*Abstract*\-- The proposed Next Linear Collider (NLC) will require over
1400 adjustable quadrupoles between the main linacs' accelerator
structures. These 12.7 mm bore quadrupoles will have a range of
integrated strength from 0.6 to 132 Tesla, with a maximum gradient of
135 Tesla per meter, an adjustment range of +0 --20% and effective
lengths from 324 mm to 972 mm. The magnetic center must remain stable to
within 1 micrometer during the 20% adjustment. In an effort to reduce
estimated costs and increase reliability, several designs using hybrid
permanent magnets have been developed. All magnets have iron poles and
use either Samarium Cobalt or Neodymium Iron to provide the magnetic
fields. Two prototypes use rotating rods containing permanent magnetic
material to vary the gradient. Gradient changes of 20% and center shifts
of less than 20 microns have been measured. These data are compared to
an equivalent electromagnet prototype. (See High Reliability Prototype
Quadrupole for the Next Linear Collider by C.E Rago, C.M SPENCER, Z.
Wolf submitted to this conference.)

I. Introduction

The Next Linear Collider \[1\] (NLC) is a future electron/positron
collider that is based on copper accelerator structures powered with
11.4 GHz X-band RF. It is designed to begin operations with a
center-of-mass (cms) energy of 500 GeV or less, depending on the physics
interest, and to be adiabatically upgraded to 1 TeV cms with a
luminosity of 2\~3 x 10^34^ cm^-2^s-^1^. The facility is roughly 30 km
in length and supports two independent interaction regions. For the main
linac there will be over 1400 quadrupoles between the accelerator
structures. To reduce costs and increase reliability, adjustable
permanent magnets are considered for these structures. Based on
Fermilab's experience with permanent magnets used in their Recycler,
collaboration between SLAC and Fermilab is exploring designs and
prototypes.

Manuscript received September 24, 2001

\*<Volk@fnal.gov>

Work supported by the U.S. Department of Energy under contract No.
DE-AC02-76CH03000 and DE-AC03-76SF00515.

(1) Fermi National Accelerator Laboratory PO Box 500, Batavia IL, 60510
    USA

(2) Stanford Linear Accelerator Center 2575 Sand Hill Road, Menlo Park
    CA, 94025 USA

II\. Magnet Requirements

The general linac magnet requirements are the same for all styles of
magnets and are given in Table 1 for a 1 TeV machine. The temperature
stability, harmonics, and field accuracy do not pose a problem based on
the experience from the Fermilab Recycler \[2\]. To achieve the required
pole tip field rare earth permanent magnets are required. Samarium
Cobalt (Sm~2~ Co~17~) was chosen for its high residual B field (B~r~)
and small temperature variation of the field. Neodymium Iron was also
tested in the wedge type quadrupole. For the quadrupoles with lower
gradient and integral field the amount of magnetic material or the
length of the steel pole can be reduced.

**Table I**

**Magnet Requirements for a 1TeV NLC**

+----------------------------+-----------------------------------------+
| Item                       | Value                                   |
+----------------------------+-----------------------------------------+
| Aperture                   | 12.7 mm                                 |
+----------------------------+-----------------------------------------+
| Quantity Length            | 288 324 mm                              |
|                            |                                         |
|                            | 399 432mm                               |
|                            |                                         |
|                            | 576 965mm                               |
+----------------------------+-----------------------------------------+
| Pole tip field             | 0.62 Tesla for 324mm                    |
|                            |                                         |
|                            | 0.86 Tesla for other                    |
+----------------------------+-----------------------------------------+
| Adjustment                 | +0 to --20%                             |
+----------------------------+-----------------------------------------+
| Temperature stability      | 0.5% at 25 ± 1 ^o^C                     |
+----------------------------+-----------------------------------------+
| Sextupole                  | b~3~/b~2~ \< 0.02 at r=5mm              |
+----------------------------+-----------------------------------------+
| Field accuracy             | ±0.5% at any field                      |
+----------------------------+-----------------------------------------+
| Center location            | To Fiducial ± 0.1mm                     |
+----------------------------+-----------------------------------------+
| Magnetic Center stability  | ± 0.001 mm over range of adjustment     |
+----------------------------+-----------------------------------------+

The Beam Based Alignment (BBA) process for these quads drives the
magnetic center stability requirement of ±0.001 mm. When a beam position
monitor detects movement of the beam the position of the related
quadrupole will be adjusted to bring the beam back on the correct
trajectory. The BPM to quadrupole center calibration process requires
that the quad strength be lowered by 20% in five steps over several
seconds during which the magnetic center must not shift by more than 1
micrometer. This calibration will be done monthly.

III\. Corner Tuner Quadrupole

Four prototypes of adjustable permanent magnets were designed and built.
This paper reports of two of those four. The first is a corner tuner and
the second is a wedge quadrupole. All measurements were made at the
Fermilab magnet test facility with a stretched wire system. The
resolution of the center shift was ±1 micrometer and the gradient error
±20 Gauss.

