

**Figure 2-16: Dynamic aperture of pbar bunch #6 with beam-beam effects
in the C0 collision lattice.**

![](media/image22.wmf){width="5.490277777777778in"
height="3.8465277777777778in"}

**Figure 2-17: Current Run II B0/D0 collision lattice. Dynamic aperture
including beam-beam effects.**

## Beam Halo Calculations and Collimators

*Calculations in progress. NM, SD.*

## Emittance Growth Calculations

*Calculations to be done.*

3.  []{#__RefHeading___Toc63699076 .anchor}LHC Style Quadrupoles

## Overview and Conceptual Design

The C0 IR described in section 2.0 requires quadrupoles of a new design
for the Q1 through Q5 magnets. Table 3-1 shows the locations, gradient,
magnetic length and mechanical slot length requirements of these
elements. The nominal operating temperature is 4.5K.

![](media/image23.wmf)

**Table 3-1: Q1 -- Q5 Parameters**

To meet these requirements, we propose a design based on the collared
coil assembly of the well proven LHC IR quadrupole currently in
production, with the magnet length, iron yoke, cryostat, cryogenic
system, and interconnects re-optimized for the C0 IR. Figure 3-1 shows a
cross-section of the collared coil of such a magnet.

![](media/image24.wmf){width="2.875in" height="2.5in"}

**Figure 3-1: LHC Quadrupole Collared Coil.**

The coil bore is 70mm, which allows for use of a beam tube with inside
diameter 63mm. The reuse of the body design of the LHC quadrupole
provides confidence that these magnets can work with minimal redesign,
optimized for the Tevatron system. The C0 optics requires a gradient
which is 20% lower than that of the LHC quadrupole. Independent of this,
no changes in the coil design or body mechanical support are envisioned.
Optimizations will focus on reducing the iron yoke diameter and overall
cryostat size such that the height of the beam above the tunnel floor in
the Tevatron can be accommodated without any new civil construction in
the tunnel.

Changes that have been made include

-   Reducing the iron yoke OD

-   Reducing the overall magnet OD

-   Changing the mechanical support of the ends

-   Changing the quadrant splice design

-   Changing the expansion loop design

-   Changing the pipes included and the interfaces of the cryostat

-   Reducing the overall diameter of the cryostat

The redesign of the iron yoke results in a yoke OD of 266.7mm, and an
anticipated total OD including stainless steel skin of approximately
280mm. Figure 3-2 illustrates the yoke redesign.

![](media/image25.jpeg){width="2.6631944444444446in" height="3.0in"}

**Figure 3-2: C0 IR Magnet Yoke Cross Section**

Given the smaller magnet, and the elimination of a superfluid helium
heat exchanger required in the cryostats of the LHC Inner Triplet, the
C0 quadrupole cryostats are expected to be only 1/2 the diameter of the
LHC cryostats, and allow for the beam height to be located 10" above the
nominal Tevatron tunnel floor. The cold magnetic length of any of the Q1
to Q5 magnets is expected to be approximately 0.24m shorter than the
warm mechanical length of the cold mass, end plate to end plate, as
depicted in Figure 3-3. The length of the quadrant splice block,
expansion loops, bus connections, instrumentation wires, and other
components are included in the cryostat layouts, and at this stage
appear consistent with the mechanical slot lengths listed in Table 3-1,
as constrained by the lattice design. These lengths are still being
optimized.

![](media/image26.jpeg){width="6.502083333333333in"
height="3.9659722222222222in"}

**Figure 3-3: Magnetic / Mechanical Length Schematic (dimensions in
inches)**

The following sub-chapters document the basic quadrupole design, noting
the important similarities and differences between the two designs.
Necessary R&D and infrastructure is summarized in the last sub-chapter.

## Magnet Coils and Mechanical Description

The collared coil of the assembly shown in Figure 3-1 consists of a
two-layer coil of 70mm bore, completely supported by steel collars. The
inner coil is formed from 37 strand Rutherford cable, using SSC type
wire which is uncoated and unannealed. The outer cable is 46 strand
Rutherford cable, again from uncoated and unannealed SSC type wire. Both
cables are insulated with two wraps of Kapton insulation, with the
outermost wrap including a polyimide adhesive. The end parts are of
G11CR.

Table 3-2 details the strand parameters. The conductor for the inner
layer has a minimum critical current of 378 A, measured at 7T and 4.22K.
The conductor for the outer layer has a minimum critical current of 185
A, also measured at 7T and 4.22K. The values are determined in the
standard way, and the specifications are taken directly from SSC and the
LHC IR Quadrupole program.

**Table 3-2:** Strand mechanical and electrical specifications

  ---------------------- ------ -------- ----------- --------- -----------
  Parameter              Unit   Inner                Outer     
                                cable                cable     

                                Value    Tolerance   Value     Tolerance

  Diameter               mm     0.808    0.0025      0.6505    0.0025

  Cu/SC ratio                   1.3 : 1  0.1         1.8 : 1   0.1

  Surface coating               None     \-          None      \-

  Anneal                        None     \-          None      \-

  Minimum critical       A      378      \-          185       \-
  current                                                      

  Minimum RRR                   70                   70        

  Twist direction               Left                 Right     

  Twist pitch            mm     13       1.5         13        1.5
  ---------------------- ------ -------- ----------- --------- -----------

Fig. 3-4 shows the cable size parameters and Table 3-3 summarizes the
cable mechanical and electrical specifications. Again, this
specification is identical to that used in the LHC IR Quadrupole
program, and there are multiple vendors capable of meeting these
requirements.

![](media/image27.wmf)

Figure 3-4: Cable size parameters.

**Table 3-3:** Cable mechanical and electrical specifications

  ---------------------- -------- ---------- ----------- -------- -----------
  Parameter              Unit     Inner                  Outer    
                                  Cable                  Cable    

                                  Value      Tolerance   Value    Tolerance

  Number of strands               37         \-          46       \-

  Cable width            mm       15.40      0.025       15.40    0.025

  Minor edge             mm       1.320                  1.051    

  Cable Mid-thickness    mm       1.465      0.006       1.146    0.006

  Major edge             mm       1.610                  1.241    

  Keystone angle         degree   1.079      0.05        0.707    0.05

  Transposition length   mm       114        5           102      5

  Lay direction                   Right      \-          Left     \-

  Minimum critical       kA       14.0       \-          8.5      \-
  current                                                         

  Minimum unit length    m        200        \-          200      \-

  Residual twist         degree   0 - 90                 0 - 90   

  Minimum bending radius mm       7                      15       
  ---------------------- -------- ---------- ----------- -------- -----------

Figures 3-5 and 3-6 show the inner and outer coils of the LHC
quadrupole. For C0 the straight section lengths will be modified but the
end parts will remain exactly the same.

![](media/image28.jpeg){width="5.752777777777778in"
height="4.373611111111111in"}

Figure 3-5: LHC Inner Coil. The straight section of the coil will be
modified to accommodate the shorter magnet length.

![](media/image29.jpeg){width="6.000694444444444in"
height="4.538888888888889in"}

Figure 3-6: LHC Outer Coil. The straight section of the coil will be
modified to accommodate the shorter magnet length.

The coils are cured in a two step cure cycle, which sets both the
interstrand resistance and the coil size properly. Mechanical support of
the coils is provided by Nitronic 40 collars which are stamped, and
pre-assembled into 37mm long packs and provide the required rigidity and
cooling channels. The collars are keyed with 8 phosphor bronze keys, to
a target warm azimuthal prestress of 75MPa in both the inner and outer
coils. Prestresses in the range of 55 to 100MPa are known to produce
acceptable quench performance. The LHC magnet development and production
has included magnets ranging in length from 1.8m to 5.5m having
acceptable quench performance. A summary of the 4K quench performance of
the LHC model magnets and the LHC prototype magnet is shown in Figure
3-7. The magnets showed no signs of retraining. Since the C0 designs are
in between these lengths, we can reasonably expect similarly good quench
performance at the maximum C0 operating current of 9560A.

![](media/image30.wmf){width="5.370833333333334in"
height="3.6013888888888888in"}**Figure 3-7: LHC Model Magnet and
Prototype 4.5K Quench Performance**

The iron yoke of the magnet provides flux return, and supports the
stainless steel shell that provides helium containment. Since the C0
operating gradient is 20% lower than the LHC requirement, the iron yoke
has been re-optimized and the outside diameter reduced to produce a more
compact design, with acceptable harmonics. As with the LHC design, we
expect to use the ICB welding press to close the skin, after it has been
modified for the reduced yoke diameter.

The reduced yoke diameter has an impact on the design of the mechanical
support of the ends of the coils. In the LHC magnets, a collet design
using tapered blocks and an aluminum end can was used for support of the
ends. However, this assembly has an outside diameter of 250 mm, just
slightly less than the C0 yoke diameter. Such an assembly would not
allow for bus work to pass through the magnet. To accommodate the bus
work, full-round collars will be re-introduced to the design, as was
used in the early HGQ model magnets and are typically used in other
superconducting magnets (LHC arc dipole, for example). Full round
collars are identical to the body collars, except that the mechanical
pole has been eliminated to allow for the coil end part, as shown in
Figure 3-8. Experience has shown that the full round collars can supply
the required support, but out-of-plane buckling must be controlled,
particularly during assembly. Typically the use of pre-assembled collar
packs provides a solution to this problem.

![](media/image31.wmf){width="2.8881944444444443in"
height="2.8881944444444443in"}

**Figure 3-8: Full Round Collar Design, showing coil end parts which
must be accommodated**

The ends of the cold mass are defined by steel end plates, which are
used to anchor the collared coil longitudinally, and provide the
geometry for the skin to end plate and end plate to end dome welds to be
made. These welds close the cold mass. The thickness of this assembly
may be optimized depending on the final weld geometry required for the
skin and end dome thicknesses.

The reduced overall diameter of the magnet impacts the quadrant splice
block design, which mounts to the lead end of the magnet. The LHC design
has the splices in a plane perpendicular to the beam axis, but uses a
diameter too large for the C0 design. We have assumed for C0 that the
splices will be made parallel to the beam axis, requiring a longer
splice block region, as shown in Figure 3-3.

## Field Quality

The C0 IR quadrupole design is based on the LHC quadrupole \[1\] which
was designed to operate at 1.9K in superfluid helium with the critical
current and temperature margins necessary to operate in a large
radiation induced heat load. The C0 IR quadrupole will utilize this
proven design -- particularly the collared coil assembly which
determines the basic field properties -- with modifications as necessary
to meet C0 specifications. One such modification is to the iron yoke,
originally designed for field gradients up to 230 T/m; it must be
reduced in diameter to meet the beam tube height limitations imposed by
the Tevatron tunnel.

### Iron Yoke Optimization

The cross-section of the HGQ is shown in Figure 3-9. A two-layer
collared coil is surrounded by a two-piece iron yoke held together by a
welded skin. The iron yoke is penetrated by four large round holes
required for longitudinal heat transfer by superfluid helium from the
coil to the external HeII heat exchanger and four large rectangular
holes reserved for the high-current bus-bars and electrical
instrumentation. These holes along with the high nominal field gradient
of 215 T/m resulted in the quite large iron yoke outer diameter of 400
mm.

![](media/image32.png)

**Figure 3-9: Cross-section of HGQ developed for the LHC IRs.**

![](media/image33.png)
![](media/image34.wmf){width="2.9451388888888888in"
height="2.5965277777777778in"}

**Figures 3-10a, 3-10b: Optimized HGQ magnet cross-section.**

The optimization goals for the C0 IR quadrupole were reduction of the
iron yoke OD from 400 mm to 267 mm and optimization of the yoke
cross-section, minimizing iron saturation effects while providing the
channels for power and instrumentation cables as well as for helium
flow. The inner shape and the size of the new iron yoke is similar to
the shape of the HGQ collared coil. The collared coil is supported and
aligned inside the yoke with the help of special alignment keys. As in
the HGQ, there is a small gap between the collar and yoke excluding the
yoke from the coil mechanical support structure.

The field quality was optimized using the OPERA2D \[2\] code. Iron
saturation effects were kept within tolerable limits through the use of
eight round holes: the position and size of the holes were optimized to
restrict field quality deviations to the order of 0.1510^-4^.

Figures 3-10a, -10b show the optimized iron yoke geometry and the flux
distribution in the magnet cross-section. Two 18.518.5 mm^2^ rectangular
holes are sufficient to accommodate 4-6 pairs of 12-15 kA stabilized
electrical bus-bars described in \[3\] and the other two rectangular
holes could house the necessary instrumentation wires and cables. If
required, the size of these holes could be increased without a
dramatical effect on field quality. Eight round holes with a total
cross-sectional area of 14 cm^2^ and a 1-2 mm annular channel provide
sufficient cross-sectional area for helium flow within the magnet cold
mass.

### Magnet transfer function 

Figure 3-11 shows the measured and calculated transfer function for the
HGQ short models as a function of current. As can be seen in Figure
3-11, there is good correlation between measured and calculated data at
all currents. The reduction of the magnet transfer function at high
currents is caused by iron saturation. At an operating current of 10 kA
the nominal field gradient is about 180 T/m. We are confident that the
transfer function for the modified C0 quadrupole design can be
calculated to high accuracy and will provide similar good agreement.

Determination of the field integral (g*dl*) for the C0 quadrupoles will
depend on the details of the magnet ends as well as the 'as-built' coil
length and thermal contraction when cold. This will be learned from
tests of a prototype or model magnet and adjustments to the lengths of
the production cold masses.

![](media/image35.wmf)

> Figure 3-11: Measured and calculated magnet transfer function for HGQ
> Model Magnets

### Field Harmonics

In the magnet body, the field is represented in terms of harmonic
coefficients defined by the power series expansion:

$B_{y}(x,y) + \text{iB}_{x}(x,y) = \text{10}^{- 4}B_{2}\sum_{n = 1}^{\infty}{(b_{n} + \text{ia}_{n})\left( \frac{x + \text{iy}}{R_{\text{ref}}} \right)^{n - 1}}$,

where *B~x~(x,y)* and *B~y~(x,y)* are the transverse field components,
*B~2~* is the quadrupole field strength, *b~n~* and *a~n~* are the
"normal" and "skew" harmonic coefficients (*b~2~*=10^4^) at a reference
radius *R~ref~* of 17 mm.

The field quality expected in the C0 quadrupoles can be estimated from
measurements of the roughly 1.5m long model magnets built and tested
during the R&D portion of the LHC program and from measurements of the
first few full length production magnets. Table 3-4a below shows the
mean values and RMS spread at *R~ref~*=17 mm of low-order field
harmonics over the last five short models HGQ05-09 measured at 6 kA
current, while Table 3-4b displays the same harmonics measured at 215
T/m (11922A; the LHC operating current) averaged over the first six full
length cold masses.

Differences in average multipole values between the model magnets and
production cold masses can be ascribed, in part, to different tooling
used in making the coils.

Table 3-4a: Averages and Standard Deviations of field harmonics at
[6kA]{.underline} for HGQ05-09.

  ----------------------- ----------------------- -----------------------
  **Harmonic              **Mean**                **RMS**
  Coefficient**                                   

  **b~3~**                0.49                    0.26

  **a~3~**                0.12                    0.28

  **b~4~**                -0.01                   0.08

  **a~4~**                -0.15                   0.37

  **b~5~**                -0.02                   0.07

  **a~5~**                -0.06                   0.15

  **b~6~**                -0.23                   0.17

  **a~6~**                -0.03                   0.05

  **b~7~**                0.01                    0.03

  **a~7~**                0.02                    0.03

  **b~8~**                0.00                    0.01

  **a~8~**                0.00                    0.01

  **b~9~**                0.00                    0.00

  **a~9~**                0.00                    0.01

  **b~10~**               0.00                    0.01

  **a~10~**               0.00                    0.00
  ----------------------- ----------------------- -----------------------

Table 3-4b: Averages and Standard Deviations of field harmonics at
[11.9kA]{.underline} for First 6 Full Length Cold Masses

  ----------------------- ----------------------- -----------------------
  **Harmonic              **Mean**                **RMS**
  Coefficient**                                   

  **b~3~**                0.31                    0.47

  **a~3~**                -0.57                   0.65

  **b~4~**                0.02                    0.48

  **a~4~**                0.30                    0.39

  **b~5~**                -0.03                   0.13

  **a~5~**                -0.38                   0.18

  **b~6~**                -0.02                   0.45

  **a~6~**                -0.04                   0.11

  **b~7~**                -0.01                   0.03

  **a~7~**                0.01                    0.03

  **b~8~**                0.00                    0.02

  **a~8~**                0.01                    0.03

  **b~9~**                0.03                    0.01

  **a~9~**                -0.02                   0.03

  **b~10~**               0.00                    0.02

  **a~10~**               -0.03                   0.02
  ----------------------- ----------------------- -----------------------

A detailed comparison of the field quality measurements of HGQ models
with the Fermilab Low Beta Quadrupoles \[4\] is presented in Table 3-5.
For direct comparison, the HGQ harmonics are calculated with the
Tevatron reference radius of 25.4mm and a weighted end-body average is
calculated for a 5.5m cold mass. The field quality of the HGQ is
moderately better. The allowed harmonics are smaller, particularly b5,
and the variance in normal and skew sextupole is smaller.

**Table 3-5: A comparison of the field quality of the FNAL LBQ \[5\] and
LHC IR quad model magnets. Harmonics are given in units (10^-4^ of the
main field)**

![](media/image36.wmf)

Magnetization effects are calculated to decrease b~6~ by --(1.2-1.3)
units at 4.5K at injection; its decay during the first 900 seconds is
less than 0.4 units. The effect of iron saturation on b~6~ and b~10~ in
HGQ with the optimized iron yoke is shown in Figure 3-12.

![](media/image37.wmf)

**Figure 3-12: The yoke saturation effect.**

## Quench Protection, Electrical Specifications, and Bus

Since the design of the new quadrupole magnets for the C0 IR will be
very similar to those made for the LHC, their electrical properties will
be very similar as well. Quench protection of the C0 high gradient
quadrupoles will closely follow the approach used with the LHC
quadrupoles. The design of the high current bus will also be based on
the LHC design.

