The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October2001

CHALLENGE TO A HIGH FIELD PERMANENT MAGNET OF VARIABLE
FIELD STRENGTH
M.Kumada, T.Fujisawa, Y.Hirao, NIRS, Chiba, JapanY.lwashita, NSRF, ICR, Kyoto, Japan
M.Endo, M.Aoki, T.Kohda, Sumitomo Special Metal Co.,Ltd., Osaka, Japan
I.Bolshakova, R.Holyaka, MSL, Lviv, Ukraine

Abstract
Permanent magnet is in general believed to beapplicable to only weak magnet compared toelectromagnet and superconducting magnet. It is possible,
however to make a magnet much higher than the residual
field of the material. We have demonstrated
experimentally that the permanent dipole magnet
exceeding more than by factor 3 is possible .. Challenge is
to conceive such magnet for an accelerator application
where variable field is often requested. We propose themethods by a mechanical rotation or with a combinationof electro-magnet.

1 INTRODUCTION
Permanent magnet (PM) has been applied in anaccelerator field mostly as undulator/wiggler insynchrotron radiation storage ring. There is a myth aboutPM. They are: The field strength is weak compared toelectro-magnet and superconducting magnet. Working
point of material in most of the cases is at half of aresidual field Br. PM is only good at small aperturemagnet like undulator/wiggler. PM is unstable asmagnetization strength depends upon temperature level ofa few parts in thousand. Variation of strength ofmagnetization is a few percent and a high homogeneity
required from accelerator performance is difficult.
Recently at Fermilab, large quantity of ferrite magnet
was applied to an 8 GeV antiproton storage ring [1]. They
made a remarkable progress in PM technology where they
have almost solved temperature stability problem andhomogeneity problem. The field strength of the Recycler
PM is only 1.5 kG or so, which is about 1/3 of a ferrite
material's Br. Application to PM solenoid is also very
attractive [2]. The strong PM magnet is challenged for
Wiggler magnet. 3 Tesla Permanent magnets is so far thestrongest [3]. The structure of this PM is the one proposed
by K.Halbach where a combination of iron and PM
magnet is placed periodically in a linear direction. Thisconfiguration can be extended to a circular type dipole
magnet. We found out that when the iron pole is driven
into a saturated level, the field strength inside the dipole
gap is further enhanced [4].
It was found that lowering a temperature of the magnet
has a great advantage in increasing the magnetization
strength. DC PM can be used for cyclotron or FFAG
(Fixed Field Alternating Gradient) accelerator for

accelerating charged particle. There is an additional
advantage if a PM magnet can be converted to variable
field magnet. K.Halbach gave an idea of varying fieldmagnet. It is a layered ring magnet where outer ringrotates around the centre of the ring. To avoid theinclination of a magnetic median plane, iron pole is used.
One of the authors made a highest gradient (250T/m)
Quadrupole in 1985[5]. Another method of varying field
is to combine two PM located at axial positions, which
was patented by R.F.Holsinger. There is a commerciallyavailable varying field dipole magnet on the market called
MULTIMAG magnet (Magnetic Solutions Ltd). As themechanism of it is not clearly described in a literature, wehave developed our own way of two-layer ring magnet.
Beside mechanical methods, we propose that acombination of PM magnet with electro-magnet or
superconducting magnet is promising [9] when field levelis around 3 Tesla. An example of this method is describedin the present paper.

2 HIGH FIELD PERMANENT MAGNET
In most permanent magnet combined with iron pole andyoke, the field strength is several kG even when one uses
strong NEOMAX whose B, is 1.2 Tesla level. This isbecause the magnetic field strength Bg in a dipole gap is,
Bg=~"H "'"~Bd +I m ,....0 c d +I m r(1)

where He is coercive field strength of the PM material, Bris its residual field strength, lm is its length and d is thegap length of the magnet. In most of the magnetic circuit,iron pole and iron yoke is designed so that they are not ata saturated level. Relative permeability of the iron is highand iron can be neglected to the contribution of the gap
field strength. The maximum field strength is half of Br in
this conventional configuration. It is common that thefield strength of the gap does not exceed B, even at thelimit of large lmld ratio. For a small lmfd ratio, fieldstrength of the gap is proportional to it.
K.Halbach invented an ingenious magnetic circuit [7].
In his configuration, pieces of REC (Rare Earth Cobalt)
magnet material are placed on a ring where a direction ofmagnetization is rotated locally in a way so that resultant
field forms a specified multipole field. See Figure 1. Iron
pole or yoke are not used. For a dipole, he derived asimple formula for a gap field strength Bg,- 92-The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

r2(2)Bg =Br ln(-)
rl

where r1 and r2 is an inner and outer radius of the magnet.
This equation is quite challenging, as there is no
theoretical upper limit. In fact there is a limit. To realize ahigh field as much as possible we started from thisHalbach magnetic circuit. Permeability of the REC orNEOMAX or ferrite material is about 1.05, close to unity.
Superposition holds. The field source located at long
distance can contribute to the field at the centre
accumulatively. Efficiency is poor from outer location.
To improve the efficiency, we introduced an iron pole tothe Halbach REC configuration as in Figure 5. REC isreplaced to NEOMAX. The field strength of the Extended
Halbach magnet can be written as,
I
Brim +~Bso
Bg~------~~----(3)s1 sd +_,_ __!_+I __!_~·s,meither by a rotation of magnetization direction or with acombination of conventional electro-magnet or
superconducting magnet [9]. In NIRS, a model magnet ofmoderate field strength of I T varying field magnet wasdesigned and constructed and magnetic field is measured.
In an accelerator magnet, a direction of magnetic plane in
the gap has to be kept constant although direction of themagnetization varies in magnet material. In previous caseof varying field gradient of 250 Tim Quadrupole magnet[5], this was done by a single layer rotation with iron pole.
This time, the dipole field was varied with a rotation of
two layers as shown in Figure 1. The outside view of themodel magnet is in Figure 2. A mechanism to rotate eachlayer independently can be seen in the Figure.

