**Summary of Radiation Damage Studies on Rare Earth Permanent Magnets**

J T Volk\* Fermilab

**Abstract**

With the proposed use of permanent magnets for both the NLC and VLHC the
issue flux loss due to radiation damage needs to be fully understood.
There exist many papers on the subject. There are many difficulties in
drawing conclusions from all of these data. First there is the
difference methods of dosimetry, second different types of magnets and
magnetic arrangements, and third different manufactures of magnet
material. This paper provides a summary of the existing literature on
the subject.

**Introduction**

Rare Earth Permanent Magnets (REPM) have been widely used in
accelerators since the early 1980s. Wigglers, Undulators and Quadrupoles
have been used in light source and damping rings. Currently there are
proposals for permanent magnet quadrupoles for use in the NLC^1^ and the
VLHC^2^. The advantages of permanent magnets are zero operating costs
and reduce capital costs by eliminating power supplies can cables. The
main disadvantage is the loss of strength of the magnets due to
radiation damage.

**Literature**

There have been many studies and papers published regarding radiation
damage. Roger Carr and Andy Ringwall^3^ of SLAC have collected a list of
such papers. These can be found at:
<http://www-project.slac.stanford.edu/lc/local/notes/dr/Wiggler/wiggler_rad.html>

These papers are concerned with radiation damage in Rare Earth Permanent
(REP) magnets, both Samarium Cobalt and Neodymium Boron Iron. There is a
wide Varity of sources from the US, Europe and Japan. Most of these
studies were instigated by accidental exposure of magnets to beam. Some
of the papers are systematic studies of radiation exposure to magnetic
material. Some report on dosimetry and other on exposures to magnets in
accelerators.

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\*Volk@fnal.gov

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

**Magnet Manufacturing**

All REPM magnets are made by first milling the material to a very fine
powered. The particle size is on the order of microns. The proper
proportions of material are mixed and water is added to make slurry. The
slurry is then pressed either in a die or isostatically. During the
pressing process a magnetic field is applied either parallel or
perpendicular to the pressing direction. The field aligns the grains of
material and defines the easy axis. The magnetic material is then
sintered in a kiln and ground to the proper dimensions. The material and
the processing steps all have an effect of the properties of the final
magnets.

**Measurements**

Brown^4^ et al from Los Alamos and Coninckx^5^ et al at CERN did some
measurements of Samarium Cobalt magnets in the early 1980\'s. One of the
first observations was that all magnet material was not the same.
Different manufactures showed different rates of demagnetization.
Coninckx\'s group was able to reverse the magnetization on a sample from
Vacomax after the exposure of over 10^10^ rads. Figure 1 shows
demagnetization for various samples of Sm. Cobalt as
![](media/image1.wmf)Figure 1: Demagnetization for various samples of Sm
Cobalt.

reported by Coninckx. Similar results using different manufactures were
reported by Brown. Coninckx used secondary spray from a target at the
SPS while Brown used neutrons with energy of 0.1 to 30 MeV. The change
in field observed by Brown was lower than the change observed by
Coninckx. It was suggested by Coninckx that there were changes in the
cristallographic structure of the material.

Brown also measured the change in magnetization as a function of the
length versus diameter (L/D) of different samples. He made the
observation that small L/D had a higher flux loss. As stated in the
paper \"it should be realized that the samples with the smallest L/D
ratio have the highest demagnetizing field and ... the highest decay
rate\"

Brown also observed the replacing Neodymium (Nd A=60) with Dysprosium
(Dy A=66) increases coercivity and resistance to radiation induced
demagnetization.

Luna^6^ et al. Irradiated both Samarium Cobalt and Neodymiun Iron magnet
with ^60^Co and 85 MeV electrons. For 1.4 10^9^ rads of ^60^Co they
observed no loss in field for either Samrium or Neodymium. For direct
electron radiation they did observe a 1.5% decrease in remanence for
Neodymium. In their paper they published a table of known results for
different experiments.

![](media/image1.wmf)Table 1 Summary of Radiation Damge from Luna et al.

**Theory**

Once permanent magnets are removed from the magnetizing field free poles
are established and a field potential -H~d~ exists between the free
poles^7^. The

Figure 2: Fields inside permanent magnet material

magnitude of H~d~ is dependnet on the geometry of the magnet and B = J-
H~d.~ Hence there is always a demagnetizing field present in permanent
magnets.