### Inductance, resistance and stored energy

The new C0 quadrupole coil configuration (number of turns, cable
dimensions, end effects, etc.) will be the same as LHC quads, only the
length of the coils will be different. Although the inductance depends
on the yoke structure (thickness, shape and material properties of the
yoke) as well, its contribution to the total inductance is small. For
design purposes using LHC magnet inductance values in calculation will
be adequate. The LHC magnet inductance is 3.09 mH/m (at 10kA). Based on
this inductance, the expected stored energy will be 138 kJ/m (at 9450A,
I/Ic=0.875, at 4.5K)

The inductance and Q value measured with an HP4284 LCR meter @ 1kHz for
a 5.5 m long LHC quadrupole cold mass assembly is 13.4 mH and 5.2,
respectively. The room temperature value of the resistance of a cold
mass is 2.3 . The typical RRR value is \~150.

### Voltage taps and heaters

The LHC cold mass has voltage taps attached to each quarter coil and
each cold mass has two quench heaters (covering all four quadrants)
whose room temperature resistance value is 19.5 . The C0 IR cold masses
will be instrumented with quarter coil voltage taps. The peak heater
surface power must be kept above 55 W/cm^2^. This requirement will
determine the heater resistance and obviously it will be different for
each different length of cold mass.

### Quench Detection and Protection

Based on measured values from LHC cold masses, the key quench related
properties are estimated as follows:

-   Quench velocity: 75m/sec ± 25 m/sec (depends on the quench location;
    at I/Ic=0.875; 1.9K; at 4.5K one can expect 20 m/sec increase)

-   Quench Integral limit: 21 MIITs (over 400K hot spot -- estimate
    only)

-   Quench Integral starting from the time the heater is fired: 17 MIITs

(available 4 MIITs for quench detection or 40 msec at 10kA)

-   Quench Detection threshold 0.3 V which is at \~10msec for I/Ic=0.875

-   Quench heater operation is expected to be better or equivalent at
    4.5K

For the LHC the quench heater firing unit parameters are the following:

-   Capacitance: 7mF

-   Voltage: 900V

It is important to keep the strip heater peak surface power the same so
that we can expect similar heater behavior for the C0 IR design. The
quench heater copper to stainless steel strip ratio should be adjusted
to the magnet length. Peak voltage plays a bigger role than the total
power, so there is no need to change the capacitance value.

### Bus

The superconducting bus used for the LHC is suitable for conducting the
current to the new magnets. The bus consists of LHC inner cable soldered
to a same size cable made from pure copper. This bus was intensively
tested at various current values (600A -- 12000A) and it was proven that
it can be protected adequately if we keep the QI within 150 MIITs
(maximum temperature rise will be \~300 K - estimated). We will be well
within the QI limit even if the quench detection threshold is set as
high as 0.25V.

## Cryostat Requirements

Cryostats provide the magnet closures, proper mechanical and electrical
interfaces, mechanical support, thermal insulation, and alignment
information needed for a magnet to actually be installed in an
accelerator. The fundamental criteria for the new C0 quadrupoles is
accommodating the Tevatron beam height off the tunnel floor, without
requiring any further civil construction in the tunnel. For economy the
Q1 -- Q5 cryostat designs will be as similar as possible.

![](media/image38.png){width="5.75in"
height="3.464583333333333in"}Figure 3-13 shows a preliminary layout of
the cryostat for the C0 IR. With the reduced magnet diameter, it appears
possible to position the magnet beam line correctly in the tunnel.

**Figure 3-13: Very Preliminary Cross Section of Cryostat**

Schematically the Q1 to Q3, Q4, and Q5 cryostats, the main buswork and
the associated spools are shown in Figures 3-14, 3-15, and 3-16. The
lead end of each magnet is denoted by the elongated end volume and the
script L. Details of the spools are discussed in Chapter 4.

![](media/image39.wmf){width="5.5625in" height="1.2916666666666667in"}

**Figure 3-14: Q1 -- Q3 Schematic. The IP is to the right, and the
triplet mirrors about the vertical axis of the IP when moving from the B
sector to the C sector**

![](media/image40.wmf){width="5.458333333333333in"
height="1.2965277777777777in"}

**Figure 3-15: Q4 schematic. The Q4 / X2 spool combination translates
when moving from the B sector to the C sector**

![](media/image41.wmf){width="5.458333333333333in"
height="1.2916666666666667in"}

**Figure 3-16: Q5 schematic. The Q5 / X2 spool combination translates
when moving from the B sector to the C sector**

The Q1, Q2 and Q3 quadrupoles will be powered in series, with a trim
power supply (not shown) across Q2 allowing for modest variation of it's
gradient as needed by machine operations. The orientation of lead and
return ends in the triplet allow for minimal bus work to be used, and,
if the bus work fix point in the Q2 can be placed at the lead end of the
magnet, the expansion loops might be placed in the X1 spool. This also
depends on the design of the splice block at the lead ends of the
magnets, and the bus expansion loop requirements which are not known at
this time.

The BPM shown at the IP end of Q1 may be mounted either internal or
external to the cryostat, the choice will depend on details of the
design and layout. Details of the vacuum interconnect, gate valve, and
other requirements are to be determined.

Preliminary estimates of the end lengths required to close the magnet
volumes (including the lead splice block) and accommodate all connection
requirements indicate that the cryostatted magnet length will be on the
order of 0.464m longer than the mechanical length discussed in section
3.1 (and shown in Figure 3-3). Summing the current estimates of length
shows any cryostatted magnet to be on the order of 0.704m longer than
the cold magnetic length. Referring to Table 3-1, the minimum difference
listed between the slot length and the magnetic length is 0.964m. The
current design estimates are less than this, showing no interferences in
the design at this conceptual stage.

The Q4 and Q5 magnet arrangements are shown in Figures 3-15 and 3-16,
respectively. Given their pairing with a dedicated spool, the bus
routing is relatively simple. However, these magnets have the constraint
that the end not attached to an X2 spool must be compatible with a
standard Tevatron arc interface, and the cryostat must accommodate any
through piping, bus, or instrumentation required by the Tevatron string.
The asymmetry of the Tevatron interconnect places a more difficult
requirement on the X2 spool design, discussed in Chapter 4.

![](media/image42.png){width="5.997222222222222in"
height="3.09375in"}**Figure 3-17: Complete Cryostat Assembly Preliminary
Concept**

Figure 3-17 shows a concept of the completed cryostat assembly. Each
magnet will be supported at 2 locations along the length, with the
internal and external supports at the same location. Alignment fiducials
are located on either side of the external reinforcing sections, and by
using the single stretched wire measurement system the average cold
magnetic axis can be related to these fiducials to within 200 m. Lifting
of the magnet is accomplished through the use of slings in the region
near the reinforcing section.

## Cryogenic Specifications

Each cryostat requires piping as shown in table 3-6. The Q1 through Q3
cryostats are fed in a loop, and thus require return piping. The Q4 and
Q5 are located in the arcs of the Tevatron, and require only through
pipes. The pipes will need to be sized not only for cryogen flows, but
also to accomodate any bus or instrumentation routing required, as is
the case for the single phase helium. Similar to the existing Tevatron
LBQs installed at B0 and D0, it is envisioned that the magnet will be
cooled by a two phase heat exchanging jacket, as shown in Figure 3-18.

**Table 3-6: Piping Requirements**

![](media/image43.wmf){width="4.2652777777777775in"
height="1.4951388888888888in"}

![](media/image44.png){width="3.875in" height="3.0680555555555555in"}

**Figure 3-18: Two-phase cooling shell**

Analysis of MTF data from previous LBQ tests suggest this re-cooling
method is on the order of 65% effective, better than the standard arc
dipole helium flow arrangement. Given that the overall size of the C0 IR
quadrupole cold mass is very similar to the existing LBQs, we expect the
cooling efficiency to be similar.

The heat load to 4K is estimated to be 12W for each Q2 and 7W for each
Q1, Q3, Q4, and Q5 assembly

## Design Changes, R&D, and Infrastructure Needs

The LHC IR Quadrupole program provides firm groundwork on which to base
the C0 IR Quad design. The body mechanics and harmonics of the LHC
design are well understood and repeatable; the cable is readily
procured, and the production facility is in large part already
completed. Many of the results, particularly at 4.5K, have been quoted
in this chapter. However, there are details that are different and must
be accounted for in the design of the C0 IR.

First, the reduced yoke diameter changes the harmonics of the magnet,
and this must be thoroughly calculated. However, good agreement between
electromagnetic calculations and measurements is usually seen.
Finalization of the detailed yoke design should verify this.

The yoke diameter also impacts the mechanical support of the ends of the
coils. Early LHC model magnets were successfully assembled with full
round collars over the return end of the magnet. HGQ01 and HGQ02 had
full round collars over the return end only; HGQ03 and HGQ04 have full
round collars over both ends (the lead splices in early LHC model
magnets were of such a design that full round collars were not possible
on the lead end). Test results from these model magnets (only HGQ01
through HGQ03 were tested), suggest there was no difference between the
end with the full round collars and the end with the end can / collett
design; however, these magnets were not particularly good performers and
this result is not conclusive. Longitudinal restraint of the magnet was
explored with a series of experiments done on HGQ05 and HGQ07. No effect
on quench performance was seen, though end restraint does give some
control over the magnet length change with cooldown.

Next, the reduced diameter changes the splice block, and the magnet to
magnet splices. This is an intricate design task, and impacts the
cryostat lengths. The single largest input needed is confirmation of the
bus design, and the routing and fix points of the bus design.

The bus design is expected to be very similar to the LHC bus, however
given the magnet diameter we may need to explore ways to make it more
flexible. The use of LHC outer cable as opposed to inner cable is one
possibility. Once this is fixed, details of the bus slots in the yoke,
the required lengths and space for splices in the interconnects, and the
required volumes for expansion loops can be determined.

The major R&D item then is the rebuild of an LHC model magnet,
preferably HGQ09, with full round collars over the end to confirm that
the mechanical support provided by the collars is acceptable. Detailed
design work for the bus and quadrant splice block must also be completed
early to allow the overall design to progress.

As far as infrastructure, the LHC production facility in the Industrial
Center Building provides the basis for the C0 production. The change in
cold mass diameter and length(s) will require new mandrels for winding
and curing of coils, and potentially new handling tooling if the current
fixtures are simply too long for practical use. The yoke/welding press
will need to be reworked to the smaller diameter of the cold mass, and
qualification runs made to prove the weld quality.

In the Magnet Test Facility, C0 will require a new test stand, capable
of supplying 4K helium and 10kA. The varying designs of the magnet and
spool interconnects mean the test stand will require several adapters to
accommodate the various interconnects. Most of the measurement equipment
from LHC can be used directly for the C0 magnets. The baseline design
will include 2 pair of Tevatron (ASC) HTS current leads. We will scale
back to one pair if early tests indicate one pair is sufficient.

The BTeV feed box will have standard Tevatron test stand instrumentation
(in and out thermometry, pressure taps, voltage taps on current leads, a
gauge panel, etc.) We do not propose new features for precise thermal
tests except better 80K thermal shielding for lower heat loads. Thus,
heat load measurements of the +/-5 Watt variety typical of the Tevatron
test stands will be adequate. In addition to the standard
instrumentation, we will include nitrogen gas flow instrumentation for
the feed box HTS leads and for spool pieces with HTS leads.

The BTeV feed box will operate in typical Tevatron magnet test modes and
will have the standard MTF Tevatron test temperature range (from 4.8K
down to 3.6K minimum, at the Tevatron pressure of 2.2 bar) and helium
flow range (about 15 to 40 grams/sec). Helium subcooling will be
provided by the existing stand 6 cold pump and subcooler.

The C0 quadrupoles will require a dedicated turnaround box in addition
to the feed box, but it will be as simple as possible with no valves and
little instrumentation \-- basically a turnaround \"cap\" similar to
what was used for the Tevatron low-beta magnets.

![](media/image45.wmf){width="5.865277777777778in"
height="4.489583333333333in"}

**Figure 3-19: Preliminary C0 Feed Can Flow Schematic**

***[References]{.underline}***

\[1\] M Andreev, et al, "Mechanical Design and Analysis of LHC Inner
Triplet Quadrupole Magnets at Fermilab", (presented at MT-16 September
1999, Florida) *IEEE Transactions on Applied Superconductivity*, v.10,
no.1, p.115 (March 2000)

\[2\] Vector Fields, Inc., Illinois, 60505, USA

\[3\] P Bauer, et al, "Busbar Studies for the LHC Interaction Region
Quadrupoles" (presented at ASC September 2000, Virgina Beach, VA) *IEEE
Transactions on Applied Superconductivity*, v.11, no.1, p.1613 (March
2001)

\[4\] P Schlabach, private communication

\[5\] Body harmonics are from model magnets hgq05-09; data for b~13~
only is from model magnets hgq01-03,05; lead end data is from models
hgq06-09.

4.  []{#__RefHeading___Toc63699091 .anchor}New Spools

## Overview and Conceptual Design

Spools typically contain the magnetic correction system, power leads
(HTS and/or conventional), beam position monitors (BPM's) and all
necessary interfaces. The correction system includes dipole, quadrupole,
and sextupole correctors combined in different packages. The different
correction schemes at various locations along the interaction region
(IR) dictate the total number of spool designs. Based on the current IR
layout, we require five different spool designs. Table 4-1 lists the
different spool designs with corresponding corrector magnets and
required maximum gradients, allotted slot lengths and necessary power
leads.

**Table 4-1: Elements in different spool designs. Field values listed
are the maximum required. "SL" designates safety leads.**

<table>
<colgroup>
<col style="width: 7%" />
<col style="width: 10%" />
<col style="width: 10%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 8%" />
<col style="width: 9%" />
<col style="width: 8%" />
<col style="width: 7%" />
<col style="width: 9%" />
<col style="width: 14%" />
</colgroup>
<tbody>
<tr class="odd">
<td><strong>Spool</strong></td>
<td><strong>Location</strong></td>
<td><strong>Slot Length, m</strong></td>
<td><p><strong>VD</strong></p>
<p><strong>T. m</strong></p></td>
<td><p><strong>HD</strong></p>
<p><strong>T. m</strong></p></td>
<td><p><strong>SQ</strong></p>
<p><strong>T.m/m</strong></p></td>
<td><p><strong>Sx</strong></p>
<p><strong>T.m/m<sup>2</sup></strong></p></td>
<td><p><strong>Q<sup>*</sup></strong></p>
<p><strong>T.m/m</strong></p></td>
<td><strong>BPM</strong></td>
<td><p><strong>HTS</strong></p>
<p><strong>Leads</strong></p></td>
<td><strong>Other Leads</strong></td>
</tr>
<tr class="even">
<td>X1V</td>
<td>packb43</td>
<td>1.83</td>
<td>0.48</td>
<td></td>
<td></td>
<td>450</td>
<td>25</td>
<td></td>
<td></td>
<td>3x50A+SL</td>
</tr>
<tr class="odd">
<td>X1H</td>
<td>packb44</td>
<td>1.83</td>
<td></td>
<td>0.48</td>
<td></td>
<td>450</td>
<td>25</td>
<td></td>
<td></td>
<td>3x50A</td>
</tr>
<tr class="even">
<td>X2L</td>
<td>packb47</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td></td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>2x50A+SL</td>
</tr>
<tr class="odd">
<td>X2R</td>
<td>packb48</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td></td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>2 x50A</td>
</tr>
<tr class="even">
<td>X3</td>
<td>packc0u</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td>7.5</td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>3x50A+200A</td>
</tr>
<tr class="odd">
<td>X3</td>
<td>packc0d</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td>7.5</td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>3x50A+200A</td>
</tr>
<tr class="even">
<td>X2R</td>
<td>packc12</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td></td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>2x50A</td>
</tr>
<tr class="odd">
<td>X2L</td>
<td>packc13</td>
<td>1.43</td>
<td>0.48</td>
<td>0.48</td>
<td></td>
<td></td>
<td></td>
<td>V&amp;H</td>
<td>2x10kA</td>
<td>2x50A+SL</td>
</tr>
<tr class="even">
<td>X1V</td>
<td>packc16</td>
<td>1.83</td>
<td>0.48</td>
<td></td>
<td></td>
<td>450</td>
<td>25</td>
<td></td>
<td></td>
<td>3x50A</td>
</tr>
<tr class="odd">
<td>X1H</td>
<td>packc17</td>
<td>1.83</td>
<td></td>
<td>0.48</td>
<td></td>
<td>450</td>
<td>25</td>
<td></td>
<td></td>
<td>3 x 50A+ SL</td>
</tr>
</tbody>
</table>

![](media/image46.jpeg){width="4.661111111111111in"
height="3.5541666666666667in"}

**Figure 4-1: Conceptual drawing of an X2 spool layout**

The X1 spool has a slot length of 1.83 m with horizontal dipole (HD) or
vertical dipole (VD) corrector depending on the location, strong quad
(Q\*) and sextupole (Sx) correctors. The X2 spool has a slot length of
1.43 m with horizontal and vertical dipole correctors. This spool also
contains horizontal and vertical BPM's and a pair of 10 kA HTS power
leads. The X3 spool which sits in the triplet region has the same
allotted slot length as the X2 spool and has skew quadrupole corrector
(SQ) in addition to both horizontal and vertical dipole correctors. It
also has both horizontal and vertical BPM's and a pair of 10 kA HTS
power leads. There will be a trim supply at this location which requires
additional 200 A leads. Safety leads (SL) are also required at B43, B47,
C13 and C17 locations. Figure 4-1 shows a conceptual layout of an X2
spool.

## Corrector Design

The most significant change in corrector requirements for the C0
interaction region is the addition of 'strong' quadrupole correctors
with an integrated gradient of 25T-m/m. The other corrector strength
requirements are comparable to existing Tevatron correctors. In
addition, the new correctors do not contain octupole coils or skew
sextupole coils, as do some of the original Tevatron correctors. Table
4-2 below summarizes the corrector strengths compared to existing
Tevatron coils.