The corner tuner is a hybrid permanent magnet quadrupole. The magnet
uses precision-machined poles (1008 carbon steel) to form the gradient
field and permanent magnet material (Sm~2~ Co~17~) behind each pole to
drive the gradient. To adjust the gradient there are rotating permanent
magnets in each of the four corners behind the poles. Figure 1 is a
PANDRIA flux plot showing a cross section of the magnet the outer
dimensions are 165 by 165-mm.

![](media/image1.wmf)

Fig. 1. Corner tuner cross section showing the poles, magnet material
and tuning rods. The field lines are also shown in this plot.

![](media/image2.wmf)

Fig. 2. Center shift vs intergrated gradient for the corner tuner model.

This design is similar to the Fermilab Recycler quadrupoles. Figure 2
shows the center shift versus the gradient strength for the prototype
quadrupole. The center is seen to move more than 50 micrometers for a
full rotation of the tuning rods. Studies using PANDRIA indicate that
the quadrupole center is dependent on the balance in the strength of the
tuning rods and the precision in the support bearings. Further work on
this prototype was stopped in favor of the wedge quadrupole.

IV\. Wedge Tuner Quadrupole

The next type of quadrupole also used precision-machined poles to shape
the field. The Samarium Cobalt magnets were placed behind the poles and
wedged in between the poles to provide higher field hence the name wedge
quad. (Figure 3) The outer dimensions of the flux return were 101.6 by
101.6 mm. Variation in the gradient was accomplished by the use of
rotating magnetic material behind each pole. The advantage of this
design is that the tuning rods were placed in a region of parallel
field. This reduced the dependence of the precision of the bearing and
strength balance of the tuning rods. All prototype magnets had a pole
length of 203 mm. This fit the Electric Discharge Machine (EDM) at the
Fermilab Shops. All the pole pieces were made on an EDM to provide
precise dimensions for optimal field shaping. MANAQUENCH of Valparaiso
Indiana \[3\] supplied the Samarium Cobalt magnetic material and the
Nd-Iron cylinders were supplied by Dexter magnetics \[4\].

![](media/image3.wmf)

Fig. 3. Wedge quadrupole cross section showing the poles, magnet
material and tuning rods. The field lines are also shown in this plot.

The first version of the wedge quad (FWSQ001) had wedge magnets
dimensions of 12.7 mm by 10.2 mm by 25.4 mm and pole magnets of 9.25 mm
by 9.25 mm by 25.4 mm. Six magnets were arranged along the length of the
pole for a total magnet length of 152 mm. This generates an integrated
field of 20 Tesla. The tuning rods were made of 6 cylindrical magnets
each 8.3 mm in diameter and 25.4 mm long, magnetized through the
diameter. These magnets were glued in an aluminum tube with spacers
between each magnet. As the glue set up an external magnet field was
applied to keep the field orientation aligned through the diameter of
the tube.

Strips of high Nickel steel between each of the pole magnets
accomplished temperature compensation. These strips were in contact with
the pole and the flux return. The Curie point of these strips is 45 C.
When the magnet is cold and the field is strong these strips act as
shunts to the field. As the magnets warms the shunts release field into
the gap. By balancing the volume of magnets to strips of steel a
temperature variation of less than one part in 10^4^ was achieved.

To allow for rotation of the tuning rod aluminum disks were attached to
the ends of the rods. Holes were drilled in each disk at 15-degree
intervals. As the rods were rotated a pin in each disk held the rod at a
given angle. Figure 4 shows the variation of the quad center as a
function of gradient. Each curve is generated when the rods are shifted
to different holes. The different curves indicate an imbalance in the
strength of each tuning rod.

A fixture of parallel steel plates was fabricated. Each tuning rod was
inserted into this fixture and a Hall probe was used to measure the
relative strength of each rod. A variation of 5% in the strength of the
rods was found. Modeling this variation in PANDRIA indicates that a 5 to
10 micrometer center shift could be caused by this imbalance.

![](media/image4.wmf)

Fig. 4. Y center vs. integrated gradient strength in Tesla for a 200-mm
pole length. Each curve represents a different position of the tuning
rods. The different paths indicate an imbalance in the strength of the
rods.

This magnet was rebuilt using Neodymium Iron magnets of the same
dimension. There was an increase in gradient of 20%. The center shift as
a function of change in field was similar.

A second wedge type quad was made. The permanent magnets in this version
were 50% larger to increase the gradient, the cross section is the same
as Figure 3. The pole magnets were 12.7 by 12.7 mm and the wedge magnets
were 12.7 by 20.3 mm. This gave a gradient increase of 30%. The
arrangement of the magnets was similar to the first wedge quadrupole.

