Abstract

Fermilab has nearly completed an upgrade to its accelerator complex
which is called the Fermilab Main Injector (FMI). In addition to the FMI
ring itself, which is built of standard electromagnets, there are
additional components. Two of these components, a beamline used for
transporting 8 GeV protons from the existing Booster to the new FMI
ring, and a new storage ring for antiprotons, are made using permanent
magnets. The storage ring has been named the Recycler because its
function is to store leftover p-bars from the previous Tevatron Collider
cycle after they have been decelerated to 8 GeV. Both the Recycler and
the 8 GeV transfer line use magnets of similar technology. The magnetic
material is strontium ferrite, chosen for reasons of economy and high
H~c~. The temperature dependence of the ferrite is compensated by a
Ni(30%)Fe(70%) alloy operating near its Curie temperature. Field quality
is provided by steel pole pieces and custom shims. The Recycler Ring
requires about 360 gradient magnets, 110 quadrupole magnets, and small
numbers of Lambertson and special magnets. Nearly all of the magnets
have been built. We present details of magnet design, manufacturing, and
testing.

1\. Permanent Magnet Development

Fermilab carried out a program of research into the development of
"hybrid" permanent magnets. The hybrid design uses permanent magnet
material to drive the flux, and steel pole pieces are used to determine
the field quality. Among the choices for magnetic material, strontium
ferrite (Ceramic 8) was chosen because of low cost, stability over time
and stability against thermal and radiation effects \[[^2]\]. The
material is readily available from vendors supplying the automotive and
other industries.

*1.1. Ferrite Stability*

One concern was that magnets built using ferrite should have stable
magnetization over the lifetime of the machine (10-30 yr). To test this,
a set of 10 test magnets were built and monitored over an extended
period. Results were consistent with a model showing that the
magnetization decays logarithmically with time. A typical test magnet
had a decay constant of --(1.95±0.13) x 10^-4^ per log cycle, where the
age was measured in days \[[^3]\]. Data on a more recently built
Recycler gradient magnet show a decay constant of --(3.7±0.9) x 10^-4^.
This would correspond to a first year loss of about 0.1%, and a total of
0.2% loss over a 10 year lifetime, which is within our ability to tune
the machine energy by moving the gradient magnets \[[^4]\].

Another concern was irreversible damage due to thermal excursions.
Positive temperature excursions to ≥40ºC are observed to be reversible
\[Error: Reference source not found\], while negative excursions will
cause some magnetization loss, at least initially. Cooling a ferrite
magnet to 0ºC typically causes a one-time loss of about 0.1%, while
subsequent cooling cycles have no effect. To protect against accidental
demagnetization in the Fermilab environment, all magnets are cooled to
0ºC in a custom refrigerator prior to final testing.

*1.2. Temperature Compensation*

A property of ferrite that must be taken into account is that its
magnetization has a temperature dependence, dB~r~/dT = -0.2 %/ºC.
Temperature control of each magnet in the Recycler would be impractical;
however, an alternative approach was used. This technique \[[^5]\] uses
a 30%Ni-70%Fe alloy interspersed among the ferrite bricks as a flux
shunt. This alloy has a low Curie temperature (\~55 ºC) and its
permeability is a nearly linear decreasing temperature dependence. By
adjusting the ratio of compensator alloy to ferrite, a temperature
independent field in the magnet aperture is achieved.

2\. Magnets for the 8 GeV Transfer Line

A part of the overall Main Injector project was a new beamline to
transport 8 GeV protons from the existing Booster to the new Main
Injector. We chose to make this transfer line out of permanent magnets
in order to gain experience in using permanent magnet technology with
the eventual goal of applying this experience to the Recycler Ring
\[[^6]\]. Field quality requirements were less severe, and this turned
out to be a useful and significant step up the permanent magnet learning
curve. Three major types of magnets were required: a) dipoles of length
2.46 m with integrated fields of 0.57 T-m (45 needed); b) combined
function (gradient) magnets with the same integrated field as the
dipoles, but length 4.0 m, and with an integrated gradient of 1.85 T (65
needed); and c) pure quadrupoles, 0.5 m long, with gradient 1.48 T (9
needed). Details of the design and performance of these magnets have
been presented elsewhere \[[^7], [^8], [^9]\].

For both the gradient and dipole magnets, bricks were stacked behind the
pole pieces on the top and bottom, and in order to achieve a reasonably
high field in a small volume, bricks were also stacked along the sides.
The dipoles, which used 2 layers of bricks on the top, bottom, and
sides, attained fields of 0.23 T. The field quality was, however,
sensitive to the location of the side bricks, which were not completely
hidden behind the poles. We therefore chose not to use side bricks in
the Recycler magnet design.