**Table 4-2: Corrector maximum strength comparison**

  ------------------- --------------------- ------------------- ----------
  Corrector type      Existing Correctors   C0 Requirements     units

  dipole              .460                  .480                T-m

  quadrupole          7.5                   7.5                 T-m/m

  quadrupole          none                  25                  T-m/m

  sextupole (up)      449                   450                 T-m/m^2^

  sextupole (down)    346                   450                 T-m/m^2^

  octupole            30690                 none                T-m/m^3^
  ------------------- --------------------- ------------------- ----------

There are two types of corrector spools necessary for the C0 IR. The
shorter spool ("56in"=1420mm) has 800 mm available for correction
elements containing both normal and skew dipoles and a skew quadrupole.
The longer spool ("72in"=1830mm) has 1200 mm available for correction
elements containing either normal or skew dipole, normal quadrupole of
25 T-m/m maximum strength and a normal sextupole of 450 T-m/m^2^ maximum
strength.

New correctors will be needed to meet C0 requirements. Our baseline
approach uses the 'traditional' cos(nθ) design for the magnetic
elements, with a separate correction element for each term. The higher
order correctors are nested concentrically around the beam pipe, but the
strongest lower order corrector is mounted separately. An alternative
approach, unique in its flexibility, is a new design in which one unit
(a 'flatcoil array') can generate all the required fields and thus
reduce the number of different spools and spares required. The two
approaches differ in both design and powering schemes. While the
baseline design is quite similar to correctors in the Tevatron and those
being built for the LHC, the flatcoil array is a new concept which will
necessitate some additional R&D. In this section we describe only the
baseline version of the correctors. A discussion of the flatcoil array
correctors is given in some detail in Appendix 13.2 while the initial
R&D required is discussed in Section 4.7.2 below.

### 56" (1420mm) spool

In order to meet spatial constraints, some of the correction coils must
be nested on top of others. The normal and skew dipoles are combined in
one magnet assembly since they generate the same field strength and thus
have similar magnetic lengths. All coils are based on the same ribbon
cable with 10 strands of 0.3 mm diameter, slightly keystoned for maximum
efficiency. The conductor critical current density is assumed to be that
of the SSC conductor. The coil cross-sections are optimized for the best
field quality achievable without wedges using the ROXIE code \[1\]. At
this stage of optimization, the magnetic permeability of the iron yoke
is taken to be constant and equal to 1000. The coil inner diameter is
fixed at 80 mm.

Figure 4-2 shows cross-section and the field plot in the ND/SD coils at
maximum required strength in both coils and Tables 4-3 and 4-4 list the
field harmonics. The peak field point is in the outer layer of the
(inner) ND coil. The maximum field in the SD coil is 7% lower.

The cross-section and field plot in the skew quadrupole coil is shown in
Figure 4-3 and field harmonics in Table 4-5. Peak field point in this
case belongs to the pole turn of the inner layer.

![](media/image47.wmf){width="2.5993055555555555in"
height="2.588888888888889in"}
![](media/image48.wmf){width="3.1194444444444445in"
height="2.5965277777777778in"}

**Figure 4-2: ND/SD coil cross-section (left) and field distribution
(right).**

**Table 4-3: ND harmonics at 1" radius (SD=off), nominal current.**

![](media/image49.png){width="4.114583333333333in" height="2.25in"}

**Table 4-4: SD harmonics at 1" radius (ND=off), nominal current.**

![](media/image50.png){width="4.135416666666667in" height="2.25in"}

![](media/image51.wmf){width="2.651388888888889in"
height="2.4555555555555557in"}
![](media/image52.wmf){width="3.2368055555555557in" height="2.45in"}

**Figure 4-3: SQ coil cross-section (left) and field distribution
(right).**

**Table 4-5: SQ harmonics at 1" radius, nominal current.**

![](media/image53.png){width="4.125in" height="2.2395833333333335in"}

The parameters of the correction elements are summarized in Table 4-6.
Since they are more complicated in design, the nested ND/SD coils are
provided with 55-59% quench margin while the single SQ coil has 38%
margin. To provide the necessary integral field strengths, the ND/SD
coils have a magnetic length of 0.35 m and the SQ coil length is 0.14 m.
Given reasonable assumptions for the coil end lengths, the physical
lengths of ND/SD and SQ magnets are 0.55 m and 0.25 m respectively.
These lengths fill all the space available for correction elements.

**Table 4-6:** 56" spool corrector parameters.

  ------------------------------- ------------ ----------- ----------- -------
  Parameter                       Unit         ND          SD          SQ

  n                                            0           0           1

  Coil IR                         *mm*         40.0        48.0        40.0

  Yoke IR                         *mm*         60.0                    53.0

  Strands/cable                                10                      

  Bare strand diameter            *mm*         0.300                   

  Cu/nonCu ratio                               2.0                     

  J~nonCu~(5T, 4.2K)              *A/mm^2^*    2750                    

  Maximum strength required       *T·m/m^n^*   0.48        0.48        7.5

  Current @ maximum strength      *A*          27.2        23.6        49.0

  Quench margin at nominal        *%*          54.7        58.8        38.2
  current in all the coils                                             

  Inductance                      *H/m*        15.16       25.03       6.48

  Stored energy at I~nom~         *kJ/m*       5.61        6.97        7.78

  Magnetic length                 *m*          0.350       0.351       0.143

  Physical length                 *m*          0.55                    0.25
  ------------------------------- ------------ ----------- ----------- -------

### 72" (1830mm) spool

Similar to the 56" spool, some of the coils in the 72" spool must be
nested. To reduce Lorentz forces, the normal quadrupole and sextupole
coils are combined in one magnet assembly. All coils are based on the
same ribbon cable used in the 56" spool. Again, the coil cross-sections
are optimized for the best field quality achievable without wedges using
ROXIE code; the magnetic permeability of the iron yoke is taken to be
constant and equal to 1000; the coil inner diameter is fixed at 80 mm.

Figure 4-4 shows the cross-section and field plot in the NQ/NS coils at
the nominal current and Tables 4-7 and 4-8 list the field harmonics. The
peak field point is in the inner layer of the (inner) NQ coil. The
maximum field in the NS coil is 6% lower.

The cross-section and field plots for the normal dipole coil is shown in
Figure 4-5 and field harmonics in Table 4-9. Peak field point in this
case is in the pole turn of the inner layer.

![](media/image54.wmf){width="2.6375in" height="2.4305555555555554in"}
![](media/image55.wmf){width="3.1729166666666666in"
height="2.4305555555555554in"}

**Figure 4-4: NQ/NS coil cross-section (left) and field distribution
(right).**

**Table 4-7: NQ harmonics at 1" radius (NS=off), nominal current.**

![](media/image56.png){width="4.125in" height="2.25in"}

**Table 4-8: NS harmonics at 1" radius (NQ=off), nominal current.**

![](media/image57.png){width="4.114583333333333in"
height="2.2395833333333335in"}

![](media/image58.wmf){width="2.6590277777777778in"
height="2.2888888888888888in"}
![](media/image59.wmf){width="3.120833333333333in"
height="2.279861111111111in"}

**Figure 4-5: ND coil cross-section (left) and field distribution
(right).**

**Table 4-9: ND harmonics at 1" radius, nominal current.**

![](media/image60.png){width="4.135416666666667in"
height="2.2604166666666665in"}

Parameters of the correction elements are summarized in Table 4-10. The
nested NQ/NS coils have 41-43% quench margin while the single ND coil
has 39% margin. To provide the necessary integral field strengths, the
NQ/NS coils will have magnetic lengths of 0.68 to 0.70 m and the ND coil
of 0.20 m. Given reasonable assumptions on the coil end lengths, the
physical lengths of NQ/NS and ND magnets are 0.8 m and 0.4 m
respectively. This utilizes all the space available for correction
elements.

**Table 4-10:** 72" spool corrector parameters

  ------------------------------- ------------ ----------- ----------- -------
  Parameter                       Unit         NQ          NS          ND

  n                                            1           2           0

  Coil IR                         *mm*         40.0        48.0        40.0

  Yoke IR                         *mm*         60.0                    53.0

  Strands/cable                                10                      

  Bare strand diameter            *mm*         0.300                   

  Cu/nonCu ratio                               2.0                     

  J~nonCu~(5T, 4.2K)              *A/mm^2^*    2750                    

  Maximum required strength       *T·m/m^n^*   25          450         0.48

  Current @ maximum strength      *A*          40.0        36.6        43.0

  Quench margin at nominal        *%*          40.6        42.9        39.2
  current in all the coils                                             

  Inductance                      *H/m*        5.42        6.24        17.01

  Stored energy at I~nom~         *kJ/m*       4.34        4.18        15.73

  Magnetic length                 *m*          0.676       0.696       0.200

  Physical length                 *m*          0.8                     0.4
  ------------------------------- ------------ ----------- ----------- -------

## Dimensional Specifications

The length of the corrector packages described in the previous section
is designed such that the overall length of the spool matches that of
the allotted slot length. Figures 4-6 and 4-7 show the dimensional
specifications for the X1 and X2 spools respectively. For the X1 spool,
there are no HTS power leads. Hence the outer vacuum vessel houses only
the helium vessel that contains corrector package and the necessary
interfaces.

![](media/image61.jpeg){width="6.402083333333334in"
height="3.814583333333333in"}

**Figure 4-6: Dimensional specifications for X1 spool.**

In the X2 spool design, there are two pairs of 5 kA HTS power leads
fixed to the top plate. Note that existing HTS power leads are rated for
6 kA and hence we are using a pair of 5 kA leads to reach 10 kA. The
nitrogen dewar will also be supported from the top plate. The bottom
portion of this support structure will be welded to the helium vessel
that houses the corrector package. The two rings that are welded to
either side of the helium vessel will be used to align the corrector
magnet within the helium vessel. Vacuum breaks and the bellows (for
Tevatron interface) will be attached to one side of the helium vessel
and flanges to the other side.

![](media/image62.jpeg){width="6.310416666666667in" height="4.30625in"}

**Figure 4-7: Dimensional specifications for X2 spool.**

The beam tube has an inner diameter of 63 mm and an outer diameter of
66.7 mm. It will be insulated with Kapton which raises the outer
diameter to about 67.1 mm. Note that the bore diameter for corrector
magnets is 80 mm and for quadrupole magnets is 70 mm.

BPM's will be embedded in the spool and are located next to the helium
vessel inside the vacuum break and the bellows. The allotted slot length
for BPM's is 10 inches. The BPM design will be similar to those already
installed in the Tevatron.

## Cryogenic Specifications

Table 4-11 gives the expected heat loads for various components in the
spool pieces. The design goal for the heat load to 4K in a given spool
piece is ≤10W. (This is a conservative number based on measurements of
existing spool heat loads and is consistent with allocated
refrigeration.)

Table 4-11: Expected heat loads

+----------------+---------+----------------+----------------+--------+
| ### Item       | **Heat  | **Helium       | **Nitrogen     | **     |
|                | to 4K   | consumption    | consumption    | Design |
|                | (W)**   | (l/hr)**       | (l/hr)**       | goal** |
+----------------+---------+----------------+----------------+--------+
| Each HTS lead  |         | 0.7            | 3.6            |        |
+----------------+---------+----------------+----------------+--------+
| Each AMI lead  |         | 12.0           |                |        |
+----------------+---------+----------------+----------------+--------+
| Each corrector |         | 1.0            |                |        |
| pkg            |         |                |                |        |
+----------------+---------+----------------+----------------+--------+
| Spool piece    | 10      |                |                | 5      |
+----------------+---------+----------------+----------------+--------+

The 2-phase flow is designed such that it will flow in and out at the
top (see Fig 4-1). Liquid drops and fills the 2-phase volume up to the
exit port. Each spool will require 3 Kautzky valves: for single-phase,
2-phase, and nitrogen. Furthermore, X1 and X2 spools need to have
insulation vacuum breaks. Note that while X1 and X2 spools have piping
for only inlet, X3 spools will have both inlet and return feedthroughs.

## Quench Protection

Preliminary calculations indicate that the new corrector magnets (using
the skew dipole parameters from Table 4-6 above) can be adequately
protected with an external dump resistor of 7.5 Ω. The quench protection
threshold should be 1V or less. During a quench, some fraction of the
magnet coil becomes resistive which helps to absorb the stored energy.
Even if we neglect this extra resistance, the magnet peak temperature
will be well under 300K. Also, the peak voltage to ground is estimated
to be less than 370V, the maximum voltage across the dump resistor.
Although the magnet operating current is roughly 40% of the critical
current value, we still expect relatively fast (larger than 1-2 m/s)
quench propagation velocity since the coils are epoxy impregnated which
reduces the coil cooling drastically. Detailed calculations will be done
for the complete set of correctors.

## Connections and Interfacing

Table 4-12 summarizes the interfaces required for each spool. Both X1
and X2 spools at all locations interact with Tevatron interfaces at
least on one side. This requires that the cryostat for the quadrupole
magnets at these locations also have standard Tevatron interfaces.
Figure 4-8 shows the closer view of the X2 spool with all its
interfaces.

Table 4-12: Upstream (US) and downstream (DS) interfaces for various
spools

  ---------------- ------------------- ---------- -------------- -------- ---------- -------------- --------
  ***Location***   ***Designation***   ***US      ***US          ***US    ***DS      ***DS          ***DS
                                       comp.***   interface***   bus***   comp.***   interface***   bus***

  packb43          X1V                 Quad       Tev            Tev      Dipole     Tev            Tev

  packb44          X1H                 Quad       Tev            Tev      Dipole     Tev            Tev

  packb47          X2L                 Q5         Modified Tev?  Tev, LHC Dipole     Tev            Tev

  packb48          X2R                 Cold       Tev            Tev      Q4         Modified Tev?  Tev, LHC
                                       bypass                                                       

  packc0u          X3                  Q3         New            LHC      Q2         New            LHC

  packc0d          X3                  Q2         New            LHC      Q3         New            LHC

  packc12          X2R                 Dipole     Tev            Tev      Q4         Modified Tev?  Tev, LHC

  packc13          X2L                 Q5         Modified Tev?  Tev, LHC Dipole     Tev            Tev

  packc16          X1V                 Quad       Tev            Tev      Dipole     Tev            Tev

  packc17          X1H                 Quad       Tev            Tev      Dipole     Tev            Tev
  ---------------- ------------------- ---------- -------------- -------- ---------- -------------- --------

![](media/image63.jpeg){width="4.031944444444444in"
height="3.3409722222222222in"}

**Figure 4-8: Closer view of the TeV interface on X2 spool.**

The X3 spool is within the triplet region and is connected to Q2 and Q3
quadrupoles. This allows the X3 spool to have interfaces that are
different from standard Tevatron interfaces. These interfaces are
currently being finalized. In addition, the X1 and X2 spools have a
Tevatron through bus, whereas the X3 spool has LHC type bus.

Both the X2 and X3 spools will have a pair of 10 kA HTS power leads. The
design of these power leads is still under consideration. There are
three possible options - test the current 5 kA leads and check if they
can carry 10 kA and then use them; double up the current 5 kA leads to
reach 10 kA, or develop new 10 kA leads. The first option is currently
being investigated and the next section will detail the test results.
The second option is being used as the baseline design, and all the
spools are designed to accommodate two pairs of 5 kA HTS power leads. At
present we have not found a vendor interested in pursuing the third
option, and long lead times may make it prohibitive.

Apart from the 10 kA HTS power leads, the spools also have leads for the
corrector magnets. For the baseline design, the corrector leads will
carry currents less than 50 A. In addition, the X3 spool will have 200 A
power lead for a trim supply across the Q2 LHC style quad.

## Measurements and R&D to Date

### HTS Leads

The 10kA current leads for the high gradient quadrupoles in the C0 IR
will be made from high temperature superconductor (HTS) to avoid
additional loading of the 4.5K He system. In the present Tevatron
configuration, four spool pieces have been modified to incorporate 5kA
HTS leads, and one of these has been installed in the ring for several
years. One of these modified spool pieces is shown in Figure 4-9 below.
The HTS lead assembly and the LN2 reservoir are clearly visible in the
foreground and right side of the picture, respectively. The cost and
time scale associated with development of new, optimized 10kA HTS leads
does not fit within BTeV constraints, so we have adopted a baseline
configuration in which the 10kA power leads are composed of pairs of the
existing 5kA design. The drawbacks of this approach are obvious \-- it
doubles the number of lead assemblies, associated piping,
instrumentation, and space allotment.

![](media/image64.png){width="3.329861111111111in" height="2.475in"}

**Figure 4-9: modified H-spool with HTS lead package on the floor at
MTF.**

Based on R&D tests performed during the 5kA lead program, it appears
that it may be possible to operate the leads at higher currents by
increasing the coolant flow. We are in the process of developing plans
(see Appendix 13.3) to re-test an existing HTS spool to investigate the
limits of its electrical and thermal stability. The spool will be
mounted on a test stand at the Magnet Test Facility and run at currents
up to 10kA, while carefully monitoring the temperatures and voltages
across the HTS and conventional lead portions of the assembly. While
there is some risk associated with the test, we are reasonably confident
that we can detect any runaway condition and protect the leads from
damage. The results from this test are expected in the spring of 2004.

### Flat Coil Corrector Design

The flat coil array alternative for the corrector design is a departure
from conventional approaches. Flat (or 'race track') coils have been
used in many applications, but the geometry, construction method, and
wide range of operating conditions (and resultant force configurations)
of the proposed design are relatively unexplored. A short, focused
development effort will be necessary to provide experience in
fabrication and assembly of the magnet modules, and data to confirm the
basic design.

Pending the availability of resources, we plan to fabricate three flat
coils and the yoke and spacer pieces necessary to assemble one quadrant
of a corrector (see Figure 4-10 below). Following the successful
assembly of the quadrant, mechanical and electrical tests will be
performed warm before proceeding with a cold test. A cold test would
most likely be performed in a dewar with appropriate current leads,
mounting fixtures, and diagnostic instrumentation.

