Feb 10, 2001

G. W. Foster

# Section 5.1.3 Corrector Magnet System Requirements - Phase I

\*\*\*THIS SECTION HAS SOME WRONG NUMBERS BUT THE IDEAS ARE OK\*\*

## **Introduction**

## The LF magnet system has a complete set of dipole, quadrupole, and multipole correctors distributed throughout the arcs. The magnets are independently powered with short cables from power supply modules located at each half-cell boundary. This provides maximum flexibility for diagnosis and manipulations of the beam optics. All correctors are factory installed, aligned, pre-cabled and tested on the 65m magnet assembly. There are on average \~3.5 corrector magnets in each half-cell for each bore of the machine, for a total of 12,000 corrector magnets in the ring. The aperture requirements for correctors are discussed in section \[\*\*\*vacuum\].

### Reliability

## A large machine can typically function properly with a number of broken correctors. However, corrector failures during a collider store often cause the store to be lost. Thus the Phase I corrector power supplies (sect \*\*\*) will be fully redundant, with a "hot spare" supply for all loads either ready to take over or actively involved in load sharing. This redundancy increases the (relatively small) direct hardware cost of the power supplies and does not affect the cabling or power dissipation requirements. The increased reliability from redundancy is desirable and appropriate given the scale of the machine. Corrector reliability is not a machine safety issue since the long fall time (milliseconds to seconds) of the magnetic field in the corrector allows the beam to be safely aborted.

## The power distribution to each module is also doubly redundant as described in section \*\*\*. Each supply module can accept input power in either direction in the tunnel from loop feeders with remote disconnects. Thus any single power feeder can fail (open or short circuit) without a loss of input power to any supply module. We expect this redundancy to provide an appropriately reliable corrector system.

### Technology Choice: Superconducting or Warm Correctors

Both superconducting and warm (copper/iron) corrector designs were
developed and evaluated in the course of this study. Warm correctors
were chosen for reasons of simplicity, flexibility, and cost.

#### Superconducting Corrector Option

The main advantage of a superconducting corrector is that very strong
correctors can be made in relatively compact packages. The cold
corrector can share the insulating vacuum with the transmission line,
and be clamped directly onto the transmission line without large
cold-to-warm forces. If a cold-bore corrector design is chosen, its
cryopumping will reduce the number of ion pumps needed to remove CH4
from the beam pipe vacuum. The overhead paid for this includes current
leads, leak checking, quench protection, thermal shields and intercepts,
warm bore or extra gate valves on the beam pipe, vacuum feedthroughs,
and so on. The estimated heat leak and cold mass of the first-pass
corrector design (see fig \--) would approximately double that of the
main transmission line.

Fig 1 -- Superconducting Corrector Option \[ref \*\*\*\] Developed for
Design Study.

#### Normal Conducting Corrector Magnets

The chosen correctors are classical room temperature, air cooled, iron
dominated magnets with copper coils. The design parameters benefit from
the small aperture requirements of the Phase I machine. The design fits
well with the vacuum system of the Phase I magnet. These are well
developed technologically, with a good experience base for projecting
costs, reliability, and power consumption. Collaboration with industry
is straightforward with these magnets. Magnet details are given in
section \*\*\*.

Warm correctors with large iron yokes cannot easily coexist with the
100kA transmission line current. The best solution is to re-route the
transmission line downwards towards in a 20-30cm chicane as it passes
the corrector magnet. See fig.2.

Fig 2 -- Normal conducting Corrector Option Chosen for Design Study.

### ORBIT CORRECTOR DIPOLE REQUIREMENTS

#### Location of Orbit Correctors

The Phase I machine follows the canonical approach of having one
Horizontal (or Vertical) dipole corrector at each Focusing (or
Defocusing) "quad location" in the lattice. Correctors are identical in
the straight sections and the arcs. Approximately 20 locations have both
H and V correctors to provide complete orbit control for injection,
extraction, beam cleaning, IR's, etc. These require no special spool
pieces or special integration since the correctors are "C-magnets"
clamped over unoccupied beam pipe in the straight sections.

#### Strength of Orbit Correctors

The parts cost and power dissipation of a warm corrector increases
linearly with its strength. Thus there is incentive to provide the
minimum strength necessary to get the job done. The orbit corrector
strength must satisfy several requirements. The most stringent by far is
the requirement to regulate the orbit at full energy, in the presence of
installation misalignments, bend strength errors, and geological
settling of the tunnel. The final requirement (discussed below) is that
a single corrector must be able to "bump the orbit at the next
corrector" by at least 3mm TBD at top energy of 20 TeV. This requires a
corrector of 0.5 TBD Tesla-meter.

1\. During commissioning, correctors must have sufficient strength to
thread the orbit

from BPM to BPM to establish a closed orbit, in the presence of both
routine field and alignment errors and occasional (several mm) alignment
blunders. The corrector strength should not limit initial beam threading
as long as there is physical aperture between BPM/corrector locations.
This is automatically satisfied at injection energy where the maximum
orbit bump is 20x the high field bump or \~60mm TBD. This is far outside
the range of expected misalignments.