Commissioning of the 8 GeV line occurred in 1997, and beam transmission
is currently \> 99% \[Error: Reference source not found\]. No
realignment of magnets has been necessary, and magnet stability and
reliability has been excellent.

3\. Recycler Magnets

In Table I are listed the types of permanent magnets that are needed,
along with the number required in the ring itself, in associated
beamlines, and spares. Most of these magnets are now built and are in
the process of installation. The large quadrupoles and the mirror
magnets are the last magnets to be built for this phase of the project
and are being constructed now. Small quadrupoles to be mounted on
rotating stands for use in a phase trombone for tune adjustment are to
be built later.

  ------------------- --------- ------------- ------------ -------------------
  *magnet*            *\# in    *\# in        *\# spares*  *status\
                      ring*     beam-lines*                *

  *gradients*                                              

  RGF                 108       2             3            complete

  RGD                 106       3             2            complete

  SGF                 64        7             4            complete

  SGD                 64        8             1            complete

  *quadrupoles*                                            

  50.8 cm\            90        9             0            complete
  (initial phase)                                          

  101.6 cm            10        0             2            in assembly

  50.8 cm\            32        0             0            to do later
  (upgrade)                                                

  *other:*                                                 

  mirror magnets      2         6             4            in assembly

  Lambertsons         0         5             0            complete
  ------------------- --------- ------------- ------------ -------------------

Table I. List of permanent magnets needed for Recycler.

*3.1 Gradients*

Unlike the 8 GeV line, which only required one style of gradient magnet,
4 distinct styles were needed for the Recycler. Two of them (RGF, RGD)
are used in the normal arc cells; the pole tips, besides being shaped to
provide the gradient, also provide sextupole for chromaticity
correction. The other two styles (SGF, SGD) are used in the dispersion
suppression cells. They are 2/3 the length of the arc gradients, have
stronger gradients, and no sextupole. Table II provides a summary of the
specifications.

  ----------------- ---------- ------------- --------------- -------------
  *magnet*          *pole      *BL (T-m)*    *gradient, b2   *sextupole,
                    length                   (units @ 2.54   b3 (units)*
                    (m)*                     cm)*            

  arc focussing     4.4958     0.61824       619.74          8.7
  (RGF)                                                      

  arc defocussing   4.4958     0.61824       -598.08         -15.1
  (RGD)                                                      

  dispersion        3.0988     0.41216       1275.96         0.0
  suppression,                                               
  focussing (SGF)                                            

  dispersion        3.0988     0.41216       -1303.08        0.0
  suppression,                                               
  defocussing (SGD)                                          
  ----------------- ---------- ------------- --------------- -------------

Table II. Recycler Ring gradient magnet specifications.

These magnets employ a hybrid design similar to that used for the 8 GeV
gradients, with some modifications: see Figure 1. Two layers of bricks
were used on top and bottom, and no side bricks. The pole pieces also
differed in the choice of manufacturing technology. In the 8 GeV line,
the poles were form ground, but this was expensive and was not projected
to provide a high enough production rate. For the RGDs and RGFs, the
poles were made by extrusion followed by two cold-draw passes through
precision carbide dies \[Error: Reference source not found\]. We
achieved a high production rate at moderate cost with this technique.
For the dispersion suppressor gradients, we chose to use laminated poles
because of the difficulty of producing a cold-draw die of the required
cross section. The laminated poles required the use of a steel backing
plate to transmit the magnetic flux longitudinally.

Measurements were an integral part of the assembly / trimming process.
Strength was initially measured with a flipcoil. The magnet was then
frozen and measured cold and again after warmup back to room temperature
to get the temperature compensation, which was adjusted as needed. The
longitudinal field distribution was measured by a Hall probe scanner,
from which the bend center was determined. Finally, a rotating Morgan
coil was used for harmonics measurement and trimming.

![](media/image1.wmf){width="2.459722222222222in"
height="3.2354166666666666in"}

Figure 1. Isometric view of a Recycler gradient magnet.

Tolerances for systematic and magnet-to-magnet (random) errors in the
multipoles and strengths were specified in \[[^10]\]. Allowed strength
variation was 5 units systematic and also 5 units random. Each magnet
was trimmed by adding/subtracting whole or fractional bricks until the
strength was within 5 units of nominal. Trimming of the multipoles to
decapole was accomplished by cutting a custom pair of shims that were
attached to the end of the poles. The magnet was measured with a
rotating coil, and the data were used to prescribe a tool path for a
milling machine to cut a shim of the required shape \[[^11]\].