![](media/image65.png){width="3.696527777777778in"
height="3.3118055555555554in"}

**Figure 4-10: Three coil prototype**

***[References]{.underline}***

\[1\] S Russenchuck, "A Computer Program for the Design of
Superconducting Accelerator Magnets", CERN AT/95-39, LHC Note 354,
Geneva, Switzerland, (September, 1995)

5.  []{#__RefHeading___Toc63699104 .anchor}Power Supplies

## High Current Power Supply Layout

The low beta quadrupole power supplies for the C0 interaction region
will be located in the B4, C0, and C1 service buildings. A listing of
these supplies is given in Table 5-1 below.

**Table 5-1: High current power supply layout**

+----------------+--------------------+---------+--------+-----------+
| **B4-Service   |                    |         |        |           |
| Building**     |                    |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| **Circuit**    | **Magnet**         | **      | **     | **        |
|                |                    | Power** | Volt** | Current** |
+----------------+--------------------+---------+--------+-----------+
| C:QB45         | B45-\"old-Q1\"     | 150 KW  | 30 V   | 5,000 A   |
+----------------+--------------------+---------+--------+-----------+
| C:QB46         | B46-\"old-Q1\"     | 150 KW  | 30 V   | 5,000 A   |
+----------------+--------------------+---------+--------+-----------+
|                |                    |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| **C0-Service   |                    |         |        |           |
| Building**     |                    |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| **Circuit**    | **Magnet**         | **      | **     | **        |
|                |                    | Power** | Volt** | Current** |
+----------------+--------------------+---------+--------+-----------+
| C:C0Q5         | B47-Q5, C13-Q5     | 300 KW  | 30 V   | 10,000 A  |
+----------------+--------------------+---------+--------+-----------+
| C:C0Q4         | B48-Q4, C12-Q4     | 300 KW  | 30 V   | 10,000 A  |
+----------------+--------------------+---------+--------+-----------+
| C:C0Q123       | B49-Q1, Q2, Q3     | 300 KW  | 30 V   | 10,000 A  |
|                |                    |         |        |           |
|                | C11-Q1, Q2, Q3     |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| C:C0QT2u       | B49-Q2             |         | 10 V   | 200 A     |
+----------------+--------------------+---------+--------+-----------+
| C:C0QT2d       | C11-Q2             |         | 10 V   | 200 A     |
+----------------+--------------------+---------+--------+-----------+
|                |                    |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| **C1-Service   |                    |         |        |           |
| Building**     |                    |         |        |           |
+----------------+--------------------+---------+--------+-----------+
| **Circuit**    | **Magnet**         | **      | **     | **        |
|                |                    | Power** | Volt** | Current** |
+----------------+--------------------+---------+--------+-----------+
| C:QC14         | C14-\"old-Q1\"     | 150 KW  | 30 V   | 5,000 A   |
+----------------+--------------------+---------+--------+-----------+
| C:QC15         | C15-\"old-Q1\"     | 150 KW  | 30 V   | 5,000 A   |
+----------------+--------------------+---------+--------+-----------+

These high current supplies will be purchased from industry in a similar
fashion as the Main Injector P1/P2 Quadrupole supplies. A detailed
specification will be written for fabrication of the cabinet and high
power conversion equipment (input circuits, bridge and filter). Fermilab
will supply the regulation chassis that will be integrated into the
supply cabinet and then tested by the vendor.

The main strategy to be used in the purchase will be to specify supplies
that are unfiltered at the output voltage of 30 volts and an output
current of 5,000 amps. Then for the 10,000 amp supplies we will use two
of these supplies with a filter choke used for isolation and integrated
into the required filter. In the case of the 5,000 amp supplies a single
converter unit will be used and the choke used in the 10,000 amp units
will be used in the required filter to meet specifications. This
strategy will allow us to purchase multiple converter units and common
filter parts.

## Buswork

Bus work to and from the magnet loads is the main resistive loss in the
system and will drive the power supply voltage. The correct amount of
copper to use in the bus work is such that the installation cost is
equal to the power bill for running the system for a set period of time
(like five years). As with the Main Injector, this works out to be on
the order of 4 square inches of copper bus per 5,000 A RMS of current.
For the 10,000 A runs the plan is to install two 4 square inche runs in
parallel for supply and return.

## Electrical Specifications

Table 5-2 lists the main electrical parameters for each high current
circuit. In the table, dI/dT is the maximum ramp rate, which occurs
during the acceleration cycle in all cases.

**Table 5-2: Electrical parameters for high current circuits**

+------------+-----------+--------+---------+--------+--------+-------+
| **         |           |        |         |        |        |       |
| B4-Service |           |        |         |        |        |       |
| Building** |           |        |         |        |        |       |
+------------+-----------+--------+---------+--------+--------+-------+
| *          | **Ind**   | **d    | **L\*   | **Bus  | **     | **PS  |
| *Circuit** |           | I/dT** | dI/dT** | L**    | R\*I** | V**   |
|            | **\[H\]** |        |         |        |        |       |
|            |           | *      | **\[Vo  | **\[fe | *      | **\   |
|            |           | *\[A/s | lts\]** | et\]** | *\[Vol | [Volt |
|            |           | ec\]** |         |        | ts\]** | s\]** |
+------------+-----------+--------+---------+--------+--------+-------+
| C:QB45     | 0.01075   | 70     | 0.8     | 218    | 5.0    | 5.8   |
+------------+-----------+--------+---------+--------+--------+-------+
| C:QB46     | 0.01075   | 70     | 0.8     | 100    | 2.3    | 3.1   |
+------------+-----------+--------+---------+--------+--------+-------+
|            |           |        |         |        |        |       |
+------------+-----------+--------+---------+--------+--------+-------+
| **         |           |        |         |        |        |       |
| C0-Service |           |        |         |        |        |       |
| Building** |           |        |         |        |        |       |
+------------+-----------+--------+---------+--------+--------+-------+
| *          | **Ind**   | **d    | **L\*   | **Bus  | **     | **PS  |
| *Circuit** |           | I/dT** | dI/dT** | L**    | R\*I** | V**   |
|            | **\[H\]** |        |         |        |        |       |
|            |           | *      | **\[Vo  | **\[fe | *      | **\   |
|            |           | *\[A/s | lts\]** | et\]** | *\[Vol | [Volt |
|            |           | ec\]** |         |        | ts\]** | s\]** |
+------------+-----------+--------+---------+--------+--------+-------+
| C:C0Q5     | 0.0646    | 155    | 10.0    | 370    | 8.5    | 18.5  |
+------------+-----------+--------+---------+--------+--------+-------+
| C:C0Q4     | 0.0132    | 155    | 2.0     | 642    | 14.8   | 16.8  |
+------------+-----------+--------+---------+--------+--------+-------+
| C:C0Q123   | 0.0096    | 155    | 1.5     | 780    | 17.9   | 19.4  |
+------------+-----------+--------+---------+--------+--------+-------+
|            |           |        |         |        |        |       |
+------------+-----------+--------+---------+--------+--------+-------+
| **         |           |        |         |        |        |       |
| C1-Service |           |        |         |        |        |       |
| Building** |           |        |         |        |        |       |
+------------+-----------+--------+---------+--------+--------+-------+
| *          | **Ind**   | **d    | **L\*   | **Bus  | **     | **PS  |
| *Circuit** |           | I/dT** | dI/dT** | L**    | R\*I** | V**   |
|            | **\[H\]** |        |         |        |        |       |
|            |           | *      | **\[Vo  | **\[fe | *      | **\   |
|            |           | *\[A/s | lts\]** | et\]** | *\[Vol | [Volt |
|            |           | ec\]** |         |        | ts\]** | s\]** |
+------------+-----------+--------+---------+--------+--------+-------+
| C:QC14     | 0.01075   | 70     | 0.8     | 218    | 5.0    | 5.8   |
+------------+-----------+--------+---------+--------+--------+-------+
| C:QC15     | 0.01075   | 70     | 0.8     | 100    | 2.3    | 2.3   |
+------------+-----------+--------+---------+--------+--------+-------+

## AC Power and LCW Requirements

AC power for the High Current supplies will be derived from the Tevatron
Feeder #23. At B4 and C1 a 750 KVA pulsed power transformer (13.8 KV to
480 V) will be installed that will feed a 1200 A panel board to be used
for the two high current loads driven from each building. At C0 a 1.5MVA
pulsed power transformer (13.8 KV to 480 V) will be installed that will
feed a 2,000 A panel board to be used for the three high current loads
to be driven from C0.

*LCW requirements to be added. JR*

## Corrector Power Supply Configuration

The independent corrector power supplies required for the C0 IR are
detailed in Table 5-3 and 5-4. For B4 and C1 sectors, the count of
independent channels goes from 22 for Run II to 35 for the C0 IR. The B4
and C1 service building corrector power supply installations will be
maintained as is and the additional 13 channels will be located in C0
with a new bulk supply and individual switch mode, four-quadrant power
supplies providing the regulation off of the bulk supply. The proposed
supplies are a very mature design and is a virtual copy of the Main
Injector system which is barely 5 years old.

**Table 5-3: Correctors in B4 and C1 for Run II**

  -------------- ---------- -------------- --------------------- -----------------------
  **name**       **type**   **location**   **PS**                **PS @ B4 or C1**

  **packb43**    D spool    B43-1a         T:VDB43, T:QDD1,      T:VDB43
                                           T:SD, C:S1B3A, T:OD   

  **packb44**    C spool    B44-1a         T:HDB44, T:QFA4,      T:HDB44
                                           (T:SF)                

  **packb45**    B spool    B45-1a         T:VDB45, T:QDD1, T:SD T:VDB45

  **packb46**    C spool    B46-1a         T:HDB46, T:QFA4,      T:HDB46
                                           T:SF, T:SQ            

  **packb47**    DR spool   B47-1a         T:VDB47, T:QDD1,      T:VDB47, C:S2B4A
                                           T:SD, C:S2B4A         

  **packb48**    A spool    B48-1a         T:HDB48               T:HDB48

  **packb49**    H spool    B49-1a         T:HDB49, T:VDB49      T:HDB49, T:VDB49

  **packc11**    H spool    C11-1a         T:HDC11, T:VDC11      T:HDC11, T:VDC11

  **packc12**    F spool    C12-1a         T:VDC12, T:O2         T:VDC12, T:O2

  **packc13**    C spool    C13-1a         T:HDC13, T:QFA4,      T:HDC13
                                           T:SF, T:SQ            

  **packc14**    F spool    C14-1a         T:VDC14, T:QDD1, T:SD T:VDC14

  **packc15**    A spool    C15-1a         T:HDC15,T:QFA4, T:SF  T:HDC15

  **packc16**    F spool    C16-1a         T:VDC16,T:QDD1,T:SD   T:VDC16

  **packc17**    C spool    C17-1a         T:HDC17, T:QFA4,      T:HDC17
                                           T:SQ,T:SF,T:O1        

  **other PS at                                                  T:HB42
  B4**                                                           

  **other PS at                                                  T:VDC18, T:HDC19,
  C1**                                                           T:Q39C

                                           **Total=**            **22**
  -------------- ---------- -------------- --------------------- -----------------------

Table 5-4: Correctors in B4 and C1 for the C0 IR

  ------------- ---------- -------------- ------------------- -------------------
  **name**      **type**   **location**   **PS**              **PS @ B4 or C1**

  **packb43**   X1 spool   B43-1a         T:VDB43,T:QB43,     T:VDB43,T:QB43,
                                          T:SDB44             T:SDB44

  **packb44**   X1 spool   B44-1a         T:HDB44, T:QB44,    T:HDB44, T:QB44,
                                          T:SFB44             T:SFB44

  **packb45**   P spool    B45-1a         T:VDB45, T:SQ       T:VDB45

  **packb46**   P spool    B46-1a         T:HDB46, T:SQ       T:HDB46

  **packb47**   X2 spool   B47-1a         T:VDB47, T:HDB47    T:VDB47, T:HDB47

  **packb48**   X2 spool   B48-1a         T:HDB48, T:VDB48    T:HDB48, T:VDB48

  **packb49**   HTS spool  B49-1a         C:VDB49, T:SQ       C:VDB49

  **packc0u**   X3 spool   B49-3a         T:HDB49,T:VDB49,    T:HDB49,T:VDB49,
                                          T:SQB4              T:SQB4

  **packc0d**   X3 spool   C10-2a         T:HDC11,T:VDC11,    T:HDC11,T:VDC11,
                                          T:SQC1              T:SQC1

  **packc12**   X2 spool   C11-5a         T:VDC12, T:HDC12    T:VDC12, T:HDC12

  **packc13**   X2 spool   C13-1a         T:HDC13, T:VDC13    T:HDC13, T:VDC13

  **packc14**   P spool    C14-1a         T:VDC14, T:SQ       T:VDC14

  **packc15**   P spool    C15-1a         T:HDC15, T:SQ       T:HDC15

  **packc16**   X1 spool   C16-1a         T:VDC16, T:QC16,    T:VDC16, T:QC16,
                                          T:SDC17             T:SDC17

  **packc17**   X1 spool   C17-1a         T:HDC17,T:QC17,     T:HDC17,T:QC17,
                                          T:SFC17             T:SFC17

  **other PS at                                               T:HB42, T:QB42
  B4**                                                        

  **other PS at                                               T:VDC18, T:HDC19
  C1**                                                        

                                          **Total=**          **35**
  ------------- ---------- -------------- ------------------- -------------------

## B4 and C1 QPM Modifications

The only modification necessary to the QPMs at B4 and C1 will be the
addition of one HFU at each location and two lead voltages at each house
for the high temperature leads in the spool at B48-6 and the feed can at
C10-3A.

## Electrostatic Separator Power Supplies

*Text to be added. MDC, GK.*

6.  []{#__RefHeading___Toc63699112 .anchor}Cryogenic Systems

The C0 low beta cryogenic components are cooled by a hybrid cryogenic
system that consists of the C1 and B4 satellite refrigerators, and the
Central Helium Liquefier (CHL). The heat load of the magnets, static and
dynamic, is removed by the single-phase, and then is absorbed by the
latent heat of vaporization of the two-phase helium. The single-phase
helium is also used to cool correction, safety, power and crossover
leads. To lower the operating temperature of the magnets, a single stage
cold compressor is used in each house. The total load on the cryogenic
system is comprised of magnet strings static and dynamic heat load, lead
flows, and cold compressor heat of compression.

## Heat Load

Table 6-1 represents the heat load estimate for B4 and C1 cryogenic
components. The total heat load is comprised of a refrigeration and
liquefaction portion. The refrigeration part of the heat load is used to
cover conduction and radiation static heat leak as well as dynamic
losses of the cryogenic components. Liquefaction is used to reduce the
heat leak associated with leads. The values of existing component heat
loads are estimated based on MTF test results, Tevatron operational
experience, and engineering calculations. For the C0 quadrupoles,
spools, and power lead cans, design parameters for heat leak are used.
All of the heat loads are referenced to the 4.5K temperature level. The
increase in component heat leak at the normal lower temperature of
Tevatron operation is ignored. It should be noted that the additional
load associated with the production of the lower temperature
refrigeration is not negligible.

**Table 6-1: C0 IR Cryogenic Component Heat Load.**

## Cryogenic Capacity Limitation

The total cryogenic system refrigeration and liquefaction requirements
are provided by the satellite refrigerators and the CHL. The total
usable cryogenic system capacity is reduced by the amount necessary to
compensate for the heat of compression of the cold compressor for
operation below 4.5 K. Heat of compression is determined by the mass
flow rate and pressure ratio of the cold compressor.

Mass flow rate depends on the heat leak of the tunnel cryogenic
components. Pressure ratio across the cold compressor is determined by
the maximum allowable superconductor operating temperature. For a given
component, the superconductor temperature depends on the effectiveness
of the heat transfer between single-phase and two-phase, as well as
dynamic coil losses. Components with ineffective heat transfer are
required to be operated at lower temperature and thus lower two-phase
pressure and higher cold compressor pressure ratio.

Heat of compression is linear with cold compressor mass flow rate, but
is exponential with pressure ratio. Therefore, it is important to not
only minimize the heat leak of a component, but also to design the
components in such a way as to efficiently transfer the heat to the
two-phase in order to minimize the peak single-phase temperature.

The addition of an interaction region to the Tevatron adds both a
refrigeration and liquefaction load to the system. Refrigeration loads
are jointly satisfied by the satellite refrigerator and CHL. Liquefier
loads, such as power lead flows, are satisfied entirely by CHL. The
addition of a C0 interaction region to B0 and D0 puts a large burden on
CHL to support the liquefier load required by the large number of
conventional 2,000 amp and 5,000 amp power lead flows. A design
constraint for the C0 IR was to leave the existing B0 and D0 IRs in
place and powered. In order to not overload CHL with the C0 IR power
lead requirements, high temperature superconductor (HTS) lead designs
are being applied in as many circuits as practical. This is particularly
important since the design calls for several 10,000 amp circuits.

## Layout

Layout of cryogenic components for the C0 IR are presented in drawings
1650-MC-257471 and 1650-MC-257471 for the upstream (B4) and downstream
(C1) systems, respectively. Similar to the existing B0 and D0 IRs, the
turnaround box is located before the triplet. This requires both a
supply and return circuit for the single-phase, two-phase and nitrogen
within the triplet. Quench relieving of the triplet is accomplished on
the single-phase supply and return in the turnaround can as well as on
each end of the single-phase supply for Q2.

The Tevatron bus power leads are located in an H spool on the B4 side
and in the turnaround can on the C1 side. This will require
superconductor in the separator bypass on the C1 side. In order to
minimize spare requirements, the B4 bypass will also have conductor
which will not be connected.

The requirement to mirror the full triplet necessitates the need for a
single-phase, two-phase and nitrogen interface transition on the C1
side. This transition is accomplished within the C1 turnaround can.
Unlike B0 and D0, this allows the separator bypasses to be identical on
the B4 and C1 sides. The B4 and C1 turnaround cans are inherently
different due to the transition and different power lead requirements.

## Cryogenic Controls Modifications

Cryogenic controls software modifications are minimal. The ramp permit
will be updated to include low beta power leads and spools temperature.
Cooldown, Quench Recovery, Kautzky and Lead Controls Finite State
Machines will be modified as well.

