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

AN 0 2 SHEET BEAM GENERATORFOR A NON-DESTRUCTIVE BEAM PROFILE MONITOR
T. Fujisawa. NIRS, Chiba, Japan
Y. Hashimoto and T. Morimoto, KEK, Tsukuba, Japan

Abstract
An oxygen molecular sheet beam was generated byusing a nozzle beam method and focused with amulti-pole magnet. The principle and calculationsofthe focusing effect are discussed and the preliminary
experimental results are shown.
1. INTRODUCTION

A highly dense neutral gas beam is required as atarget of a non-destructive beam profile monitor whose
schematic view is shown in Fig. 11). An oxygen
molecular sheet beam is obtained in the gas jet chamberby using the nozzle beam method 2). The sheet beam runs
to the detector chamber through the slit chamber and themagnet chamber. In the slit chamber, the divergedmolecules are rejected and in the magnet chamber partsof the beam are focused at the median plane with themulti-pole magnet. In the monitor chamber the sheet
beam collides with an ion beam to detect the beamprofile.
Proton Beam

Fig. 1. Schematic view of a beam profile monitor
The method to focus the sheet beam with themulti-pole magnet is based on the fact that an oxygen
molecule has a magnetic moment of as large as 2 Bohrmagnetons and a spin of 1. The similar method is appliedin an atomic beam type polarized proton ion source 3). Ina polarized proton ion source, hydrogen atoms passthrough along a center axis of a six-pole separation
magnet. In a present case, however, since a molecularoxygen beam is not cylindrical but a sheet beam, thegradient of the inhomogeneous magnetic field has to be
up-down symmetry and uniform along the beam width.
The beam profile monitor has been fabricatedand studied by using an 8 Mev proton beam
extracted from the NIRS cyclotron. A clear beamprofile has been observed4l.
2. PRINCIPLES AND BASIC CALCULATION

2-1 Estimation of Focusing ForceIn terms of the classical mechanics, a particle having
a magnetic moment associated withaspin(s)precesses
about the orientation of an external
magnetic field (H) with the Larmor frequency ( 11 )given byll = gp sH!h,(1)where g, f1 , and h are the gyro-magnetic ratio, the Bohrmagneton, and the Plank constant, respectively. On theother hand,the product of h 11 is interpreted
quantum -mechanically as an energy shift caused by an
external magnetic field. Thus, a particle having amagnetic moment associated with a spin acquires anextra energy (W) in an external magnetic field asexpressed
W=gp mH(2),
where m is the z component of the spin.
From Eq. (2), the force acting on the particle in an
inhomogeneous magnetic field is given by
F=- grad (gp mH).
(3).
This force is familiar in the Stem-Gerlach experiment.
If the g and m are independent of a magnetic field, Eq.
(3) is rewritten as ·F=-gpm · grad(H)(4).
The magnitude ofF for m=l is calculated to be 5.6 X
10-16 dyne when the magnitude of grad(H) is 30 k
gauss/em which is realized in a usual polarized proton
ion source 5'6). The strength of this force corresponds tothe acceleration of
1.0 4 X 107 crnlsec 2 for a particle
whose mass is 32 atomic mass units. The mean velocityof 0 2 molecules is expected to be 73000 crnls in thenozzle beam. On the above-mentioned conditions, if thefield length along the beam path is Scm, a focal length of
the beam having a width of 5 mm is estimated to be 25em. It, however, is noteworthy that if particles on them=l state are converged, those on the m=-1 are diverged
and particles on the m=O state are not deflected.
2-2 Rotational Levels of an Oxygen Molecule
An oxygen molecule is not spherical, and normally
rotating. Thus, it is necessary to take account of thecoupling between the rotational angular momentum (K)and the spin (s) 7' 8) in the calculations of the focusing
effect. Figure 2 shows energy levels of K=l given by
Tinkham9J. The other levels are not discussed here
because the temperature of the nozzle beam gas is
assumed to be several "K and the level energy of K=3 is
27 "K higher than that of K=l in no magnetic field. The
symbols J and M are quantum numbers of a total angularmomentum (J=K+s) and of its magnetic sub state. Theenergy shift of M=2 (-2) is nearly same to that of-378-

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

m=l(-1) discussed in Section 2-1.

In the arrangement of magnets as shown in Fig. 3, thedirection of the magnetic field changes from 90 to -90
degree in the distance of 6 mm. If the velocity of theparticle in the nozzle beam is 700 m/sec , it takes 8.6f.1 sec for a particle to pass through the distance of 6mm. During the period of 8.6 f.1 sec, the direction ofmagnetic moment precesses 24000 times
in themagnetic field of 1 k gauss. Since the magnetic field ishigher than 1 k gauss in the most of the focusing area, thedirection of the magnetic moment is expected to follow
the orientation of the magnetic field 6)•.:n. 40
Wj22(H)20~ Wj21(H)c:J----·~Wj20(H)0~ Wj2ni(H)w--.

Wj2n2( H) -20•-27.5..-40
05.o.

H

2-4 Velocity Distributions
To estimate the focusing effect it is necessary totake account of the velocity distribution of particles inthe gas. The velocity distribution f(v) of particles in thenozzle beam is given bl)
f(v)=av 2exp(-m/v-u 0) 2/2kbT),
where a, mr. U 0 , kh, and T 1 are a normalization constant,the mass of particle, the mean velocity of the gas, theBoltzmann constant and the temperature of the gas,
respectively. Figure 4 shows an example of T 1=l0o K.
Thus the beam intensity distribution is given by theequation of vf(v)= av 3exp(-mP(v-u 0) 2/2khT 1). From Fig. 4,
it seems that the aberration due to the velocity
distribution is not so serious if the gas is cooled at thetemperature of 10 oK .