![](media/image4.wmf)

Figure 2. Histogram of measured b4 (normal octupole) before and after
shims were installed to the magnet end.

An example of the correction achieved by shimming is shown in Figure 2,
which histograms the normal octupole (b4) before and after shimming. The
pre-shim standard deviation was σ = 0.46 units, and was narrowed after
shimming to 0.12 units. The mean of the distribution was also decreased,
from 0.28 units to ‑0.05 units afterwards.

Measurement results for RGFs are summarized in Table III. Results for
the other gradient series were similar. Excellent field quality and
temperature compensation were achieved. Measurements of all Recycler
magnets are maintained in spreadsheets accessible over the web
\[[^12]\].

  ---------------- ---------------- ------------------ ------------------
                   **Ideal**        **mean**           **std dev**

  *(dB/B)/dT*      0.0              0.09               0.31

  *∆B/B*           0.0              -0.04              3.89

  *b2*             619.7            619.74             0.62

  *a2*             0.0              0.31               0.78

  *b3*             8.7              8.61               0.27

  *a3*             0.0              -0.04              0.38

  *b4*             0.0              0.09               0.24

  *a4*             0.0              0.14               0.30

  *b5*             0.0              0.02               0.23

  *a5*             0.0              0.07               0.25

  *b6*             0.0              -0.24              0.28

  *a6*             0.0              -0.11              0.20
  ---------------- ---------------- ------------------ ------------------

Table III. Comparison of desired values of temperature compensation,
strength deviation from nominal, and harmonics with measured quantities
for the RGF series.

Gradient production began in November, 1997, and was completed in July,
1998. An average rate of 40 magnets/month (2 per day) was sustained over
the course of production, and a peak of 3.6 magnets/day was achieved.
Figure 3 shows a stack of completed magnets.

![](media/image5.png)Figure 3. A stack of completed gradient magnets in
the staging area awaiting installation in the Recycler.

*3.2 Quadrupoles*

The 8 GeV quadrupole design was sufficiently versatile to be used with
only minor modification for the Recycler. The basic pole subassembly
with flux return frame was used, but in two varieties that differed by
overall length and pole aperture. Within each major variety, differences
among magnet types were achieved by modifying the total amount of brick
and compensator used. Focusing or defocussing is achieved by a rotation
of 90º about the magnet axis. Magnets of a given series are all either
focussing or defocusing, as shown in Table IV. Details of quadrupole
production are given in \[[^13]\].

  ------------ ----------- ------------- -------- ------------- -------------
  series       number      design        F/D      aperture,     pole length\
                           gradient\              pole radius\  (m)
                           (T)                    (mm)          

  *small                                                        
  quads*                                                        

  RQAA         1           0.50895       F        41.73         0.508

  RQAB         1           0.91262       F        41.73         0.508

  RQAC         2           -1.07770      D        41.73         0.508

  RQMD         25          -1.28618      D        41.73         0.508

  RQME         8           -1.11610      D        41.73         0.508

  RQMF         22          1.33453       F        41.73         0.508

  RQSA         2           -0.44421      D        41.73         0.508

  RQSB         2           -0.32594      D        41.73         0.508

  RQSC         2           0.54029       F        41.73         0.508

  RQSD         2           -0.36430      D        41.73         0.508

  RQTD         16          -0.85698      D        41.73         0.508

  RQTF         16          0.84745       F        41.73         0.508

               99                                               

  *big quads:*                                                  

  RQEB         5           1.87589       F        58.42         1.016

  RQEC         5           -2.23971      D        58.42         1.016

  RQED         2           1.69712       F        58.42         1.016

               12                                               

  *upgrade                                                      
  quads                                                         
  (rotatable                                                    
  stands)*                                                      

  RQRA         32          1.41170       F        41.73         0.508
  ------------ ----------- ------------- -------- ------------- -------------

Table IV. Specifications of Recycler quadrupole magnets

Tuning of the magnet strength and harmonics was done using steel rings,
or washers. These washers were mounted on threaded rods located behind
the poles in each of the four corners of the magnet, so that each pole
could have its magnetic potential independently tuned. The magnet was
deliberately built a few percent above nominal strength, because adding
washers could only be used to decrease the strength. Washers could
adjust b3, a3, and a4 in either direction, according to washer
distribution. Harmonics b4 and b6 were adjusted via washers in the pole
piece ends. A summary of magnet measurements after tuning is shown in
Table V.