Additional platinum thermometers and flow control is required for each
of the conventional power leads. Each 5kA HTS lead has four platinum
resistors and flow controls. Since 10kA HTS leads may consist of two 5kA
HTS leads, each 10kA spool will have a total of eight platinum
thermometers and flow controls per spool -- four for helium and four for
nitrogen. Similar to the Tevatron leads, flow control is accomplished
with sets of fixed size orifices and solenoid valves. A considerable
amount of lead flow tubing and controls cable runs will have to be made
to the B4 and C1 refrigerator and C0 compressor buildings.

It is known that there is a long term drift in calibration of
Allen-Bradley carbon resistor thermometers. Any new cryogenic
components, like spools, that require thermometry should have a pair of
the standard 18 calibrated Allen-Bradley carbon resistors and a single
calibrated Cernox^TM^ thermometer. Unlike 18 carbon resistors that can
be driven by the pulsed current of the Tevatron thermometry crate, the
Cernox^TM^ sensors require a variable current source to maintain the
constant voltage signal across the resistor. To drive a Cernox^TM^
thermometer, Lake Shore Cryotronics temperature transmitter model 234
can be used. The transmitter output can be read into ACNET via an ADC
channel of the Tevatron satellite I/O crate.

It is desired to try out a new controls scheme to protect Kautzky valves
that are located in hard-to-access locations due to the proximity of
detector related shielding. The scheme prevents valve chattering which
can significantly reduce the valve lifetime. It relies on forcing the
relief valve to stay open until the single phase pressure has stabilized
below its set point. This scheme is planned to be implemented at B0 and
D0 during 2004 Tevatron shutdown.

7.  []{#__RefHeading___Toc63699117 .anchor}Vacuum Systems

## Layout

*Drawing or spreadsheet of all tunnel vacuum devices from B43 to C17 to
be included. RR*

## Requirements for Cryogenic Vacuum

The Tevatron beam pipe is at 4.5K, therefore cryopumping is very
effective in maintaining good vacuum. Keeping the Tevatron at cryogenic
temperatures requires an insulating vacuum for thermal isolation. The
operational requirement for the insulating vacuum is 1x10^-4^ Torr warm
and 1x10^-8^ Torr cold.

## Requirements for Warm Vacuum

Even though 95% of the Tevatron total length is cryogenic, poor vacuum
in warm sections of the Tevatron is currently the major source of beam
halo background in the collider detectors at B0 and D0 \[1\]. Generally
the vacuum requirement for the Tevatron warm straight sections is an
absolute pressure of 1x10^-9^ Torr. This should be used as an
operational goal for warm vacuum sections which do not contain
electrostatic separators. Individual components should be designed for
better than that, perhaps 3-5x10^-10^ Torr, if this can be achieved by
reasonable means such as hydrogen degassing, electropolishing and
baking. Hydrogen degassing of stainless steel parts is considered
particularly important, as this process has historically achieved the
most satisfactory results and improvements over the untreated product.
The only warm straight section without electrostatic separators and
within the scope of this project is the 2.6 meter section near B47-4
which will be used for collimators. Previous experience (14 previous
collimator installations in the Tevatron for Run II) has shown that,
with proper vacuum techniques, a vacuum of 1x10^-9^ Torr can be
maintained in these devices.

The vacuum requirement for warm sections which contain electrostatic
separators is more stringent. Electrostatic separators run at voltages
as high as 125 kV per plate and exceedingly good vacuum is required in
order to avoid excessive sparking. A separator spark will generally
cause a loss of luminosity and sometimes will even cause the beam to
abort. The operational goal is 5x10^-11^ Torr. Long term experience with
electrostatic separators in the Tevatron has shown that this is
achievable. The 8.7 meter B49 and C11 warm sections will each contain 3
electrostatic separators.

The vacuum in the BTeV detector itself may be poorer, with pressures on
the order of 1x10^-8^ Torr being discussed as an operational goal. Gas
load migrating from this region into the Tevatron regions will be
mitigated by 50 l/sec ion pumps located at the boundaries of this
region.

***[References]{.underline}***

\[1\] A Drozhdin, et al, "Beam Loss and Backgrounds in the CDF and D0
Detectors due to Nuclear Elastic Beam Gas Scattering", PAC 2003,
Portland OR, 2003

8.  []{#__RefHeading___Toc63699121 .anchor}Controls

## Integration with Current Tevatron Systems

One additional abort input module will be required at B4,C0, and C1
service buildings to accommodate inputs from the low beta power supplies
and QPMs. Modifications will be made to the abort application to include
these new inputs. No changes are necessary to the Tevatron permit system
itself. One additional Camac crate will be installed at the B4 service
building which presently has only two Camac crates.

No changes to MDAT itself are required, however, a new Tevatron state
will be defined to distinguish between running with collisions at C0 and
B0/D0.

The additional separators at C0 will require power supply controls and
vacuum monitoring hardware. Additional collimators will require a
standard motion control VME crate and motor power supply. Processor
boards and controller cards can be moved from other unused collimator
locations. All of these will be using standard controls hardware
designs, the same as used for existing separators and collimators.

Sufficient Ethernet bandwidth is available in the service buildings for
controls requirements.

## Low Beta QPM System

There will be three new quench protection monitor VME crates, one each
at B4, C0, and C1 service buildings. These QPMs will be functionally
identical to those existing at B0 and D0 but will have fewer circuits in
each. The detection algorithms will be the same. There will be no dumps
or quench bypass switches, and heaters will be fired to provide quench
protection. Each QPM will have uninterruptible power for up to 30
minutes, a 6 second circular memory buffer for quench analysis, and a
suite of applications programs for control and data display. The QPMs
will communicate via Ethernet to the ACNET control system in the
standard fashion. Standard low beta QPM voltage to frequency converters
and Tevatron heater firing units will be used.

The crate at C0 will monitor the Q1,2,3 triplet, Q4 and Q5 circuits. The
major difference from B0/D0 in these circuits is the maximum current and
the allowed number of MIITs. Quench detection thresholds will be
adjusted if necessary.

The B4 and C1 QPMs will service the Q6 and Q7 circuits which are single
magnet circuits using the 54" low beta quadrupole magnets ("old-Q1's")
no longer used at B0 and D0. The major difference for these circuits
will be the number of voltage taps available and therefore the number of
magnet cells used in the quench detection algorithm. The fewer number of
voltage taps effectively increases the quench detection voltage from
0.33 volts to 0.5 volts. The quench limits will be lowered to compensate
for the fewer taps to keep the effective quench detection threshold at
the same .33 volts.

Connections to the refrigerators at B4 and C1, the abort and Tevatron
clock will be done in the same fashion as for B0 and D0. The existing
B0/D0 low beta QPMs have no MDAT connections and these are also not
required for the C0 IR.

## Controls Modifications

Tables 8-1 through 8-3 list controls software and hardware modifications
required to commission the C0 IR. No major new controls software is
required, but minor modifications to a large suite of programs, and some
duplication of existing software will be necessary. A significant number
of database entries will also need to be made for new power supplies,
separators, vacuum devices, etc. Software specific to Tevatron
instrumentation is discussed in Section 9.3.

If the conventional nested coil correctors are used in the new spools,
then the standard corrector power supply controls will be used. The only
software modification will be to add the new correctors to the existing
applications programs and database entries for the new devices.

If the new flat coil style correctors are used (described in Appendix
13.2), then a microprocessor will be used to generate the required
current programs for the twelve individual coils. Database entries for
each type of correction (dipole, quadrupole, sextupole) will be used to
drive a matrix algorithm in the microprocessor to determine the current
in each of the twelve coils. The microprocessor board and up to 12 D/A
convertors will be housed in a VME crate. The same microprocessor could
be used for quench protection of the corrector coils if necessary. If
this type of corrector package is selected, the estimate for
modifications to C49 in Table 8-1 should be increased and the
microprocessor front end development would require additional effort
from what is listed in Table 8-2.

**Table 8-1: Application programs and CLIB routines requiring
modification for commissioning the C0 IR**

  ------------------------ ----------- ----------------------------------
  **Program Name**         **Index     **Changes Needed**
                           Page**      

   UL_CBSAUX                CLIB        Add c200 modules at B4,C0&C1
                           routine     

  Low Beta Quench          java        Add houses for B4,C0 & C1 QPMs
  Protection                           

  Tevatron LCW             T12         Add new devices; modify graphics

  Tevatron Power Supply    T21         Add PSs for C0 IR
  status                               

  Tevatron Orbit           C50         Add BPMs

  Tevatron Vacuum          T18         Add/modify vacuum devices

  Tevatron Abort Status    T67         Add c200 at C0,B4 & C1

  Ramp Generator for       C49         Add C0 IR PSs & correctors; new
  Collider                             squeeze

  Tevatron Sequencer       C48         Add C0 IR squeeze

  Tevatron Separators      C13, C15    Add new separators

  Scraping Program for     C10         Add new collimators
  Collider                             

  ADC compare              C23         Add new devices

  HOPS                     I15         Add new power supplies

  Tev Magnet Database      T126        Add new magnets

  Sequencer                C48         Add new squeeze sequence
  ------------------------ ----------- ----------------------------------

**Table 8-2: Front-end code modifications required for commissioning the
C0 IR**

  ------------------ ----------------------------------------------------
  **Front-end**      **Modifications needed**

                     

  QPM                New QPM code for B4, C0, and C1 QPMs

  Vacuum             add CIA crates for new separators

  Collimator         New collimator motion control front end at B4

  TLLRF              change in Tevatron orbit length

  Refrigerator       added instrumentation

  TEVCOL (OAC)       addition of new collimator

  GLFRIG (OAC)       addition of new calculation of CC control at B4/C1

  CBSHOT(OAC)        addition of SDA data for C0

  MCRVCR(OAC)        addition of Video recording of C0 data for SDA

  VLOGGR (OAC)       addition of new Tevatron State transition
  ------------------ ----------------------------------------------------

**Table 8-3: Controls hardware modifications/additions required for the
C0 IR**

  ------------------ ------------- ------------------------------- ------------
  **System**         **Item**      **Description**                 **Number**

  vacuum             CIA crate &   Required by separators          1
                     PS                                            

                     Interface     Arcnet interface to front end   1
                     board                                         

  Power Supplies     c460          Control cards for correctors    16

                     C468          Control cards for power         9
                                   supplies                        

  Camac              Crate         One additional crate at B4      1

                     C290          Multiplexed Analog to Digital   1
                                   convertor                       

  Quench Protection  QPM           VME Crate w PS and I/0 boards   3

                     c184 or Enet  For remote rebooting of QPMs    3

  Abort              C200          Abort                           3

  Separators                       c185                            6

                                   c465                            3

                                   c052                            3

  Collimators        VME crate     Five slot crate with power      1
                                   supply                          

                     Power supply  Motor power supply for 8 motors 1
  ------------------ ------------- ------------------------------- ------------

9.  []{#__RefHeading___Toc63699125 .anchor}Beam Instrumentation

## Synchrotron Light Monitor

The synchrotron light monitor \[1\] is located in a unique warm straight
section in the Tevatron at C11. It is located directly between 2
dipoles, one half-length and one full-length, so that it can monitor
both proton and antiproton off-axis synchrotron light, generated at the
magnetic transition at the far end of the dipoles \[2\]. This monitor is
the only non-destructive technique currently available in the Tevatron
for monitoring beam profiles during a collider store. When the C0 area
of the Tevatron is converted to a "normal" straight section, this unique
warm straight section at C11 will be lost.

We propose replacing this synchrotron light monitor with two separate
monitors. One located at the special "mini-bypass"\[3\] adjacent to the
B spool at D47 will measure pbar synchrotron light. A proton synchrotron
light monitor will require a minor lattice modification. An appropriate
mini-bypass can be made just downstream of the D47-5 dipole by sliding
the 32" quad and associated A spool \~50" downstream and shortening the
D48 warm straight section. This will be possible after the D48 separator
is removed, which is currently planned for the 2004 Summer shutdown.
This quad move will generate a \~5% beta wave \[4\] which can be
cancelled by independently powered trim quads in the E19 -- E28 region
and the "Bartelson" quads in the region D14 -- D17.

*Need concept description for detector and signal processing.
(emphasizes any differences with current detector. moveable mirror with
window on tee shared with vacuum port..... abort gap, coherent
oscillations, calibration, ......) S Pordes*

## Instrumentation between B4 and C1

There are currently 12 Beam Loss Monitors (BLM) located in each of the
B4 and C1 houses. This is more than the usual number per house because
additional BLMs were required in this area for the C0 abort. This number
is adequate for the C0 IR. They will be repositioned in the tunnel for
optimum utility.

There are currently 19 Beam Position Monitors (BPM) located in the B4
and C1 houses. For the C0 IR this number will be increased to 29. The
in-progress Tevatron BPM upgrade can accomodate this number of BPMs
without adding an additional BPM front-end crate. The new BPM pickups
will be identical to either of two designs already present in the
Tevatron \[5\]. The Tevatron BPM upgrade will provide a BPM relative
position accuracy of \<20m \[6\].

Tiltmeters similar to what currently exist on the B0 and D0 low beta
quadrupoles will be installed on the C0 low beta quadrupoles \[7\]. This
is an essential piece of instrumentation because the Tevatron orbit and
coupling are very sensitive to motion of these quadrupoles due to the
large functions. Unlike on the B0 and D0 low beta quads, robust mounting
and alignment of these tiltmeters will be designed into the cryostat
housing of the C0 low beta quads.

## Instrumentation Software Modifications

Table 9-1 lists the Tevatron instrumentation which will require minor
modification to associated software -- either application programs,
front-end code, or Open Access Clients (OAC). These instruments are
generally dependent on the global Tevatron lattice, Tevatron state,
and/or synchronizing clock events (TCLK)

Flying Wires

Synchrotron Light Monitor

Mountain Range Display

Ion Profile Monitor (new device)

1.7 GHz Schottky Monitor

Beam Position Monitors

***[References]{.underline}***

\[1\] A Hahn, P Hurh, "Results from a Prototype Beam Monitor in the
Tevatron Using Synchrotron Light", 1991 PAC, p1177, (1991)

\[2\] R Coisson, "Angular-spectral Distribution and Polarization of
Synchrotron Radiation from a "Short" Magnet", *Phs. Rev. A*,
[20]{.underline}, #2, p524, (1979)

\[3\] Two bypasses of this type were initially installed to accommodate
"Roman Pot" detectors.

\[4\] J Johnstone, "Tevatron Optics with Magnet Moves for Roman Pots at
CDF", Fermilab-TM-2157 (2001)

\[5\] [Tevatron Low Beta Quadrupoles -- Requirements and
Specifications]{.underline}, (the "Pink Book"), Fermilab, (1990)

\[6\] J Steimel, et. al, "Tevatron Beam Position Upgrade Requirements",
Fermilab Beams-doc-554, (2003)

\[7\] Applied Geomechanics model 711. A 2-axis tiltmeter with 100
nanoradian resolution.

10. []{#__RefHeading___Toc63699129 .anchor}Commissioning

## Operational Scenarios

The procedure for operating the Tevatron collider is to load all
waveforms (power supply ramps, etc) and timer channels into the control
cards in the field prior to beginning the collider fill process. The
sequencer (control room application program) then coordinates the
sequence of events that initiate beam transfers, state changes, and
changes in operating conditions. Since the low beta squeeze process will
be different for C0 operation and B0/D0 operation, modifications will be
necessary in order to switch between the two modes. Beam transfers into
the Tevatron and the acceleration to 1 TeV will be identical for the two
operating modes.

There are two possible simple methods of integrating C0 operation into
collider operation without completely redefining the current control
process. One method is to use the identical set of clock events for C0
operation as for B0/D0 operation to control the optics changes for each
mode. In this case the waveforms for the power supplies would be
reloaded at the beginning of each collider fill, depending on which mode
is desired. The second method is to load both sets of waveforms to the
power supply controllers, and determine which set plays by triggering
different clock events.

**[Option 1]{.underline}** (using the same events and reloading
waveforms):

This method has the advantage that fewer application programs need to be
modified. A second operational file will be defined in the power supply
waveform generator page (C49), and the proper file will be activated
between stores. A file for dipole correction elements will need to be
loaded from the orbit correction program after the C49 file is
activated. This process currently takes about ½ hour. It is not
particularly prone to errors, however the chance for a mistake by the
operator will increase with the number of files that need to be loaded.

**[Option 2]{.underline}** (using separate clock events and having both
sets of waveforms loaded):

This method has the advantage that a single file of ramp waveforms can
be used for both modes of operation, and file activation will not be
required between stores. More changes will need to be made to C49 to
recognize the different sequences. The orbit correction program will
need to know about the second set of waveforms as well. The waveform
generators, and the design of the sequencer in general, was originally
set up to handle this type of mode switching. Figures 10-1 and 10-2 show
how some of the waveform ramp cards will be set up in this option. In
these examples, XX and YY represent the new clock events for low beta
squeeze and unsqueeze of C0 operation.

![](media/image66.png){width="6.0in" height="3.1770833333333335in"}

**Figure 10-1: Example of the configuration of a tune quad circuit.**

![](media/image67.png){width="6.0in" height="3.1770833333333335in"}

**Figure 10-2: Example of the configuration of the low beta controller
card.**

## Commissioning Plan

Standard commissioning stuff. MDC with review by J Annala.

11. []{#__RefHeading___Toc63699132 .anchor}Conversion of C0 to a Normal
    Straight Section

## Overview

During an early shutdown (currently scheduled for late summer of 2005),
the remnants of the Fixed Target abort system at C0 will be removed and
replaced with a standard long straight section to allow installation of
BTeV experiment components.

### Motivation

Currently, the Tevatron straight section at C0 includes the collision
hall for BTeV and the remnants of the decommissioned Tevatron abort
extraction system for Fixed Target operations. Even before the
installation of the low-β\* insertion at C0 (currently scheduled for
2009), BTeV plans a phased installation of components into the collision
hall during annual accelerator shutdowns for maintenance and upgrades
starting in 2006. There are two main reasons for this.

