The 9th Symposirun on Accelerator &ience and Technology, Tsukuba, Japan 1993

Compact Strong Permanent Magnet Symmetric Lens
Yoshihisa !washita
Accelerator Laboratory, Nuclear Science Research Facility
Institute for Chemical Research, Kyoto University
Gokanosho Uji, Kyoto 611, JAPAN

Abstract
A compact strong Permanent Magnet Symmetric (PMS)lens which produces the axial magnetic field is studied. The
proposed lens has no iron pole piece except for the return
poles on both ends which are required for magnetic fieldshielding purpose in some applications. It can produce themagnetic field on the axis more than the remanent field of themagnet material by the perpendicular field superimposition.

I. INTRODUCTION
A 7-MeV proton linac was constructed at Institute for
Chemical Research, Kyoto University.[l,2] The linac isconsisting of a 2-MeV RFQ linac and a 7-MeV Alvarez(DTL). The operating frequency is 433.3 MHz and thestructure dimension is compact. In order to match the RFQ
acceptance, the input beam has to be focused strongly to theRFQ. Unfortunately, the entrance side of the RFQ is occupiedby the vacuum port and the final focus element has to beinstalled into the hole in the end plate of the RFQ. The holehas diameter of 40 mm and the depth of 60 mm. A compact
focusing device which can fit in this size had to be devised.
For future study of the simultaneous acceleration of both
positive and negative ions, a magnetic lens which produces
the magnetic field of axial symmetry was picked up. The field
can be produced by a "solenoid". Applications of anisotropic
magnet have been studied for charged particle beam
manipulations [3,4,5]. With a careful study of the radiallyoriented anisotropic magnets, it was found that a compact
strong Permanent Magnet Symmetric (PMS) lens can be
fabricated in the limited size by application of theperpendicular field superimposition.

materials, no demagnetization isexpected. Although it is only alogarithmic increase, the fieldstrength seems to have nolimitation in this respect.
The field concentration byperpendicular filed superimposition is verified by a rough experiment. Eight pieces of 10 x 10 x
30 mm magnets made of
NEOMAX 35H, which has Br of
1.1 [T], are placed as shown inFigure 1. One block is consisted Figure 1. Geometry forof four pieces which attract each field concentration test.
other. Two of the blocks are
fixed on jaws of an iron vice, and put close by pressing withthe vice to the gap of about 2 mm. The maximum field ismeasured by an axial Hall probe as 1.6 [T] which is more thanthe Br. The Hall probe has the thickness of 2 mm.
Neglecting the second term of the equation (1) which
express the contributions from the outer surfaces andsubstituting the values for land b, we get Bmax=l.6 [T].
Because the jaws of vice is made of iron, it acts like returnyoke and reduces the effects of the outer surfaces. The
magnetic field produced by the magnets with the iron returnyoke is also calculated by P ANDIRA [6] as shown in Figure
2. It also shows the value 1.6[T] as a maximum.
According to the result of above experiment, the perpendicular superimposition can hold good for producing at least
1.5 Br. Further study is needed to clarify the demagnetization
process in the perpendicular direction and a limitation.

II. PERPENDICULAR FIELD
SUPERIMPOSITION
Let us consider the anisotropic magnet configuration in thetwo dimensional space as shown in Figure 1. The magnetic
field has the direction of Z on the Z axis, and the maximum atthe center. The analytical expression for the maximum field is
calculated as follows;
Bmax =s;{lo{1 +~:)- log(1+ ::)} .

(1)

It can be shown that the value is not finite when lib ~ ookeeping l!r finite. Because the produced field is perpendicular
to the easy axis of the magnet material, the operating point in
the B-H curve will stay in the upper half. If the magnet
material has no knee in the second quadrant of the B-H curve,
which is easy requirement for almost all rare earth magnet-267-Figure.2 Flux plot calculated by PANDIRA

III. PROPERTY OF MAGNETIC FIELD LENS

V.PMS LENS

The focal strength 1/ffor charged particles with the energyof eV in a magnetic field lens of axial symmetry is given by

For fabrication of the real magnet, several constraints had
to be considered. The ring should be azimuthally segmented torealize the radially oriented anisotropic property using theavailable material. The return iron yoke has to be locatedaround the magnet to reduce the leakage field on the axis
particularly to the RFQ side. It is achieved by the iron case ofthe magnet. The corners of the magnets near the axis arerounded so that the Bz has less r dependence and the lens hasless aberration. The bore hole of the iron case at entrance side
is made large to accept a beam with large diameter. Themagnet material is NEOMAX 40 which has the remanent field
Br of 1.29 T nominal. The final dimensions are shown in
Table 1. Photo 1 shows the assembled PMS lens.

1e J- B 2 dz [m],-=--.

fBmoV

(2)

-where e and mo are the charge and the mass of the particles atrest respectively.[7] It should be noted that the focal strengthis proportional to B 2 and 20% increase in the focal strength
will be obtained by 10% increase of the remanent field which
will be achieved by material developments. The drawback isthat the temperature coefficient of the focal strength is twiceas large as that of the remanent field. On the other hand, thisproperty can also be used as a focal strength adjustment bymeans of the temperature control. The typical temperature
coefficient of the Nd-B-Fe magnet is 0.1% I ·c.