O-P Kähkönen^11^ et al. theorized that knock on particles would raise
the temperature in a local area of the lattice above the Curie point and
if there was a sufficient demagnetizing field present then the spins can
flip and a new domain can be created with a field direction opposite to
the rest of the magnet. This can have a cascading effect since there is
now a larger demagnetizing frield present. Starting from Laplace\'s
equation for heat flow and using a Greens function they give the
temperature required to heat a sphere of radius R as

T~1~ = T~o~ + (T~c~-T~o~)(2πR^2^/3d^2^e^-1^)^3/2^ (1)

Where d^3^ is the volume of one atom.

The energy of the knock on atom is then

E = 3/2 k~B~(T~1~-T~o~) (2)

If a sufficient number of domains are flipped then there will be a
measureable loss in magnetic field. The parameterization they give is:

ΔM/M = 2 V~grain~/V~sample~ P Np (3)

Where P = n σ L (L the sample thicknes) and N~p~ is the number of
incident particles. The amount of demagnetization depends on the grain
size of the material and how the material was manufactured. This
explains the differences between REPM made by different manufactures. If
the grain size is different due to the manufacturing process then the
changes in the remanence will vary.

**Observations**

Finer milling of the material would produce a smaller grain size. This
explains the different demagnetization curves for different
manufactures. Magnetic material in the presence of an
external-demagnetizing field would experience more radiation damage than
the same material with no demagnetizing field. A defect in most studies
is the irradiation of free bricks instead of magnets in a circuit. Free
bricks will be more susceptible to demagnetizing fields than bricks in a
magnetic circuit. While it is not good practice, it is possible to
design a magnet with internal demagnetizing fields. In magnet designs
keeping the load line far away from the knee of the demagnetization
curve is an important consideration. Magnet material with a large
coercivity is desirable for use in permanent magnets. This will help to
keep demagnetizing fields as low as possible.

**Tests**

To test Kähkönen theory two magnets with a known load line one with high
coercivity material and another with lower coercivity material should be
built and irradiated until a noticeable change in the field is observed.
The lower coercivity magnet should show loss in field with less
radiation than the higher coercivity magnet. The magnets should then be
disassembled and the magnetic material re magnetized. The field after
re-magnetization should be the same as the original field. Similar
magnets should also be built and not irradiated to measure the effects
of aging in the magnetic system. The manufacture of the magnetic
material should be carefully controlled at all steps to ensure uniform
and small grain size.

**Conclusion**

The model of Kähkönen with a dependence of demagnetization on grain size
can explain the different rates of demagnetization as seen by many
experiments. The idea of local heating exceding the Curie temperature
and allowing for flipping of the magnetic domains also explains why Dy
is better than Nd for radiation hardness. A heaveir element will resist
flipping direction. For any radiation damage study to be meaninful it
should be done on complete magnet with a known load line. Testing of
indivudual bricks will not neccessaryly indicate how magnet will preform
in a given situation. In addition the temperature rise caused by
radiation should be minimized so that heating of the material does not
fake a radiation induced signal.

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

2 Very Large Hadron Collider design guide <http://www.vlhc.org/>

3 Carr and Ringwall
<http://www-project.slac.stanford.edu/lc/local/notes/dr/Wiggler/wiggler_rad.html>

4 R. D. Brown and J. R. Cost IEEE transactions on Magnetics Vol. 25. No.
4 July 1989 3117

5 F Coninckx et al CERN/SPS 83-1 TIS-RP/IR/83-07

6 H.B. Luna Nuclear Instruments and Methods in Physics research A285
(1989) 349

7 From R. J. Parker PMG-88 Magnetic Materials Producers Association
<http://www.mmpa.org/>

8 E.W. Blackmore IEEE Trans. Nucl. Sci NS-32 (1985)

9 J. R. Cost Los Alamos National Lab Report LA-UR 87-1455 (1987)

10 R. D. Brown Los Alamos National Lab Report, LA-9437-MS (1982)

11 O-P Kähkönen J. Phys. Condensed Matter 4, 1007 (1992)