First, there are some prototype components such as the pixel vertex
detector that would benefit from early operation in the Tevatron. This
operation could be passive \-- observing the environment of the
circulating proton and antiproton beams and their electromagnetic pulse
and the radiation background fields. It could also be active \--
inserting a thin transmission target or turning the electrostatic
separators off to provide low luminosity collisions at C0 at the end of
collider stores. These studies could be used for testing prototype
detectors or commissioning the final detector elements and systems.
Similarly, the impact of the BTeV components on the Tevatron operations,
such as impedances, vacuum, 3-bump dipole spectrometer, and apertures,
could be studied early.

Second, the assembly hall at C0, outside of the shielding door, was
consciously made too small to stage the entire BTeV experiment before
installation. The idea was that each component of the experiment would
be fabricated somewhere else, final-assembled and tested in the assembly
hall, and, when ready, installed during the next scheduled Tevatron
shutdown. The physical size of the SM3 analysis magnet and space needed
for assembly requires that it be installed in the collision hall as soon
as testing is completed.

In order to make space for the installation of BTeV experiment
components, starting with the SM3 analysis magnet, compensating dipoles,
and muon toroid in 2006, the remnant components of the Fixed Target
abort system must be removed from the C0 collision hall and replaced by
a simple beam pipe. This will also require the replacement of two
half-length Tevatron dipoles with full-length Tevatron dipoles in the B4
and C1 cryogenic sectors. At this time the ventilation systems of the
collision hall and the Tevatron tunnel will be isolated, allowing the
collision hall to become ODH Class 0 to facilitate activities by
experimenters and contractors.

The BTeV installation, including the low-β insertion, could, in
principle, be accomplished without the intermediate step of a standard
straight section. However, this more direct approach would preclude much
early testing and, subsequently, lengthen the experiment installation
and commissioning period, which would then begin only after CDF and D0
are completed.

### Scope of Change

The Tevatron C0 straight section had previously been the site of the
abort channel for Fixed Target operations with specific abort elements
located between the B48 and C12 stations \[1\]. Since there is no plan
for further Tevatron Fixed Target operations, this abort is no longer
needed and the C0 area has been assigned to the collider experiment
BTeV. The Fixed Target abort consisted of a set of five kicker magnets
(at the B48 straight section), two half-length Tevatron dipoles (at
B48-3 and C11-3), two C-magnets, and three Lambertson magnets. In
January 2003, in order to increase the vertical aperture in the Tevatron
collider, the three Lambertson magnets were replaced with four Main
Injector dipoles (three 240" long, and one 160" long -- slot lengths are
16" longer). The five kicker magnets were also removed and replaced with
beam pipe at that time. In the C0 collision hall, the Main Injector
dipoles sit on a wall of shielding blocks and the C-magnets sit on a
steel I-beam catwalk \[2\]. Both of these magnet systems interfere with
the installation of experimental components for BTeV.

The total bend of the two half-length Tevatron dipoles plus the two
C-magnets plus the four Main Injector dipoles (with active trim shunting
of the current in the Main Injector dipoles) exactly matches the total
bend of two full-length Tevatron dipoles. The basic plan is to remove
the two half-length Tevatron dipoles, the four Main Injector dipoles,
and the two C-magnets, and replace them with two full-length Tevatron
dipoles (to be purchased from inventory, reducing the number of spares
available) plus additional vacuum pipe (see Figure 11-1). The
full-length dipoles will be placed approximately at the position of the
half-length dipoles. Since the effective magnetic bend points will
change, all the elements between these half-dipoles must be repositioned
transversely inward (toward the center of the Tevatron ring) with the
maximum move of 4.2 inches at the 99" quadrupoles near B49 and C11. This
will reconstitute a normal long straight section \[3\] \[4\].

![](media/image68.png){width="6.122222222222222in"
height="4.493055555555555in"}

**Figure 11-1: The existing C0 abort (dashed) and future straight
section (solid) trajectories.**

Since the removal of the Main Ring accelerator, there remains an excess
capacity in the Low Conductivity Water (LCW) system in the Tevatron
tunnel. This system will be slightly reconfigured to cool the BTeV SM3
analysis magnet, the compensating dipoles, toroid, water-cooled power
bus, and power supplies (in the C0 collision hall), both for the final
installation and for component testing in the assembly hall.

The removed four Main Injector Dipoles and two C-magnets will be
replaced with (\~107 feet total length) of 4 inch diameter,
electro-polished, hydrogen-degassed, stainless steel vacuum pipe which
will be baked out. The vacuum goal for this section of beampipe is
1x10^-9^ Torr. The existing ion pumps and controls in this region will
provide adequate vacuum pumping. A series of simple stands (existing
design) will support the vacuum pipe at beam heights of 10.4 inches, 40
inches, and 100 inches above the existing floors.

Two additional horizontal and vertical readout Beam Position Monitors
(BPM) will be installed on the C0 side of the last Collins straight
section quadrupoles QUADC0U (near B49) and QUADC0D (near C11). These
will provide additional diagnostics in understanding the local 3-bump
made by the SM3 analysis magnet and compensating dipoles. Signal
analysis and readout hardware for these BPMs can be easily accomodated
in the existing B4 and C1 BPM controls system.

Although not needed for the configuration change to the straight
section, eventually, for the installation of the low-β\* insertion, the
warm Tevatron power bus must be relocated to the outer wall or ceiling
of the flare tunnel and massive amounts of new water cooled bus must be
installed for the LHC quadrupoles and relocated Q1 quadrupoles from
CDF/D0. In order to minimize time impact during the shutdown for the
installation of the low-β\* insertion, these bus relocation and
additions should be done starting during the early shutdown for straight
section reconfiguration and continuing through the shutdowns in between.

### Tevatron Beam Optics Considerations

The reconfiguration to a normal straight section changes the
longitudinal positions of two bend points, while maintaining the
longitudinal positions and strengths of all quadrupole magnets.
Therefore, the Tevatron tune is (to very high order) **not** changed,
and the lattice functions around the ring are negligibly perturbed. The
moving of the bend points does mean that the components in between will
move slightly in the transverse horizontal plane, radially inward. The
circumference of the Tevatron orbit will thus be decreased by 1.6 mm, in
the direction which will reduce the present 39 mm mis-match between the
Tevatron and Main Injector rings.

With the B2 compensating dipoles installed in the C0 collision hall, the
physical aperture at C0 will be a minimum at the injection energy with
beam on the helix. Figures 11.2 and 11.3 show the physical aperture in
the C0 straight section in units of transverse beam 's for 20-mm-mrad
(95% normalized emittance) and ~p~/p = 5x10^-4^, which are typical
injected proton beam parameters in Run II operation. The size of the
beampipe in a B2 magnet is 2.0" horizontally and 4.0" vertically. We
have assumed a minimum beampipe ID of 2.0" between the B2's for these
plots. Under these conditions the minimum aperture is 10.8 and is
located at the outboard end of the downstream B2 compensating dipole in
the horizontal plane. For comparison, in the present Tevatron
configuration, the minimum injection energy aperture is at the F0
injection Lambertson and is nominally \~5 \[5\]. The nominal injection
energy apertures at B0 and D0 low beta quads are \~10. The C0 Lambertson
magnets mentioned earlier in this section were removed in 2003 because
their vertical aperture was \~3. The beam trajectories, beam sizes, and
apertures must be considered when installing BTeV experiment equipment
and beam pipes in the region between the B2's (± 27' from I.P.). The
present configuration of horizontal and vertical correctors near C0
allow for independent horizontal and vertical beam position and angle
control at C0 in the range of ±9mm and ±0.100mrad at 1 TeV, which is
more than adequate steering capability.

The present warm gap next to the half-dipole at C11 is unique in the
Tevatron. It provides a location between two cryogenic dipoles for a
single synchrotron light monitor to view off-axis synchrotron light from
both proton **and** anti-proton beams. With the replacement of the
half-dipole with a full dipole, this location will be lost, and
alternatives for the synchrotron light monitor must be considered (see
section 9.1).

![](media/image69.png){width="4.690277777777778in"
height="3.5243055555555554in"}

![](media/image70.wmf){width="4.502777777777778in"
height="3.482638888888889in"}

**Figures 11-2 and 11-3: Horizontal and vertical aperture and beampipe
radius vs. distance from C0. Bottom trace in each plot is the aperture.
Beam is @ 150 GeV and on the injection helix.**

## Installation Plan

The early shutdown for the installation of the normal straight section
is anticipated to be 8 weeks in duration. Not only is the straight
section reconfiguration planned for this shutdown, but also considerable
utility outfitting in the collision hall (see C0 Outfitting Project
CDR)**.** Based on the effort that was required for the replacement of
the C0 Lambertson magnets with MI dipoles in January, 2003, it is
anticipated that the rigging work to remove the four Main Injector
dipoles and the concrete shielding block base can be accomplished within
the first week of the shutdown. In the collision hall, this would leave
the middle 5 weeks of the shutdown exclusively for utility outfitting,
with the final 2 weeks for vacuum pipe installation, leak checking, and
bake-out, along with finishing the utility outfitting work.

Certain activities can be accomplished before the early shutdown begins.
These include design and procurement of beam tubes, vacuum components,
magnet and beam tube stands, LCW components, simple cryogenic piping
extenders, jumpers between power bus and cryo lead boxes, and
pre-fabrication of isolation doors between tunnel and collision hall.

The following is a listing of the "work crews" required to complete the
conversion to a straight section denoted by the tasks they are to
accomplish. This planning is in a preliminary stage. There will likely
be some consolidation of crews designation to optimize manpower. The
jobs are listed in approximate order of activities.

Once the early shutdown begins, the following tasks must be accomplished
in this approximate order for the Tevatron to begin operation again. We
are then committed to completion of all items ̶ operation of the
Tevatron with any of these items only partially complete is not
possible.

> 1\) Warm-up cryogenic houses B4 and C1 (cryo technicians)
>
> 2\) Unhook water, bus jumpers, vacuum, instrumentation (technicians
> and electricians):
>
> \- Remove water hoses and power cables from 6 warm magnets & 2 cryo
> lead boxes
>
> \- Let up to atmosphere warm vacuum and remove components
>
> \- Remove guard rails from shield block wall, isolation gratings, LCW
> piping, cable trays, and supports in region of FMI dipoles and
> C-magnets
>
> 3\) Open shield door (PPD/FESS + riggers or technicians)
>
> 4\) Remove FMI dipoles & 61 concrete blocks and catwalk for C-magnets
> (Rigging crew with heavy fork lift)
>
> 5\) Tunnel magnet moves (technician or rigging crew):
>
> \- Remove: 2 half dipoles, 2 C-magnets, two warm bypasses, and remnant
> (vertical) MR B2 magnet at B48-4 location
>
> \- Reposition transversely: 3 full length, 4 quadrupoles, 6 cryo
> boxes: which include 55.6" bypass, 43" spool, 125.9" spool, 50" spool,
> and two turn-around boxes
>
> \- Install: 2 full dipoles, one warm bypass (existing standard
> 48-section bypass)
>
> 6\) As-found, rough component placement, and final alignment of
> components and vacuum pipe (alignment crews)
>
> 7\) Cryo device moves: undo 17 cryo interfaces, move remaining
> components and install new cryo components, make up 16 cryo interfaces
> (one interface will be eliminated in this reconfiguration), leak check
> all cryo components (cryo/vacuum technicians)
>
> 8\) Bus modifications: possibly start on bus modifications for low-β
> quads (continues thru 2009) (electricians)
>
> 9\) LCW modifications: extend LCW into collision hall and assembly
> bldg -- interface w/construction (pipefitters)
>
> 10\) Extensions for cryo relief, suction, and gas piping
> (cryo/pipefitter)
>
> 11\) Rehook-up lead boxes to Tevatron power bus (electricians)
>
> 12\) Install warm beam pipe in place of MI and C-magnets, install beam
> tube supports, warm vacuum beamline diagnostic components, beam tubes,
> vacuum pumps, vacuum monitoring components, leak check, and bakeout
> (vacuum technicians)
>
> 13\) Install two new BPMs (Instrumentation technicians + electricians)
>
> 14\) Install two walls at tunnel-collision hall interface (mechanical
> technicians)
>
> 15\) Close shield door after completion of collision hall outfitting
> (PPD/FESS + technicians)
>
> 16\) Cool-down cryogenic houses B4 and C1 (cryo technicians)

### Tunnel modifications

The required modifications to the existing Tevatron tunnel are minimal
for this straight section phase. The two junctions of the tunnel with
the collision hall will be sealed with solid doors, separating the
ventilation systems for the tunnel and the collision hall, providing
Oxygen Deficiency Hazard isolation, and maintaining independent search
and secure zones for the tunnel and collision hall. The beam pipe and
LCW supply and return pipes will penetrate these doors. These doors will
have to be able to be opened or removed to allow optical survey and
alignment tasks into, and through, the collision hall, as needed.

### LCW modifications

The additional BTeV components for the interaction region will need
approximately 250 gpm LCW. This LCW at C0 will provide heat dissipation
for the SM3 vertex analysis magnet, the two 10 foot-long B2 compensating
dipoles, a muon toroid magnet, magnet power supplies (in the C0 assembly
building), and copper buswork. The magnets will be power tested in the
assembly hall before moving to the collision hall, so provision to bring
LCW into the assembly hall is also required. Table 11.1 outlines the LCW
requirements for each of the primary components. Later, LCW may also be
required to heat the power leads for the superconducting quadrupoles for
the low-β\* insertion. The flow requirements are clearly dominated by
the vertex magnet. The maximum temperature rise will be approximately
23º F. The flow to the water-cooled bus will be restricted to about 5
gpm per bus pair.

**Table 11-1: LCW requirements for 2005 shutdown**

  ------------- ----- ---- --------- ----------- ------- --------- ------ ------------ ------------- ---------- ---------- ----------------
  System        qty        Current               Power             Min.                Temperature              Diff.      
                                                                   Flow                Rise                     Pressure   
                                                                   Rate                                         Req'd      

                                     *A*                 *kW*             *GPM*                      *F*                   *psi*
                                                                          \[*L/s*\]                  \[*C*\]               

  Vertex Magnet       1              4200                440              151 \[9.52\]               23 \[13\]             120

  Vertex Power        2              \-                  35               11 \[.69\]                 \-                    100
  Supply\*                                                                                                                 

  Vertex Bus          1              4200                \<5              5 \[.32\]                  \<10 \[6\]            \<100

  Toroid Magnet       1              1500                25               25 \[1.58\]                8 \[4\]               120

  Toroid Power        1              \-                  2                5.5 \[.35\]                \-                    100
  Supplies                                                                                                                 

  Toroid Bus          1              1500                \<5              5 \[.32\]                  \<10 \[6\]            \<100

  B2 Magnet\*         2              2300                76               23.4                       23 \[13\]             110
                                                                          \[1.48\]                                         

  B2 Power            1              \-                  6                5.5 \[.35\]                \-                    100
  Supply                                                                                                                   

  B2 Bus\*            2              2300                \<5              11 \[.69\]                 \<10 \[6\]            \<100

                                     **Total**           **599**          **242                                            
                                                                          \[15.3\]**                                       
  ------------- ----- ---- --------- ----------- ------- --------- ------ ------------ ------------- ---------- ---------- ----------------

\*- power and flow are for both units combined

The LCW will be supplied from the Tevatron LCW system. The existing
centrifugal pumps at B4 and C1 will provide the flow needed for BTeV.
They are each capable of providing 400 gpm with a pressure head of 140
psi (355 TDH). The Tevatron supply and return header pressures are
nominally 160 psig and 20 psig respectively. The typical supply
temperature is 90°F. All heat will be rejected to the ponds at B4 and C1
via the heat exchangers located at those service buildings.

The existing 4" Aluminum LCW header will be extended into the collision
hall to provide magnet cooling and also into the assembly hall to cool
the power supplies. The new header must provide adequate flow to the
vertex magnet when it is located in its experimental and assembly
(testing) positions. There will not need to be any significant LCW
controls or instrumentation upgrades. The current ACNET read backs of
temperature, flow, and pressure will suffice. However, local
instrumentation will be installed in the assembly hall to aid in
troubleshooting the system.

The BTeV/C0 leg of piping will be filled from the Tevatron. This can be
accommodated by the Tevatron LCW system since it has a reservoir
capacity of well over 3000 gallons and the additional volume of the new
BTeV/C0 area will only be on the order of 1000 gallons.

During the conversion of the C0 region to "normal" straight section, LCW
hoses feeding the MI dipoles and C-magnets will be removed. Also,
existing 2" LCW copper piping on the B4 and C1 side of C0 will be
removed to ease magnet removal.

### Controls, PS, and QPM modifications

One additional heater firing unit will be required at B4 and C1 service
buildings and the inductance value of one quench detection unit at B4
and C1 will increase by one magnet's inductance. Otherwise, no
modifications are necessary to the Tevatron QPMs. The shunt circuit on
the MI dipoles will be eventually removed from the service building to
make room for future PS installations. There will be a need for the
installation of two new horizontal and vertical BPMs inboard of the last
Collins straight section quadrupole, along with the associated cables
and readout electronics. The present set of Beam Loss Monitors (BLM) in
the C0 area will be moved to new locations on the beampipe.

## Recommissioning Plan

In the 2/03 shutdown the C0 Lambertson magnets were replaced with MI
dipoles, so the Tevatron Department already has experience in
recommissioning the C0 straight section after modifications. Since the
lattice change is negligible, we expect recommissioning to be
straightforward. Aside from the normal recommissioning tasks required
after a shutdown, the following steps will be required after C0 has been
converted to a normal straight section.

1\) [Recommission the QPM system:]{.underline} New database constants
(inductance and resistance) for the changed magnet strings require
verification while ramping magnets. Beam is not required for this step.

2\) [Train new magnets to 1010 GeV:]{.underline} The newly installed
full length Tevatron dipoles need to be ramped to 1010 GeV to verify
that there is adequate quench margin for 980 GeV operation. Beam is not
required for this step.

