The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Monte Carlo Simulation of Ion Optics Involved Multiple Charge ExchangeInteraction under a Solenoidal Magnetic Field
Takeshi TAKEUCHia, Katsuya YONEHARAa, Yasushi ARIMOTOb,
Tamio YAMAGATA a and Masayoshi TANAKAc
0 Department of Physics, Konan University, Higashinada, Kobe; 658 Japan
bResearch Center for Nuclear Physics, OsakaUniversity, Ibaraki, Osaka, 560 Japan
cKobe Tokiwa Jr. College, Nagata, Kobe, 653 Japan

Abstract
Ion optics of a 3 He ion involved multiple charge exchange interaction under a solenoidal magnetic field wasinvestigated by means of Monte Carlo simulation. It was
found that (1) beam emittance growth results not froman angular broadening but from a beam size enlargement, (2) the phenomena under the magnetic field Bare
simplified by a no charge exchange phenomenon undera weaker magnetic field (effective magnetic field), Beffdefined bywhere >.+ 0 and .Xo+ are mean free paths for 3 He+ ion
and 3 He0 atom, which undergo the charge exchange interactions traveling in the alkali vapor.

1 Introduction
A new type of a polarized 3 He ion source based ona principle, so called " electron pumping ", was recently
proposed [1]. The polarized ion source under this principle requires multiple electron capture and stripping collisions (hereafter, we use an abbreviated word, multiplecollisions) of a 3 He+ion with polarized alkali atoms under a strong magnetic field ( "' 3T ). Since, no one hasever attempted to solve a problems induced by the multiple collisions under a strong magnetic field, a beamemittance growth and reduction of polarized beam intensity are considered to be one of the serious problemsof this new ion source.
In the present work, the Monte Carlo simulation
were performed paying a special attention on the emittance growth and reduction of the beam intensity due
to the multiple collisions under a strong magnetic field.
The calculated results were somehow in more detail discussed, from which a new concept of an "effective field"
has been deduced. The effective field will provide a convenient tool in simply calculating the beam optics witha solenoid field in which charge changing collisions areallowed.

zero in the outside region. The magnetic field is uniformly distributed throughout the inside region of thesolenoid magnet and is zero in the outside region. Only
the processes (1) 3 He+ -+ 3 He 0 , and (2) 3 He 0 -+. 3 He+
were taken into account by the present Monte Carlci simulation as possible multiple collision processes with large
cross sections in the present 3 He+ energy ( = 20 keV ).
A series of these· processes are repeated mitil the 3 He
ion/atom hits the cell wall or reaches an exit of the alkali vapor cell either. We carry out these trials 5000times. In the process (1), the 3 He+ ion moves spirally
by the Lorenz force and becomes a 3 He 0 atom by theelectron capture collision. Then, in the process (2), the3 He 0 atom goes straight and becomes a 3 He+ ion again
by the electron stripping collision. The cross sections of(1) and (2) are 1.15 x w- 14 cm2 and 0.123 x w- 14 cm2[1-3], respectivery. Thus, the mean free paths are .X+o= 1/(u+o · p) ~ 0.43 em and .Xo+ = 1/(uo+ · p) ~ 4.06
em, respectively. We assume an incident 3 He+ beamemittance of (±1mm) x (±25mr) at the entrance of thealkali vapor cell.

3 Results and Discussion

3.1 Beam emittance growth and transmission
The beam emittance is found to be (±5mm) x(±25mr) which is five times larger than that at the entrance of the cell, (±1mm) x (±25mr), where the alkali
vapor density is 2 x 10 14 atoms/ cm3 , and the magnetic
field is 3 T. The emittance growth by a factor 5 results
only from the beam size enlargement.
,-..

~ 12._;>,
(.)

1::
Q.)

·o!+::::

108<.i-4Q.)

1::

60·a;

4til

2·-Etil

2 Monte Carlo simulation

1::
C<:l,...

We assume an idealized geometry in the Monte Carlosimulation. An alkali vapor cell ( 1 em in diameter x 30em in length) is located at the center of a superconducting solenoid magnet ( 19 em in bore diameter x 56 em inlength ). The alkali vapor cell uniformly contains alkali
atoms with a vapor density p = 2 x 10 14 atomsfcm 3 andE-<

204060Beam spreading angle (mr)Fig. 1. The calculated results of the 3 He+ beamtransmission efficiency plotted as a function of a spreading angle. Se~ text for further detail.