IV. MAGNETIC FIELD PRODUCED BY A
RADIALLY MAGNETIZED MAGNET
Let us consider a radially oriented permanent magnet ringas shown in Figure 3.

bnumber of ring2
17
outer radius of a rif!&_ ml!&_net
leng_th of a ring magnet
25
16
number of segments in a rin_g_bore radius
58
comer radius of a s~mentouter radius of iron case20
length of iron case60
corner radius and thickness of lids3bore radius of entrance lid
7.5Table 1. Model PMS d1mensmnsmmmmmmmmmmmmmmmm

Figure 3. Radially oriented permanent magnet ring
Integrating over the magnetic dipole, the magnetic field on
the axis of the magnet is given as
B(z) = Br

2{.!.r __!._b _ _!._+..!._+log(1 + r )(1 + brb(1 + b )(1 +110001)}0r1) 'r0 =F0J,bo=FGJ.
Figure 4 PANDIRA result
(3)
0.75

The magnetic field has two maximums at z=O and -1. where
the end of the magnet is located. The maximum value is

B(O)=Br{
2r~r 2 +1 2_2 2b+log
222~b +11+~1+1 /r 21+~1+1 /b }

{4 )

0.5
0.5

0.25~

•gJ

0Again, it can be shown that the logarithm term is not finite if
keeping 1/r finite, and lib ~ oo. In the real applications, twokinds of rings with different magnetization will be placed
alternatively. In the case, the magnetic field should besuperimposed and the maximum field is doubled. The
principle of the perpendicular field superimposition should
work here again. For example, a lens of two rings ( b=5 mm,r=2 em, and 1=2 em x2) has the maximum field of 1.22 Br.

"3n2.

·0.5-268-·0.25.o,5·4·3·2·1023Z[cm]Figure 5 .Magnetic field distribution

45 ·0.75

The field calculated by PANDIRA is shown in Figure 4.
Figure 5 show the magnetic field distribution plots on the axis
both the calculated value by P ANDIRA and the measured
value. The measured peak value is about 10 % smaller thanthe calculated one. The azimuthal segmentation is thought tobe the main reason of the reduction in our model magnet case.

calculated by equation (2). Because the integral over B z on
the axis of PMS lens is zero (Ampere's law), the image does
not rotate. In this calculation, the space charge effect is notincluded yet. The space charge effect will be included infurther study.

VII. ACKNOWLEDGMENT
The author would like to thank R. A. Jameson for theuseful information. The model magnet was fabricated bySumitomo Special Metal Co. LTD.

VIII. REFERENCES[1] Y. !washita, et. al."7MeV PROTON LINAC", Proc. 1990

Photo. The assembled PMS lensVI. BEAM OPTICS
The beam dynamics simulations based on the calculated
magnetic field distribution by P ANDIRA are performed. Theequations of motion in the cylindrical coordinate are{ mo v, = -qv9 B, + mo v/ fr,
mo v9 = -q(v. B,- v, B.)-mo v, v9 fr
The equations areintegrated numeri-.
cally. For lessaberration, the rdependence of B z
and JrBr should
be small. One typical result isshown in Figure 6.
The parallel beams
with 0.5 mm evenspaced radii startat z=-6 em ( leftedge ), and go
through the PMS
whose center is located at z=O. Bzand JrBr at 8 different radii whichcorrespond to theinitial positions ofthe beams areshown on the Zaxis. The x-x'phase space plots
are also shown at
the initial point
and the focal point

o_.eEnergy(5)Linear Accel. Conf., Albuquerque, p.74
[2] A. Noda, et. al. "Improvement of the Proton Accelerator
System", Bull. Inst. Chem. Res. Kyoto Univ. Vo1.70, No.I
(1992)[3] 0. C. Dermois, "The external injection system for theGroningen cyclotron", Proc. Fifth Int. Cyclotron Con f.
Oxford, 620 (1969)[4] K. Halbach, "Physical and Optical Properties of Rare
Earth Cobalt Magnets", Nucl. Instr. and Meth., 109 (1981)[5] K. Halbach, "Magnet Innovations for Linacs ", Proc. 1986
Linac Conf., Stanford, SLACReport303, 407 (1986)[6] User's Guide for the POISSON/SUPERFISH group ofcodes., LA-UR-87-115, LANL (1987)[7] C. Fert and P. Durandeu, "Magnetic Electron Lenses" in"Focusing of Charged Particles", Edited by A. Septier;Academic Press, 309 (1967): 20-JUN-93 15:09119
50.00 keV
•Veloci-t.Y-

3.095E-03 m/nSd-t-0.168

nS

Period"'80.8nSIP

4.00 mms;ze
SCALE-5000.0
INTC8Zl121- 2.579 T12 em
Fecal Leng-th- 16.19 em
lNTCBZn121/lNTCBZ1121- 1.1147
lNTIBRn12/Rn121/lNTIBR1121- 1.1074.;

5.000 mmX

X-X' PLANE

Figure 6 Beam dynamics simulation based on PANDIRA result.

-269-

20.000 mra.d