3\) [Change Tevatron injection frequency:]{.underline} This is required
because the central orbit length changes. The RF frequency (53.1 MHz)
must change by 13.3 Hz. This induces a momentum change of -13.5 MeV. No
change is required in MI operation because it phase locks to the
Tevatron frequency during beam transfer.

4\) [Local orbit correction:]{.underline} It is expected that the local
orbit will need to be corrected at all energies and at all steps of the
low beta squeeze. This step includes local aperture scans to verify that
the aperture is adequate. Since the beampipe in C0 will initially be
4"dia, we expect the aperture to be large. This step requires beam.

5\) [BPM and BLM checkout:]{.underline} The 4 new BPMs and the
repositioned BLMs require testing with beam.

6\) [Synchrotron light monitor:]{.underline} This device will require
extensive parasitic studies before it can be considered operational. See
section 9.1 for a more detailed discussion.

***[References]{.underline}***

\[1\] M Harrison, "The Tevatron Abort System", Fermilab UPC-153, 1981

\[2\] Fermilab Drawing #1780.003-ME-140999 (7 sheets)

\[3\] S Ohnuma, "Geometry of the Superconducting Ring", Fermilab
UPC-163, 1982

\[4\] CT Murphy, "The Brass Plug Monument System for Doubler Alignment",
Fermilab TM-1067, 1981

\[5\] P Ivanov, "InjectNote", Fermilab Beams-doc-990, 2004

\[6\] M Church, "Summary of B0 and D0 Aperture Scans, Alignment Studies,
and Quad Tickling Measurements Done Between 9/01 and 10/01", Fermilab
Beams-doc-900, 2003

12. []{#__RefHeading___Toc63699142 .anchor}Installation, Integration,
    Schedule, and Cost

## Tunnel installation

Tunnel drawings for the shutdown work will be created. For reference,
the present magnet and vacuum configuration appears on drawings
ME-140999, ME-140070 and ME-140071. A 3 dimensional model, with input
from the lattice design program MAD, civil construction drawings, and
shell models of tunnel elements, is being developed to help understand
interference and integration issues.

Installation work will be assigned as follows:

[Warm Vacuum]{.underline} -- AD Mech. Support Dept. technicians, with
augmentation by other FNAL technicians

[Shield door moves, concrete block removal, catwalk removal, shield wall
assembly, guard rails and interlock gates removal and
installation]{.underline} -- subcontracted T&M ironworkers, with FNAL
task manager

[Cryo beamline components]{.underline} -- AD Mech. Support Dept.
technicians, with augmentation by AD Cryo. Dept. technicians

[Cryo piping]{.underline} -- AD Cryo. Dept. technicians and possible
subcontracted T&M pipefitters

[LCW]{.underline} -- subcontracted T&M pipefitters, with FNAL task
manager

[Water Cooled Bus]{.underline} -- subcontracted T&M electricians, with
FNAL task manager

[Interlock gates wiring and switches]{.underline} -- T&M electricians,
with FNAL task manager

[Alignment]{.underline} -- FNAL Alignment and Metrology Group

[Cable pulls]{.underline} - T&M electricians, with FNAL task manager

The Alignment and Metrology Group has created a new system of
positioning which replaces the Murphy line system. This will be used to
align the beamline components of the Tevatron.

### Magnetic Element Installation

Tevatron cryogenic sectors B4 and C1 will be warmed to room temperature
to perform the installation. All Tevatron dipoles between B45 and C15
(31 magnets) will be moved longitudinally and/or transverselly to
accommodate the new lattice arrangement and the shortened Tevatron arc
length. All other magnetic elements currently installed between B43 and
C17, with the exception of the 4 66" quads at B43, B44, C16, and C17,
will be removed (26 magnets). Table 12-1 lists the magnetic elements
which will be installed in the Tevatron between B43 and C17.

**Table 12-1: Newly installed magnetic elements between B43 and C17**

  ----------------------------------- -----------------------------------
  **Device**                          **Locations**

  4 Tevatron Q1's (from A4, B1, and   B45,B46,C14,C15
  storage)                            

  2 LHC-style 54" Q5's                B47,C13

  2 LHC-style 79" Q4's                B48,C12

  2 LHC-style 96" Q3's                B49,C11

  2 LHC-style 173" Q2's               B49,C11

  2 LHC style 96" Q1's                B49,C11

  4 new X1 spools                     B43,B44,C16,C17

  4 Tevatron P spools (from A4,B1,    B45,B46,C14,C15
  and storage)                        

  4 new X2 spools                     B47,B48,C12,C13

  2 new X3 spools                     B49,C11

  1 Tevatron H spool (from storage)   B49

  **total = 29**                      
  ----------------------------------- -----------------------------------

### Electrostatic Separators

Six new separators, identical to previously built separators, are
required. There will be 2 horizontal and 1 vertical separator at B49 and
2 vertical and 1 horizontal separator at C11. These separators are
delicate, and special handling equipment and false floors must be
provided to install them. The separators are located above a 2'6" deep
channel in the tunnel floor on either side of the collision hall (see
Figure 12-1), so that holes do not have to be cored in the tunnel floor
to accommodate them. An air spring transporting cart exists for the
separators, which is towed behind a golf cart, then pushed into place
manually.

Alternatively, these separators could be mounted on girder modules
similar to those which were used at D0. Installation equipment exists
which was used for the separator girders at D0. The installation of
these girders through the D0 drop hatch requires opening up the hatch to
its largest configuration and careful handling of the girders, for which
a procedure was written at the time of the D0 installation in 1992.

The practical advantage of placing the separators on a common girder is
that the separators could be evacuated in the clean shop, backfilled
with a nitrogen purge, transported to the tunnel and installed, then
evacuated, and never opened to air in the tunnel.

![](media/image71.png)

**Figure 12-1: Tevatron tunnel plan view on the B side of the collision
hall.**

### Q1 and P Spool Removal from A4/B1

The Tevatron Q1's and the P spools currently installed at A49 and B11
will be removed from those locations and reinstalled at B45 and C15. In
the current Tevatron configuration the Q1's are not powered (they have
been removed from C49 and D11 to provide space for the D0 Forward Proton
Detector), however the present functionality of these 2 devices at A49
and B11 must be replaced.

At A49 the Q1 and P spool are adjacent and the P spool is inboard of the
Q1. A dipole is just upstream of the Q1, and the start of the bypass for
the separators is just downstream of the P spool. There is main Tev bus
through these devices, but it is not connected in these 2 devices. The
circuits used in the P spool are HDA49, VDA49, and SQA4 which are all
essential for Tevatron Run II operation. HBPMA49 and VBPMA49 are also in
the P spool and are essential for Run II operation. The Q1 slot length
is 72.827" and the P spool slot length is 56.149".

A plan to replace the present functionality of these devices at A49 is
as follows. Replace the Q1 and P spool with two devices: a (new) cold
spool containing a horizontal BPM and an H spool. The H spool has VD,
HD, and SQ coils and a VBPM. The slot length of an H spool is 49.910"
The slot length of the new HBPM spool will need to be 79.066". The H
spool should be inboard of the cold BPM spool in order to maximize the
effectiveness of VDA49 in making IR position bumps.

At the B11 location the Q1 and P spool are adjacent and the P spool is
inboard of the Q1. The end of the separator bypass is just upstream of
the P spool, and an R spool is just downstream of the Q1. A dipole is
downstream of the R spool. There is main Tev bus through these devices,
but it is not connected in the Q1 or P spool. The circuits used in the P
spool are HDB11, VDB11, and SQB1 which are all essential for Run II
operation. HBPMB11 and VBPMB11 are also in the P spool and are essential
for operation. The R spool has no internal coils and is used only to
provide an (external) turnaround for the main Tev bus. It has reversed
cryogen pipes. It has a slot length of 40.729".

A plan to replace the present functionality of these devices at B11 is
as follows. Replace the Q1, P spool, and R spool with two devices: a
(new) cold spool containing a horizontal BPM and an H spool. The H spool
has VD, HD, and SQ coils, a VBPM, and will provide an external
turnaround for the main Tev bus. The slot length of the new HBPM spool
will need to be 119.795". The H spool should be inboard of the cold BPM
spool so that the cryogen pipes can be reversed in the BPM spool. This
will require Tev through bus in the BPM spool.

### Beam Collimators and Shielding

Concrete shielding walls at the upstream and downstream ends of the C0
collision hall will be of a clamshell design and on rollers, so they can
be easily moved when changing a magnet in the area. Figure 12.1 shows
the approximate location of the shielding wall on the B side of the
collision hall. They will surround the Q1 low beta quad cryostat and
could have dimensions up to 6' thick, 12' high, and 12' wide. Gaps
around the quadrupole cryostat and cryostat stand will be filled with
easily removable sandbags. The gaps will be large enough to provide for
sighting for alignment needs.

Two new collimators, of standard design, will be installed in a a 2.6
meter warm straight section near B47-4.

## Interfacing with civil construction project

All work performed by any building trades will be the responsibility of
FESS, with the exception of ironworkers and electricians removing or
installing accelerator components and their related supports, which will
be the responsibility of the Accelerator Division. The civil
construction subproject of the BTeV project (WBS3.0) will provide AC
power distribution to the B4, C1, and C0 service buildings. They will
also provide the housing and environmental protection for the external
buswork between the C0 service building and the penetration entering the
Tevatron tunnel.

## Interfacing with Detector Installation

After C0 is converted to a normal straight section in 2005, the warm
vacuum beampipe in the collision hall is not included within the scope
of this project. The C0 IR project will provide vacuum gate valves on
the inboard ends of the Q1 quads and (possibly) the 50 l/sec ion pumps
mounted just inside these gate valves. All work between these gate
valves (or ion pumps) is the responsibility of the Detector Group.
However, the B2 compensating dipole inside the toroid must have a
provision for changing it in the event of a failure, and we envision
this to involve some sort of handling mechanism and equipment in the
accelerator tunnel. A cooperative design effort for this magnet changing
process between the Accelerator Division and the Detector Group must be
carried through.

## Schedule and Cost

To be written. Summary of Open Plan output. MC

13. []{#__RefHeading___Toc63699151 .anchor}Appendices

## Table of beamline elements between B43 and C17

  ------------ -------------- -------------- -------- --------- ------------ --------------------
  **device**   **location**   **start z      **slot   **high    **internal   **PS**
                              coordinate**   length   power     BPM**        
                                             (m)**    leads**                

  66\" quad    B43-1          0.00           2.3114             vbpmb43      

  X1 spool     B43-1a         2.31           1.8288                          T:VDB43,T:QB43,
                                                                             T:SDB43

  TB           B43-2          4.14           6.4008                          

  TB           B43-3          10.54          6.4008                          

  TC           B43-4          16.94          6.4008                          

  TC           B43-5          23.34          6.4008                          

  66\" quad    B44-1          29.74          2.3114             hbpmb44      

  X1 spool     B44-1a         32.05          1.8288                          T:HDB44, T:QB44,
                                                                             T:SFB44

  TC           B44-2          33.88          6.4008                          

  TC           B44-3          40.28          6.4008                          

  TB           B44-4          46.69          6.4008                          

  TB           B44-5          53.09          6.4008                          

  cold spool   B-44-6         59.49          0.1276                           

  old-Q1       B45-1          59.61          1.8498                          C:QB45=5KA max

  P spool      B45-1a         61.46          1.4262   5KA       hbpmb45,     T:VDB45, T:SQ
                                                                vbpmb45      

  feedcan      B-45-1B        62.89          0.7366                           

  TB           B45-2          63.63          6.4008                          

  TB           B45-3          70.03          6.4008                          

  TC           B45-4          76.43          6.4008                          

  TC           B45-5          82.83          6.4008                          

  TC           B45-6          89.23          6.4008                          

  old-Q1       B46-1          95.63          1.8498                          C:QB46=5KA max

  P spool      B46-1a         97.48          1.4262   5KA       hbpmb46,     T:HDB46, T:SQ
                                                                vbpmb46      

  TC           B46-2          98.91          6.4008                          

  TC           B46-3          105.31         6.4008                          

  TB           B46-4          111.71         6.4008                          

  TB           B46-5          118.11         6.4008                          

  54\" LHC     B47-1          124.51         2.4409                          C:C0Q5=10KA max
  quad (Q5)                                                                  

  X2 spool     B47-1a         126.95         1.4268   10 KA     hbpmb47,     T:VDB47, T:HDB47
                                                                vbpmb47      
  ------------ -------------- -------------- -------- --------- ------------ --------------------

  ------------ -------------- -------------- --------- --------- ------------ --------------------
  **device**   **location**   **start z      **slot    **high    **internal   **PS**
                              coordinate**   length    power     BPM**        
                                             (m)**     leads**                

  TB           B47-2          128.38         6.4008                           

  TB           B47-3          134.78         6.4008                           

  cold bypass                 141.18         0.3016                            

  warm                        141.48         2.5885                            
  straight                                                                    

  cold bypass  B-47-4         144.07         0.4286                            

  X2 spool     B48-1a         144.50         1.4268    10KA      hbpmb48,     T:HDB48, T:VDB48
                                                                 vbpmb48      

  79\" LHC     B48-1          145.93         2.9743                           C:C0Q4=10KA max
  quad (Q4)                                                                   

  TC           B48-2          148.90         6.4008                           

  TC           B48-3          155.30         6.4008                           

  TB           B48-4          161.70         6.4008                           

  TB           B48-5          168.10         6.4008                           

  HTS spool    B49-1a         174.50         1.2677    5KA for   vbpmb48      C:VDB49, T:SQ
                                                       main bus               

  cold spool   B49-1b         175.77         0.2741                            

  cold bypass  B49-2          176.04         0.4286                            

  separator                   176.47         2.9105                           

  separator                   179.38         2.9105                            

  separator                   182.29         2.9105                            

  cold bypass                 185.20         0.3016                            

  cryo         B49-2a         185.51         0.7366                            
  turnaround                                                                  

  96\" LHC     B49-3          186.24         3.5204                           C:C0Q123, 10KA max
  quad (Q3)                                                                   

  X3 spool     B49-3a         189.76         1.4268    10kA,     hbpmb49,     T:HDB49,T:VDB49,
                                                       200A      vbpmv49      T:SQB4

  173\" LHC    B49-4          191.19         5.4762                           C:C0Q123, 10KA max;
  quad (Q2)                                                                   C:C0QT2U, 200A max

  96\" LHC     B49-5          196.67         3.5204                           C:C0Q123, 10KA max
  quad (Q1)                                                                   

  warm bpms    C-0            200.19         0.2604              hbpmc0u,      
                                                                 vbpmcou      

  warm         C-0            200.45         12.1378                           
  straight                                                                    

  warm         C-0            212.58         12.1378                           
  straight                                                                    

  warm bpms    C-0            224.72         0.2604              hbpmc0d,      
                                                                 vbpmc0d      
  ------------ -------------- -------------- --------- --------- ------------ --------------------

  ------------ -------------- -------------- -------- --------- ------------ --------------------
  **device**   **location**   **start z      **slot   **high    **internal   **PS**
                              coordinate**   length   power     BPM**        
                                             (m)**    leads**                

  96\" LHC     C10-1          224.98         3.5204                          C:C0Q123, 10KA max
  quad (Q1)                                                                  

  173\" LHC    C10-2          228.50         5.4762                          C:C0Q123, 10KA max;
  quad (Q2)                                                                  C:C0QT2D, 200A max

  X3 spool     C10-2a         233.98         1.4268   10kA,     hbpmc11,     T:HDC11,T:VDC11,
                                                      200A      vbpmc11      T:SQC1

  96\" LHC     C10-3          235.41         3.5204                          C:C0Q123, 10KA max
  quad (Q3)                                                                  

  cryo         C10-3a         238.93         0.7366   5KA for                 
  turnaround                                          main bus               

  cold bypass  C-10-4         239.66         0.3016                           

  separator                   239.96         2.9105                           

  separator                   242.88         2.9105                           

  separator                   245.79         2.9105                           

  cold bypass                 248.70         0.4286                           

  TC           C11-2          249.13         6.4008                          

  TC           C11-3          255.53         6.4008                          

  TB           C11-4          261.93         6.4008                          

  TB           C11-5          268.33         6.4008                          

  X2 spool     C11-5a         274.73         1.4268   10KA      hbpmc12,     T:VDC12, T:HDC12
                                                                vbpmc12      

  79\" LHC     C12-1          276.16         2.9743                          C:C0Q4=10KA max
  quad (Q4)                                                                  

  TB           C12-2          279.13         6.4008                          

  TB           C12-3          285.53         6.4008                          

  TC           C12-4          291.93         6.4008                          

  54\" LHC     C13-1          298.33         2.4409                          C:C0Q5=10KA max
  quad (Q5)                                                                  

  X2 spool     C13-1a         300.77         1.4268   10KA      hbpmc13,     T:HDC13, T:VDC13
                                                                vbpmc13      

  TC           C13-2          302.20         6.4008                          

  TC           C13-3          308.60         6.4008                          

  TB           C13-4          315.00         6.4008                          

  TB           C13-5          321.40         6.4008                          

  old-Q1       C14-1          327.80         1.8498                          

  P spool      C14-1a         329.65         1.4262   5KA for   hbpmc14,     T:VDC14, T:SQ
                                                      old-Q1    vbpmc14      

  TB           C14-2          331.08         6.4008                          

  TB           C14-3          337.48         6.4008                          

  TC           C14-4          343.88         6.4008                          

  TC           C14-5          350.28         6.4008                          
  ------------ -------------- -------------- -------- --------- ------------ --------------------

  ------------ -------------- -------------- -------- --------- ------------ --------------------
  **device**   **location**   **start z      **slot   **high    **internal   **PS**
                              coordinate**   length   power     BPM**        
                                             (m)**    leads**                

  TC           C14-6          356.68         6.4008                          

  cold spool   C14-6a         363.08         0.1276                           

  old-Q1       C15-1          363.21         1.8498                          C:QC15=5KA max

  P spool      C15-1a         365.06         1.4262   5KA for   hbpmc15,     T:HDC15, T:SQ
                                                      old-Q1    vbpmc15      

  feedcan      C15-1b         366.49         0.7366                           

  TC           C15-2          367.22         6.4008                          

  TC           C15-3          373.62         6.4008                          

  TB           C15-4          380.02         6.4008                          

  TB           C15-5          386.43         6.4008                          

  66\" quad    C16-1          392.83         2.3114             vbpmc16      

  X1 spool     C16-1a         395.14         1.8288                          T:VDC16, T:QC16,
                                                                             T:SDC16

  TB           C16-2          396.97         6.4008                          

  TB           C16-3          403.37         6.4008                          

  TC           C16-4          409.77         6.4008                          

  TC           C16-5          416.17         6.4008                          

  66\" quad    C17-1          422.57         2.3114             hbpmc17      

  X1 spool     C17-1a         424.88         1.8288                          T:HDC17,T:QC17,
                                                                             T:SFC17

  cold bypass  C-17-2         426.71         0.3016                           

  open space                  427.01         0.0052                           

  separator                   427.02         2.9105                           

  separator                   429.93         2.9105                           

  separator                   432.84         2.9105                           

  separator                   435.75         2.9105                           

  open space                  438.66         0.0052                           

  cold bypass                 438.66         0.4286                           

  TB           C17-3          439.09         6.4008                          

  TB           C17-4          445.49         6.4008                          
  ------------ -------------- -------------- -------- --------- ------------ --------------------

## Alternative Corrector Approach -- "Flat Coil Array" Design

An alternative approach to corrector design based on an array of 'flat
coils' which provides a combined function magnet has been proposed. In
this design, one corrector assembly can be configured to provide any of
the required multipole combinations. Having only one design results in
several tangible benefits: lower manufacturing costs, reduction in the
total number of spares, and higher reliability.