2\. Full aperture scans are necessary to verify the clear beam path and
identify alignment problems. Again, the corrector strength necessary for
orbit correction at 20 TeV energy is sufficient to perform full aperture
scans in the +/-10mm beam pipe at any energy up to 5 TeV. (Note there is
no particular problem with magnet quenches while performing aperture
scans in the warm-iron transmission line magnet. Preserving this
capability is an additional argument in favor of normal conducting
correctors.)

3\. High-field orbit corr. - \[insert Hiroshi Simulation Words leading
to 0.5-1 T-m\]

input assumptions:

\- alignment offsets

-   rolls

-   bend strength errors

-   ground motion

-   number of magnets moved

results:

-   closed orbit distortions & corrector strength distributions

### 

  -------------- ------------------------------------------- ------------- -- ----------
  **DIPOLE                                                   **Phase I**      
  CORRECTORS**                                                                

                 Location (one per half-cell each bore)      (H/V) at         
                                                             (F/D) quad       
                                                             locs             

                 Number per Ring (both bores)                3420             

                 Magnet Type                                 Warm             
                                                             Iron/Copper      

                 Configuration                               C-Magnet         

                 Bend Field (max)                            0.7              T

                 Magnetic Length                             0.7              m

                 Physical (slot) Length                      1                m

                 Integrated Bend Strength                    0.5              T-m

                 Bore                                        warm aluminum    
                                                             pipe             

                 Magnetic Aperture (magnet gap/coil diam)    20 x 30          mm

                 Physical Aperture                           18x28            mm

                 Max Bend Angle                                               

                 at injection                                158.3            urad

                 at max energy                               7.4              urad

                 Max Orbit Deflection (2-bump)                                

                 at injection                                65.2             mm

                 at max energy                               3.1              mm

                 Equivalent Quad Displacement                                 

                 at injection                                14.7             mm

                 at max energy                               0.7              mm

                 Magnet Weight                               300?             kG

                 Coil Weight                                 150?             kG

                 Operating Current (max)                     10               Amp

                 Coil Resistance incl. Leads                 10               Ohm

                 Ohmic Voltage (max)                         100              V

                 Ohmic Power (max) incl. Leads               1000             W

                 Ohmic Power (average for ring)              200              W

                 Coil Inductance                             1                H

                 Min Ramping Time 0-100%                     20               sec

                 Max Inductive Voltage                       0.5              V

                 Inductive Stored Energy                     50               J

                 Overheating Protection                      Series Klixon    

                 Coolant                                     Air              

                 Power Supply Location                       Each Quad        
                                                             location         
  -------------- ------------------------------------------- ------------- -- ----------

###  QUADRUPOLE CORRECTOR REQUIREMENTS

#### Location and Number of Quad Correctors

The Phase I machine has an independently powered quadrupole corrector at
each "quad location" in the arcs, and at locations of straight section
quads which are not independently powered. The main function of the
correctors is to locally compensate for the gradient shifts that occur
near 2 Tesla due to iron saturation in the combined-function arc
magnets. The situation is analogous to separated-function machines
having quads and dipoles on a common bus, and which therefore require
quad correctors to account fo r the differential saturation of quads and
dipoles \[ref SSC: 2% allowance for quad:dipole tracking\].

#### ![](media/image1.wmf)

Individual correctors at each quad allow the beta functions to be
measured (via the tune shift vs. corrector current) at each quad
location. Thus beta waves can be detected and corrected at each cell.
This compensates for both systematic and random quadrupole errors, as
well as avoiding loss of aperture due to beta waves.

#### Strength of Quad Correctors

The strength of the quad correctors must exceed the gradient shift of
the combined-function magnets. The gradient drops by \~10 units TBD as
the steel saturates differentially on the high-field side of the pole
tip. To preserve the optics and phase advance, this must be compensated
for by an increased gradient from the quad corrector. The integrated
strength required by the quad corrector is about 25% less than the
integrated strength of the field defect in the arc magnets since it
operates near beta-max in the cell.

To minimize corrector strength, the design gradient of the
combined-function magnet is increased by one-half of the gradient drop
at full field. This results in a bipolar corrector current program which
swings to +/- 1/2 of the full gradient shift in the magnet.