smParameter Sm, Sg, S; respectively is cross sections ofpermanent magnet, gap, and iron. Bso is a saturated
induction of the iron pole and ~ • is a relative
permeability of the iron. Eq. (3) indicates the saturated
iron pole is effective to increase the field strength. A
saturated permeability of the iron approaches unity. Notein general the saturated induction of the iron Bso is greaterthan the residual field of the strongest permanent magnet
material NEOMAX[4,6]!
The iron pole can be designed so that some part of it is
not saturated and the other part is saturated. Thus, it isalso possible to use the iron pole as a flux compressor
where iron is not fully saturated. This effect is expressed
as a ratio of cross section of the gap to PM and iron whichis shown in the second and third term in the denominator.
At higher field level, we should take into account ademagnetisation effect of the PM material. This was notconsidered either in eq.(2) or eq.(3). Under a strong
external magnetic field the magnetization strength isreduced. In either Halbach or Extended Halbach type ofhigh field configuration, the outer part of the magnet
produces strong magnetic field at some location of theinner part of the magnet. This problem could be copedwith by selecting the material of high coercively. In a 4
Tesla model magnet, we have used two different kinds ofmaterials, namely material ofhigh Brand high He [4,6]3 VARIABLE FIELD MAGNET BY
MECHANICAL ROTATON
If a field strength of PM magnet is variable, its
application can be extended much more widespread.
Furthermore, if its field strength is realized in a Testa
region, it could be used in a field where superconductor
has been applied. PM of several Tesla is equivalent ofroom temperature superconducting magnet which people
have long been dreamed. Variable field could be possible

Figure 1. Cross-section of two layer variable fieldpermanent magnet. Red arrows show a direction ofmagnetization.

Figure 2. Outside views of two layers variable filed
permanent magnet

4 VARIABLE FIELD MAGNET WITH
ELECTRO-MAGNET
Field level of 3 Testa is difficult by a conventionat
copper type magnet. 1.8 Tesla alternating field is not easy
but possible while keeping field homogeneity within an
acceptable tolerance level. In PM 1.5 Tesla is reasonable
field strength and a required magnet size is moderate if
one uses NEOMAX. Operation in liquid nitrogen makes
it more feasible.
The first proposal is a longitudinally combined type andthe second one is a transversely combined type magnet- 93-

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

system[8,9]. An example of longitudinal hybrid magnet isshown in Figure 3. In Figure 4, cross section of
permanent magnet is superposed to copper coilelectromagnet. Figure 5 shows an example of Extended
Halbach 3 Tesla magnet with the saturated iron pole. Notethat flux is compressed and concentrated at the saturated
pole tip as expected. The effective field depend upon theratio of both magnets.

Tesla electro-magnet, the field could be altered from zero
to 3 Tesla. Choice of 1.5 Tesla in each magnet is adequate
as a saturation of the electro-magnet is moderate anddemagnetisation effect of the permanent magnet material
is in a tolerable range.
For an application to a synchrotron magnet of atransverse hybrid magnet, there is a constraint that field
gradient of each magnet has to satisfy the following
equation,dBDe
BDc =__sk_BAc
dBAc

I•(4)

dx
where we have assumed that the alternating field isexpressed as B = B DC - B AC cos( ca) .
The necessary condition of eq. (4) is to keep a betatrontune constant as possible by keeping the effective field
gradient constant with varying field strength. The timedependence is not necessary to be sinusoidal.

r-2m---...;

Figure 3. Longitudinal variable field hybrid magnet.

~=======8~00======~TrI~I

800~:.;;.;....::___.___.____jl
Figure 4. Cross-section oflongitudinal variable fieldhybrid magnet.

Figure 6. Cross-section of transverse varying field dipolemagnet. PM is immersed in a gap of copper electromagnet.

5 ACKNOWLEDGEMENT
We would like to thank Drs.Soga, Yamada, Takada,Noda, Kanaawa and members of accelerator physics andengineering division in NIRS for encouragement of thiswork.

6 REFERENCES

FigureS. 'l4 cut view ofExtended Halbach PM.
The I.5 Tesla permanent magnet is moderate in size. Torealize it, we need the ratio of outer and inner radius to beabout 3.3, as a logarithm of 3.3 is 1.2 and one gets 1.6
Tesla for Br=l.3 Tesla. For 40 mm bore diameter, therequired outer diameter of the magnet is 132 mm. A gap
size of 132 mm of a copper electro magnet is not a small
magnet but within a tolerable range. If we provide a I.5[I]G.Jackson, FERMILAB-TM-199I[2]Y.Iwashita, PAC93,Washington,D.C.,l993. p.3154.
[3]N.Nakamura et a! report, ISSN 0082-4798,Ser.A
No.3378, April 1998, University of Tokyo[4] M.Kumada eta!., patent pending.
[5] M.Kumada et.al, Proc.91 conf .on Magnet technology,Zurich, p.l42 (1985)[6] M.Kumada et.al, PACOI ,Chicago,2001[7] K.Halbach, IEEE Tran.NS-26 (1979),3882,K.Halbach,NIM, 169(1980) 1,K.Halbach,NIM, 187(1981 ),I09, K.Halbach, NIM,l98(I982)213.
[8]M.Kumada,"Magnetin
Magnetconcept"snowmas200 I workshop, Aspen Colorado,200 I[9] M.Kumada and Y.Iwashita, patent pending.

-94-