Figure 13.2-1 is a conceptual drawing of the new corrector. Table 13.2-1
lists the corrector properties, where the corrector types -- 'A,' 'B',
and 'C' -- correspond to the different C0 IR spool requirements. This
corrector is assembled from 12 identical flat coils of a 'race-track'
geometry. The coils are powered from separate power supplies and are
capable of generating all of the required dipole, quadrupole and
sextupole field combinations. For example, in the case of the normal
dipole, quadrupole and sextupole (Type C) configuration, the total field
is symmetric relative to the median plane and there are only 5
separately powered windings. The racetrack coil can be made in a very
simple manufacturing process. There are no problems to wind the coils
under tension and provide pre-stress through the differential shrinkage
of the aluminum shell with respect to the low carbon steel core. The
coil ends are very short and the corrector is very effective in the
longitudinal direction. The magnet can be assembled from 12 identical
coil blocks and each of them can be separately tested in a small test
cryostat. The magnet cold mass is easily repaired by replacing just the
bad coil segment. There are no internal splices, only joints to the
current leads which should increase the magnet reliability. While this
corrector will require a larger volume of superconductor than the shell
type design, the total magnet cost is not dominated by the
supercondutor.

**Table 13.2-1: Corrector Main Parameters**

  ------------------------------------------- --------- --------- ---------
  **Corrector type**                          **A**     **B**     **C**

  Integrated dipole field, T\*m               0.48                

  Integrated quadrupole gradient, T           25                  

  Integrated sextupole strength , T/m         450                 

  Effective length, m                         0.8       0.8       1.2

  Inner coil radius, mm                       40                  

  Inner core radius, mm                       63                  

  Outer core radius, mm                       120                 

  Operational current, A                      35 - 77             

  Coil number of turns                        760 -               
                                              1700                

  Bare strand diam., mm                       0.3 - 0.5           

  Max strand diam. with insulation, mm        0.43 -              
                                              0.63                

  Coil area, mm^2^                            368                 

  Cold mass outer diam., mm                   300                 
  ------------------------------------------- --------- --------- ---------

![](media/image72.png){width="3.623611111111111in"
height="3.2430555555555554in"}

**Figure 13.2-1: General view of corrector magnet**

### Corrector Magnetic Design

The magnetic design is simple: a combined function magnetic field is
formed by 12 identical race-track coils distributed equally with an
angular separation of 30^o^. The number of coils is the minimum
necessary to provide the required dipole, quadrupole and sextupole
fields. A rectangular coil cross-section was chosen to simplify the
winding process. In the most general case, each coil would be powered
separately. Field errors are somewhat larger than in the cos(n) cross
section design, but should be tolerable since corrector field errors can
produce only second order effects. Adjustment of the corrector currents
can compensate for field deviations caused by manufacturing tolerances,
iron saturation effects, etc. The outer coil sections produce a fringe
field, which can be eliminated by 10mm thick magnetic shield.

### Corrector Type-A

This corrector generates horizontal and vertical 0.48 T\*m dipole fields
and a 7.5 T skew quadrupole field. The corrector parameters are shown in
Table 13.2-2 and in Figures 13.2-2 through 13.2-6.

**Table 13.2-2: Corrector type A parameters**

  ------------------------------------- ---------------------------------
  Dipole field, T                       0.6

  Effective length, m                   0.8

  Dipole component ampere-turns, A      Iw~d1~ = 15200, Iw~d2~ = 13300,
                                        Iw~d3~ = 7600

  Skew quadrupole gradient, T/m         9.375

  Quadrupole component ampere-turns, A  Iw~q~= 12100

  Total coil ampere-turns at max field, 33000
  A                                     

  Maximum flux density in the yoke at   2.3
  max field, T                          
  ------------------------------------- ---------------------------------

![](media/image73.wmf)

**Figure 13.2-2: Corrector A and B cross-section**

![](media/image74.png){width="5.8125in" height="0.78125in"}

![](media/image75.png){width="4.177083333333333in"
height="2.3229166666666665in"}

**Figure 13.2-3: Dipole geometry and field harmonics ( Dip1rot.data )**

![](media/image76.png){width="4.272222222222222in"
height="4.457638888888889in"}

**Figure 13.2-4: Dipole field homogeneity**

![](media/image77.png){width="5.895833333333333in"
height="2.6145833333333335in"}

###### Figure 13.2-5: Corrector A geometry and coil ampere-turns at maximum combined field {#figure-13.2-5-corrector-a-geometry-and-coil-ampere-turns-at-maximum-combined-field .unnumbered}

![](media/image78.png){width="4.21875in" height="3.4791666666666665in"}

**Figure 13.2-6: Corrector A field harmonics (DQS1rot.data)**

The electrical connections are very simple for this type of magnet. Each
coil is powered individualy by an 80A bipolar power supply. The coil
current is the sum of all components, which produce the dipole and
quadrupole fields. The coil currents for the Figure 13.2-7 diagram are:

**I~1~ = I~v1~**

**I~2~ = I~v2~+ I~h3~ +I~sq~**

**I~3~ = I~v3~+ I~h2~ + I~sq~**

**I~4~ = I~h1~**

**I~5~ = -I~v3~ + I~h2~- I~sq\ ~**

**I~6~ = -I~v2~ + I~h3~ -- I~sq\ ~**

**I~7~ = - I~1~**

**I~8~ = -I~v2~ --I~h3~ + I~sq~**

**I~9~ = -I~v3~ --I~h2~ + I~sq~**

**I~10~ = -I~4~**

**I~11~ = I~v3~ --I~h2~ - I~sq~**

**I~12~ = I~v2~ -I~h3~ -I~sq~**

The current directions for the different field components are shown in
Figure 13.2-7 Skew fields can be obtained by an angular rotation of the
corresponding multipole ring diagram.

![](media/image79.wmf)

**Figure 13.2-7: Current distribution in corrector type A, where**

> **I~v1~, I~v2~, I~v3~ -- vertical dipole currents**
>
> **I~h1~, I~h2~, I~h3~ -- horizontal dipole currents**
>
> **I~sq~ --skew quadrupole current**

###  Corrector Type B

This corrector generates horizontal or vertical 0.48 T\*m dipole fields
with a 7.5 T skew quadrupole. All corrector parameters can be obtained
from corrector A design with only one dipole field component. The
corrector parameters are shown in Table 13.2-3 and in Figure 13.2-8.

**Table 13.2-3: Corrector type B parameters**

  -------------------------------------- --------------------------------
  Dipole field, T                        0.6

  Effective length, m                    0.8

  Dipole component ampere-turns, A       Iw~d1~ = 15200, Iw~d2~ = 13300,
                                         Iw~d3~ = 7600

  Skew quadrupole gradient, T/m          9.375

  Skew quadrupole component              Iw~q~= 12100
  ampere-turns,A                         

  Total coil ampere-turns at max field,  25400
  A                                      

  Maximum flux density in the yoke at    2.3
  max field, T                           
  -------------------------------------- --------------------------------

The coil currents for the corrector with vertical dipole are:

**I~1~ = I~v1~**

**I~2~ = I~v2~ + I~sq~**

**I~3~ = I~v3~ + I~sq~**

**I~4~ = 0**

**I~5~ = - I~3~**

**I~6~ = - I~2~**

**I~7~ = - I~1~**

**I~8~ = -I~v2~ + I~sq~**

**I~9~ = -I~v3~ + I~sq~**

**I~10~ = 0**

**I~11~ = - I~9~**

**I~12~ = - I~8~**

![](media/image80.png){width="4.6930555555555555in"
height="3.5756944444444443in"}

**Figure 13.2-8: Flux density in corrector with the vertical dipole and
skew quadrupole**

The coil currents for the corrector with horizontal dipole are shown
below. This type of corrector is powered by 5 independent power
supplies.

**I~1~ = 0**

**I~2~ = I~h3~ +I~sq\ ~**

**I~3~ = I~h2~ + I~sq~**

**I~4~ = I~h1~**

**I~5~ = I~h2~ - I~s~**

**I~6~ = I~h3~ -- I~sq~**

**I~7~ = 0**

**I~8~ = - I~6~**

**I~9~ = - I~5~**

**I~10~ = -I~4~**

**I~11~ = -I~3~**

**I~12~ = - I~2~**

###  Corrector Type C

This corrector generates horizontal or vertical 0.48 T\*m dipole fields
with 25 T quadrupole and 450 T/m sextupole fields. The corrector
parameters are shown in Table 13.2-4 and in Figure 13.2-9. The cold mass
assembly is rotated by 15º as shown in Figure 13.2-9. The magnet design
is the same as for the A and B correctors. The magnetic field, currents
and forces are symmetric with respect to the median plane, resulting in
only 5 independent power supplies needed.

**Table 13.2-4: Corrector type C parameters**

  ----------------------------------- -----------------------------------
  Dipole field, T                     0.4

  Effective length, m                 1.2

  Dipole component ampere-turns, A    Iw~d1~ = 9856.2, Iw~d2~ = 7189,
                                      Iw~d3~ = 2650.9

  Quadrupole gradient, T/m            20.833

  Quadrupole component ampere-turns,  Iw~q~= 26828
  A                                   

  Sextupole strength, T/m^2^          375

  Sextupole component ampere-turns, A 21728.5

  Total conductor current at all      50-80
  component max field, A              

  Maximum flux density in the yoke at 2.0
  max field, T                        
  ----------------------------------- -----------------------------------

![](media/image81.wmf)

**Figure 13.2-9: Cross section of Corrector C**

![](media/image82.wmf)

**Figure 13.2-10: Azimuthal currents distribution in C corrector,
where**

**I~v1~,I~v2~,I~v3~ - vertical dipole currents,**

**I~h1~,I~h2~,I~h3~ - horizontal dipole currents,**

> **I~q~ - quadrupole current,**
>
> **I~s~ - sextupole current.**

The coil currents for this corrector with vertical dipole are:

**I~1~ = I~d1~+ I~q~ + I~s~**

**I~2~ = I~d2~ - I~s~**

**I~3~ = I~d3~- I~q~ - I~s~**

**I~4~ = -I~d3~- I~q~ + I~s~**

**I~5~ = - I~2~**

**I~6~ = -I~d1~+ I~q~ - I~s~**

**I~7~ = - I~6~**

**I~8~ = - I~5~**

**I~9~ = - I~4~**

**I~10~ = - I~3~**

**I~11~ = - I~2~**

**I~12~ = - I~1~**

###  Mechanical Design Concepts

There are at least two options of cold mass fabrication and assembly.
The first one is to wind all racetrack coils separately on the aluminum
or stainless steel bobbins, then assemble two sub assemblies with 6
coils each. In this case the iron core should be split in the median
plane. After that the cold mass is vacuum impregnated with epoxy. The
second option is to split the iron core into 4 or 12 sectors and use
these parts as mandrels for coil winding, impregnation and support. In
this case, each iron block with one coil can be tested separately. Since
in all field configurations the iron blocks are attracted to each other,
only positioning pins are needed to provide proper block positioning.
Special attention is needed to provide a tight coil bobbin connection to
the yoke because under some current combinations the Lorentz forces will
be oriented inside the magnet aperture. There are also some cold mass
de-centering forces. The de-centering forces for correctors A and B are
rather low (160 kg ) but are quite a bit higher for corrector C higher
(1900 kg). The cold mass support structure should be capable of carrying
this load plus the magnet weight (\~500kg).

###  Electrical Circuits, Currents and Power Supplies

As mentioned previously, the electrical connections are very simple for
this type of magnet. External current leads are provided for each coil
and connected to separate 80 A bipolar power supplies. It is possible to
reduce the number of currents and power supplies to 5 in the case of
normal dipole, quadrupole and sextupole fields (see Table 13.2-5 ).

The coil current is the sum of all components which produce the dipole,
quadrupole and sextupole fields. The current directions for different
normal field components were shown in Figures 3.2-7 and 3.2-10 above.
Skew fields can be obtained by the angular rotation of corresponding
multipole ring diagram.

###### Table 13.2-5: Corrector currents, coils, and power supplies {#table-13.2-5-corrector-currents-coils-and-power-supplies .unnumbered}

+------------------+------------------+--------------+-----------------+
| **Corrector      | **Number of      | **Max coil   | **Max coil      |
| Type**           | PS/corrector**   | am           | current at**    |
|                  |                  | pere-turns** |                 |
|                  |                  |              | **760           |
|                  |                  |              | turns/coil**    |
+------------------+------------------+--------------+-----------------+
| A ( HD+VD+SQ)    | 10               | 33000        | 43.4            |
+------------------+------------------+--------------+-----------------+
| B (VD+SQ)        | 5                | 25400        | 33.4            |
+------------------+------------------+--------------+-----------------+
| B (HD+SQ)        | 5                | 25400        | 33.4            |
+------------------+------------------+--------------+-----------------+
| C (VD+Q+S)       | 5                | 58413        | 76.8            |
+------------------+------------------+--------------+-----------------+
| C (HD+Q+S)       | 10               | 58413        | 76.8            |
+------------------+------------------+--------------+-----------------+

The coil current can be reduced if the superconducting wire diameter is
decreased and the number of turns is increased proportionally. The
conductor diameter, number of turns and maximum current should be
simultaneously optimized with a reasonable quench current margin and
mechanical stability. There is about two times difference in maximum
currents for A,B and C magnets. It is possible to reduce the volume of
superconductor for A and B correctors by proportionally increasing the
current.

It should be noted that at the magnet ends the fields are typically
larger and have correspondingly lower current margins. This effect can
be reduced by proper profiling of the coils and yoke at the ends.

## Preliminary Test Plan for H Spool with HTS Current Leads

I.  300K tests:

-   Leak check the vacuum lines

-   Leak check the nitrogen lines -- make sure to open EVLA and EVLB
    valves

-   Electrical checkout of the lead and Stand 2 -- follow Electrical
    checkout procedure (TD note \# xxxx *\[note to be written\]*)

-   Hi-pot the leads to 2kV relative to ground

II. Cool down to 4.6K.

Follow Spool cool down procedure (Operating Procedure Number:
HTS-000228-1).

Monitor lead voltages by applying +-5 Amps on the leads.

Change polarity every 5 minutes. Set logging frequency of the slow scan
to 10

seconds.

III. A 2-phase calibration should be done first. It should be done in
     "low pressure"

("Tevatron") mode. This involves:

-   drop \"single-phase\" pressure to the 2-phase pressure by opening
    the stand JT

> valve (PV-548) wide,

-   reduce feedbox power lead flow to 30 SCFH each to ensure that there
    is no subcooling at the \"single-phase\" inlet to the magnet,

-   set spool piece corrector lead flows to 10 SCFH each

-   reduce main storage dewar pressure to about 5 psig and/or throttle a
    test stand

> inlet valve to reduce flow to between 10\" and 20\",

-   hold these conditions steady for 4 hours.

We want 2-phase flow throughout the \"single-phase\" channels. Then we
compare temperature sensor readings. All single-phase readings should
agree within 10 mK, and they should also agree with 2-phase readings.

IV. Do all tests (except the 2-phase calibration) in high-pressure mode
    (\"SSC mode\"). Hold 32 psia single-phase pressure during tests on
    stand 2.

> Current tests at 4.6K:

1.  Quench detection circuit checkout

2.  DC tests:

> Test 1.

  ------------ -------------- ------------- --------------- ---------------
  Current (A)  He flow        LN2 flow      Ramp Rate (A/s) Duration (min)
               (g/sec)        (g/s)                         

  3000         0.03           find min.     20              30
                              flow                          

  5000         0.03           find min flow 20              30

  6000         0.03           1.2           20              30

  6500         0.03           find min flow 20              30

  7000         0.03           find min flow 20              30

  7500         0.03           find min flow 20              30

  8000         0.03           find min flow 20              30

  8500         0.03           find min flow 20              30

  9000         0.03           find min flow 20              30

  9500         0.03           find min flow 20              180
  ------------ -------------- ------------- --------------- ---------------

> 3\. Coolant loss test:

Test 2.

  ------------ -------------- ------------- --------------- ---------------
  Current (A)  He flow        LN2 flow      Ramp Rate (A/s) Duration (min)
               (g/sec)        (g/s)                         

  9500         0.03           Min.flow/0    20              Until it
                                                            quenches

  9500         0.03           Min.flow      20              180
  ------------ -------------- ------------- --------------- ---------------

3.  DC tests with external B-field applied

> Under external B-field increase the current gradually. If no quench
> occurs at 9500A increase the LN2 pressure up to 40 PSIG.