![](media/image2.wmf){width="5.45in" height="4.1402777777777775in"}

###  

### 

  -------------- ----------------------------------------- ------------- -- ------------
  **QUADRUPOLE                                             **Phase I**      
  CORRECTORS**                                                              

                 Location                                  each halfcell    
                                                           in arcs          

                 Number per halfcell                       1                per bore

                 Number per Ring (both bores)              3136             

                 Magnet Type                               Warm             
                                                           Iron/Copper      

                 Gradient                                  25.0             T/m

                 Magnetic Length                           0.75             m

                 Physical (slot) Length                    1                m

                 Integrated Quad Strength                  18.8             T-m/m

                 Bore                                      warm aluminum    
                                                           pipe             

                 Magnetic Aperture (magnet gap/coil diam)  20 x 30          mm

                 Physical Aperture                         18x28            mm

                 Tune Adjustment (single corrector)                         

                 at injection                              0.197            nu

                 at max energy                             0.009            nu

                 Tune Adjustment (all correctors in ring)                   

                 at injection                              154.1            nu

                 at max energy                             7.2              nu

                 Beta Wave Generation/Trim (per corrector,                  
                 fractional tune 0.3)                                       

                 at injection                              131              \%

                 at max energy                             6                \%

                 Maximum Correctable Gradient Error in                      
                 Dipoles                                                    

                 at injection                              194              units@1cm

                 at max energy                             9                units@1cm

                 Magnet Weight                             300?             kG

                 Coil Weight                               150?             kG

                 Operating Current (max)                   10               Amp

                 Coil Resistance incl. Leads               10               Ohm

                 Ohmic Voltage (max)                       100              V

                 Ohmic Power (max) incl. Leads             1000             W

                 Ohmic Power (average for ring)            200              W

                 Coil Inductance                           1                H

                 Min Ramping Time 0-100%                   20               sec

                 Max Inductive Voltage                     0.5              V

                 Inductive Stored Energy                   50               J

                 Coolant                                   Tunnel Air       
                                                           Flow             

                 Overheating Protection                    Klixon           
                                                           Interlock        

                 Power Supply Location                     Each Quad        
                                                           location         
  -------------- ----------------------------------------- ------------- -- ------------

###  SEXTUPOLE CORRECTOR REQUIREMENTS

#### Location of Sextupole Correctors

The Phase I machine has an independently powered sextupole corrector at
each "quad location" in the arcs, and (optionally, TBD) at the ¼ cell
point. Their main function is to correct as necessary the saturation
sextupole defect that occurs at full field in the transmission line
magnet. If desirable, the independently powered sextupoles can be
programmed to correct the individual (random) sextupole component of the
arc magnets in each cell. Sextupole correctors can be grouped into
software-defined "virtual families" for chromaticity & resonance control
as well.

Tracking studies \[sect \*\*\*\] studied the extent to which a sextupole
body field error can be compensated by one or more correctors in each
half-cell. A point of reference is the Fermilab Main Injector, which
compensates more than \~20 units of saturation sextupole without
difficulties.

#### Sextupole Corrector Strength

The arc magnet pole tip design and "holes in the poles" (sect \*\*\*)
have been optimize to reduce the required sextupole corrector strength.
The resulting current program is shown in fig. \*\* .

\[plot of arc sextupole vs bend field, and corrector current vs. bend
field\]

### ALIGNMENT AND APERTURE REQUIREMENTS FOR CORRECTORS

### (Maybe this should be moved to vacuum system)

Horizontal correctors 3x2cm

Vert correctors: 2x3cm

Quad and 6-pole correctors: 2.5cm pole tip radius

Most demanding alignment: vertical alignment of horizontal corrector.

Alignment keyed to end of laminations at either magnet end.

### 

  -------------- ----------------------------------------- ------------- -- ------------
  **SEXTUPOLE                                              **Phase I**      
  CORRECTORS**                                                              

                 Location                                  each halfcell    
                                                           in arcs          

                 Number per halfcell                       1                per bore

                 Number per Ring (both bores)              3136             

                 Magnet Type                               Warm             
                                                           Iron/Copper      

                 Sextupole Strength                        0.15             T \@1cm

                 d2By/dy2                                  3000             T/m\^2

                 Magnetic Length                           0.8              m

                 Physical (slot) Length                    1.0              m

                 Integrated Sextupole Strength             0.12             T-m@1cm

                 Bore                                      warm aluminum    
                                                           pipe             

                 Magnetic Aperture (pole tip/coil diam)    25.0             mm

                 Physical Aperture (diameter)              23.0             mm

                 Chromaticity Adjustment (single                            
                 corrector)                                                 

                 at injection                                               

                 at max energy                                              

                 Maximum Correctable Sextupole Error in                     
                 Dipoles                                                    

                 at injection                              99               units@1cm

                 at max energy                             5                units@1cm

                 Magnet Weight                             250.0            kG

                 Coil Weight                               100.0            kG

                 Operating Current (max)                   1                Amp

                 Coil Resistance incl. Leads               340              Ohm

                 Ohmic Voltage (max)                       340              V

                 Ohmic Power (max) incl. Leads             340              W

                 Ohmic Power (average for ring)            255              W

                 Coil Inductance                           1                H

                 Min Ramping Time 0-100%                   20               sec

                 Max Inductive Voltage                     0.05             V

                 Inductive Stored Energy                   0.5              J

                 Coolant                                   Tunnel Air       
                                                           Flow             

                 Overheating Protection                    Klixon           
                                                           Interlock        

                 Power Supply Location                     Each Quad        
                                                           location         
  -------------- ----------------------------------------- ------------- -- ------------