10k Gauss.w.

]=2 (M= 2, 1' 0' -1' -2,.17.25.

20

10~Wjii(H)o--~ Wj!O(H)

0r~j·I~I(H)w-10!

•-10.79..-200.o.

64

H

10..10..

k GaussJ = 1 (M= 1, 0,- 1)

-~(/)
c:

£CD F(v,0,300)

Fig.2. Levels of an oxygen molecule for K=l in amagnetic field. 9) The other states are shown in Ref. 9.

~ F(v,70000,JO)

:;;

"'c::

----Qi

2-3 Adiabatic Passage
A magnetic moment of a particle is not polarized inspace but with respect to the orientation of the external
magnetic field, provided the field direction changes
slowly (adiabatic change). However, the polarization isdisturbed by a rapid change of the magnetic fieldcomparable or faster than the Lamar frequency( ).1 ).
From Eq. (1), the Lamar frequency is calculated to be 2.8
GHz at the magnetic field of 1 k gauss.

v

Velocity(cm/sec)

Fig. 4. Velocity distributions of the nozzle beam gas(dotted line) and Maxwell Boltzmann distribution (solidline).

PoleR=1.5 mm

Width=3 mm

Variable c;;lp-/\
3-12mm

Fig.3. Cross-sectional view of the focusing magnet.
The magnetic field gradient is up-down symmetry. The
fabricated magnet consists of 26 pairs of poles.

Fig.5. Upper poles of the focusing magnet.

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

The cross-sectional view of the focusing magnet
fabricated is shown in Fig. 3 I) and the picture is shown inFig.5. Material of permanent magnets is NdBFe and thepoles are made of Permendur (high permeabilitymaterial). The width of the magnet is 70 mm and thelength 150 mm. The pole gap is variable in a range of 3to 14 mm to adjust the field strength. The magnetic fields
are measured with a hole unit whose sensitive area is 70
f1 m X 70 f1 m. In a case of 5 mm pole gap, the magnetic
field is shown in Fig. 6.
10000
8000
600040002000
<I)
<I)
;:,
0~-2000
-4000
-6000
-8000
-10000"K., the mean velocity is 730m/sec, the rotational
quantum number (K) is 1, the populations ofmagnetic sub-states (M) are even, and the focal
length of the M=O sub-state is infinite. The results areshown in Fig.7.
The intensity distribution on the focal plane ismeasured with the compression gauge method. The
compression chamber has a small slit (0.5(h) x 14(w)mm 1l ) and a B-A gauge is installed in it. Moving thegauge along the focal plane, the spatial intensity
distribution was measured. Figure 8 shows the verticalintensity distribution measured on the colliding position.
The best focusing is obtained at the gap of 7 mm and thefocusing effect is observed at the gap of even 14 mm. It
seems that the intensity at the median plane increases up
to two times of that without the magnet. From thecalculation as shown in Fig. 7, the gap of 7 mmcorresponds to the focal length of 20 em.

x 0.3mmj-h=O -h=1.5jG)

0.1--gap=6~ 0.08 1 - - - - - - . f l - . - - \ \ - - - - - - l --gap=7--gap=10-~"til 0.06 1 - - - H - H - - - - - . - - - - - !
--gap=14;:,

Fig. 6. Magnetic field distribution along the beam path.
The gap between the poles is 5 mm and the parameters
are distance from the median plane.
4. FOCUSING EFFECT
The distance between the skimmer (beam source) andthe magnet center is 56 em, and the ion beam profile ismeasured at the colliding position of 50 em distancefrom the magnet. The intensity distribution of the 0 2
sheet beam on the colliding position is calculated
assuming that the temperature of the nozzle beam is I 0&!

0.02
V~

0,....

M,....

CO,....

m,....

N"'~

t'\1~

C\1x 0.5mm

Fig. 8. Measured vertical intensity distribution of an 0 2
sheet beam. The parameters are the pole gaps.

2.50E+06

5. CONCLUSION
The focusing effects of inhomogeneous magnetic
fields for an 0 2 sheet beam have been proved. Theintensity at the median plane increases up to about twotimes.

2.00E+06

co..-cc,-co,....
,....

t'\1

C'\1C'?

M'll:tPosition (x 0.5mm)
j--f=20cm --F=27cm --F=40cm --f=infinite jFig. 7. Calculated vertical intensity distributions of an
0 2 sheet b~am. The parameters of F are focal lengths ofthe velocity of 730 m/sec.

References1) Y. Hashimoto et al. Proc. 7th Euro. Particle Accel.
Conf.(2000) 1729.
2) A. Kantrowitz and J. Grey, Rev. Sci. Instr. 2, 328(1951).
3) G. Clausnitzer, et al, Z. Physik, 144, (1956) 336.
4) Y. Hashimoto, et al, PAC(2001)(Chicago).
5) T. Fujisawa, Scientific Paper of I.P.C.R.
77,(1983) 117.
6) W. Haeberli, Annual Rev. Nucl. Sci. 17(1967)373.
7) M. Tinkham and M. W.P. Strandberg, Phys. Rev. 97,No.4 (1954) 937 and 951.
8) J.M. Hendrie and Kusch, Phys. Rev. 107, No.3 (1957)716.
9) M. Tinkham, MIT, PhD thesis(1954).

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