For this magnet all of the individual magnets were selected for field
uniformity and matched to balance the strength of the poles. The time of
flight for each magnet falling through an aluminum tube was measured.
Longer time of flight corresponded to stronger magnets. The magnets were
matched with a strong magnet next to a weak magnet. The sum of the
strengths for each row of magnets was then matched to be the same. A
similar method for the rotating rods was used. A similar rotating
mechanism was used to rotate the rods. In addition, custom fitted carbon
fiber bearings were made for each tuning rod. This eliminated any wobble
in the rods. Figure 5 shows the center shift vs. gradient for this
magnet for the tuning rods in different positions. The overall center
shift was less than 20 micrometers. This is still too large for the NLC
requirements. Measurements of the tuning rods with a hall probe showed a
2% imbalance in the strength of the rods. There is a need to improve the
balance in the strengths of the tuning rods; different schemes are being
developed.

![](media/image5.wmf)

Fig. 5. Y center motion vs. integrated gradient strength in Tesla for a
200 mm pole length. Different curves are for tuning rods in different
positions

V. Radiation Damage Issues

Radiation damage in permanent magnet material has been a concern since
the early 1980\'s. There have been many studies done on both Samarium
Cobalt and Neodymium Iron. Many of the pertinent papers have been
collected on a web site hosted at SLAC \[5\]. Luna \[6\] et al. has a
summary table that gives values of demagnetization for various materials
and particles. In general Samarium Cobalt does not show significant loss
in magnetization up to 10^9^ rads for neutrons or protons. Neodymium
Iron shows no significant loss of magnetization up to 10^7^ rads. Gamma
rays appear to have little to no effect on either type of rare earth
permanent magnets.

The paper by Kähkönen \[7\] et al. gives a parameterization for the
change in magnetization of

∆M/M = 2 V~grain~/V~sample~ nLn~p~

Where n is the ion density,  is the cross section, and L is the sample
thickness. It is clear that the preparation of the magnet material, in
particular the grain size of the material, has a direct effect on the
coercivity and the radiation hardness of the magnets. This could explain
the wide variation in the amounts of demagnetization in material made by
different manufacturers.

For the design of the NLC quads it is important to understand the
expected radiation exposure of the magnets both due to normal beam loss
and possible accidents. For the NLC quads it will also be important to
control the manufacturing process used for the magnet material in order
to achieve the higher coercivity and hence radiation hardness.

VI\. Other Styles of Magnets

Cherrill Spencer and Carlo Rago at SLAC have built a prototype
electromagnet \[8\]. This is a conventional water-cooled copper
conductor quadrupole with a current of up to 133 amps. The magnet meets
all the specifications given in table 1. The center stability of 1
micrometer is achieved by always increasing the current from a lower to
a higher value.

Vladimir Kashikhin reported on two other styles of permanent adjustable.
\[9\] The first is a sliding shunt magnet where the outer flux return
slides longitudinally. Portions of the poles are raised to come into
contact with the flux return. This allows for flux to be shunted from
the gap to the flux return. The range of adjustment is 13% the center
stability is less than 20 micrometers.

A second type of permanent magnet quadrupole using counter rotating
magnets. Two quadrupoles rotate in opposite direction thereby reducing
the integrated gradient. The total range of adjustment is 20% and the
center stability is 1 micrometer.

VII Conclusions

This paper reports on two styles of permanent magnet adjustable
quadrupoles for the NLC. Of the two types the wedge tuner is closest to
meeting all the requirements for NLC. The strength of the gradient and
higher harmonics are within specifications. Further work on balancing
the strength of the tuning rods is required to meet the specification of
a center shift of 1 micrometer. The effects of radiation exposure to the
particular material used in the magnets needs to be understood. With the
proper selection of material and shielding permanent magnet quadrupoles
should be viable for the life of the NLC.

\[1\] Next Linear Collider, Tor. O. Raubenheimer "Overview of the X Band
R&D Program", and "Progress in the Next Linear Collider Design",
SLAC-PUB-8672, October 2000

\[2\] Stephen D. Holmes, "Status of the Fermilab Main Injector and
Recycler", PAC1997 Conf 97-47

\[3\] MAGNEQUENCH 405 Elm Street Valparaiso IN 46383

\[4\] Dexter Magnetic 1050 Morse Ave. Elk Grove Village IL 60007

\[5\][http://www-project.slac.stanford.edu/lc/local/notes/dr/
Wiggler/wiggler_rad.html](http://www-project.slac.stanford.edu/lc/local/notes/dr/Wiggler/wiggler_rad.html)

\[6\] H.B. Luna Nuclear Instruments and Methods in Physics Research A285
(1989) 349

\[7\] O-P Kähkönen J. Phys. Condensed Matter 4, 1007 (1992)

\[8\] Cherrill Spencer MOPO1A1-14 this confernece

\[9\] V Kashikin MOPO1A1-06 this conference