  --------------- ----------------- ------------ --------------- -------------- --------------
  Small                                                                         
  Quadrupoles:                                                                  
  Field Quality                                                                 
  Results                                                                       

  *component*     *specification*                *measurement*                  

                  *systematic*      *random*     *systematic*                   *random*

  ∆g/g            5.0               8.0          -0.82                          2.54

  b3              0.5               1.5          0.05                           0.62

  a3              \-                1.5          -0.01                          0.42

  b4              0.5               1.5          -0.02                          0.46

  a4              \-                1.5          -0.01                          0.07

  b5              0.5               1.5          -0.01                          0.43

  a5              \-                1.5          0.10                           0.49

  b6              0.5               1.5          -0.33                          0.31

  a6              \-                1.5          0.02                           0.21

  temp.                                          0.5                            0.01
  compensation                                                                  
  --------------- ----------------- ------------ --------------- -------------- --------------

Table V. Measurement summary for the Recycler small quadrupoles. All
data are expressed in units (1e-4) at 2.54 cm radius.

*3.3 Lambertsons and Mirror Magnets*

A Lambertson magnet is needed at each end of the two transfer lines
leading between the Recycler and Main Injector, and another one is
needed at the entrance of the abort line. The magnet consists of a
bending region surrounded by bricks on 3 sides; mounted on the fourth
side is a solid steel baseplate with a bored hole for the field free
region \[[^14]\]. The field from the bricks can either point inward or
outward, depending on whether upward or downward vertical bending is
needed; also, the mounting of the bend region assembly on the baseplate
can be done in two ways, resulting in 4 total Lambertson magnet
configurations.

Near the intersection of the beamlines and the ring, space constraints
prevent the use of standard gradient magnets where a pair are needed. A
mirror magnet places all of the ferrite bricks on one side of the
aperture, with a thin mirror plate on the other side to complete the
flux path \[[^15]\]. A diagram of a pair of mirror magnets is shown in
Figure 4. Three styles of mirror magnet are needed:\
a) MGD, which has the same magnetic field as the RGD, b) MGS, a magnetic
clone of the SGF, and c) MDA, which is a pure dipole.

![](media/image6.wmf){width="3.290277777777778in"
height="3.290277777777778in"}

Figure 4. A pair of MGD Mirror magnets configured so the beam in each
pipe sees the same bend & focussing field, while allowing a
center-to-center beam spacing as small as 8.9 cm. The polarization of
the permanent magnet ferrite is opposite for the two magnets.

4\. Summary

All magnets for the Recycler Ring (including the RQRA quadrupoles)
should be complete and installed by the end of November, 1998. Looking
beyond the Recycler, we will build a set of quadrupoles (essentially
RQTFs) for Mini-BooNE, a neutrino oscillation experiment at Fermilab.
Summing up our experience over the last few years, we have shown that
permanent magnets are a useful, economical option for low-field, fixed
beam energy applications.

References

[^1]: . Operated by Universities Research Association, Inc., under
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    Energy.

[^2]: . G.P. Jackson, ed., Fermilab Recycler Ring Technical Design
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[^3]: . H.D. Glass et al., "Stability Tests of Permanent Magnets Built
    With Strontium Ferrite," in Proceedings of the 1997 Particle
    Accelerator Conference (PAC97), Vancouver, Canada, 1997.

[^4]: . G.W. Foster, "Experience With Permanent Magnets in the Fermilab
    8 GeV Line and Recycler Ring," Proceedings of the 6^th^ European
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[^5]: . K. Bertsche et al., "Temperature Considerations in the Design of
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[^6]: . S.D. Holmes, "Status of the Fermilab Main Injector and
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[^7]: . H.D. Glass et al., "Permanent Gradient Magnets for the 8 GeV
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[^8]: . H.D. Glass et al., "Permanent Dipole Magnets for the 8 GeV
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    1997.

[^9]: . S.M. Pruss et al., "Hybrid Permanent Quadrupoles for the 8 GeV
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[^10]: . S.D. Holmes et al., "Magnetic Field Quality Specification for
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[^11]: . B.C. Brown et al., "Hybrid Permanent Magnet Gradient Dipoles
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    20-24, 1997.

[^12]: . URL address: http://volk-power-pc.fnal.gov/

[^13]: . B.C. Brown et al., "Hybrid Permanent Magnet Quadrupoles for the
    Recycler Ring at Fermilab," Proceedings of the 15^th^ International
    Conference on Magnet Technology, Beijing, China, Oct. 20-24, 1997.

[^14]: . M.P. May et al., "The Design and Construction of the Permanent
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    PAC'97, Vancouver, Canada, 1997.

[^15]: . G.W. Foster, "Mirror Magnet Designs for the Recycler Ring,"
    Fermilab note MI-0212, Aug 1998.