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The 11th Symposium on Accelerator Sciencr; and Technology, Harima Science Garden City, 1997

Figure 1 shows the calculated results of the 3 He+
beam transmission efficiency plotted as a function of thespreading angle of the incident 3 He+ beam with the alkali vapor density of 2 x 10 14 atoms/cm 3 at B = 3 T.
From this figure, it is found that the transmission efficiency is a constant, i.e., 10% when the beam spreading
angle is smaller than 10 mr. This efficiency corresponds
to a fraction of 3 He+ in an equilibrium charge state ata 3 He+ beam energy of 20 keV. On the other hand,when the spreading angle becomes larger than 10 mr,
the transmission efficiency tends to decrease in Fig. 1.
This decrease is due to a loss of the incident 3 He+ ionby the wall collision of the alkali vapor cell.

3.2 Ph;sical background of emittance growth and concept of effective magnetic field
Figure 2 shows the size and the phase space of thebeam at the exit of the cell for the following two cases;
with no alkali vapor (case A; collisionless) and with dense
alkali vapor (case B; multiple collisions). To see the effect of the magnetic field, the calculations are carriedout at the magnetic fields, B = 0.01, 0.1, 1, and 10 T.
In the case A, at a weak magnetic field ( B = 0.01 T ),the beam profile (Fig. 2-(a),-(e)) is approximately determined by the drift space. As increasing magnetic field,
the spatial image of the beam tends to converge upon
the center point (0,0) in the (x,y) plane gradually rotating clockwise around the z-axis.

On the other hand, in the case B, the spatial image also tends to converge upon the center point (0,0)
in the (x,y) plane. However, the speed of convergence
as a function of the magnetic field is considerably slow
compared to the case A. Based on this aspect, the beamprofile in the case B (-(k), -(o)) at B = 1 T seems toresemble that in the case A (-(b), -(f)) at B = 0.1 T. The
difference in the strength of the magnetic field between
two cases is almost the factor of 10. This resemblance
seems to further hold at higher magnetic fields, e.g., at
B = 10 Tin the case B (-{1),-(p)) and B = 1 Tin thecase A (-(c), -(g)), though a spatial diffusion in the case
B is significant.
Physical meaning of the factor, 10, could be explained as follows: The mean free path >. 0 + is approximately 10 times larger than >.+o. This indicates thata 3 He ion/atom is in a +1 ionic state for 10 % of thewhole traveling time, while in a neutral atomic state forthe rest of the whole traveling time. The magnetic field
influences only a trajectory of a 3 He+ ion through theLorenz force. The effect of the 3 He+ ion upon the magnetic field is proportional to We x t, where t is a travelingtime for a 3 He+ ion and We is a cyclotron frequency defined by the equation (1). This suggests that an effective
magnetic field for the 3 He+ ion is expressed by
Beff ~ >.

no alkali vapor (case A)(a)
200-20200i-20.

(z~ 20 (c) ,0-10-20-20IT(d)0-20I-1000..--..

..--.. -20s..._,

010........_s -10s..........

6•-10~lT~

00-20-10(h)10•0X(mm)-101010lOT01000200..........
10~...........

0lOT-10-10(1)B.

1020O.lT s -10..

>.

dense alkali vapor (case B)

10~lT>.+o+O + 0+0-20

10-10-10X(mm)010X(mm)-100

10X(mm)Fig. 2. The phase space (x-x') and position (x-y) of the :iHe+ beam at the exit of the alkali vapor cell. The left
figures (a)-{h) are the case for no alkali vapor (case A; collisionless) and the right figures (i)-(p) are the case fordense alkali vapor (case B; multiple collisions). An alkali vapor thickness of case B is 6 x 10 15 atoms/cm2 • To see
the effect of the magnetic field, the calculations are carried out at magnetic fields, 0.01, 0.1, 1, and 10 T. See text
for further detail.

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Using A+o R: 0.43 em and Ao+ R: 4.06 em, we canconclude Bef 1 R: 110 B. The effective field will provide
a convenient tool in simply the calculating beam optics
with a solenoid field inside which the multiple collisions
accompanying charge changes are allowed. Furthermore,
the restriction of this scalling law is discussed in thepaper [4].
4 SummaryIn the present parameter for polarized 3 He ion
source, It was found that the emittance grows from(±1mm) x (±25mr) to (±5mm) x (±25mr), i.e., theemittance growth occurs not in the spreading angle, but
in the spatial size. At the initial beam spreading angle
less than 10 mr, the transni.ission efficiency was about
10 %. The concept of the effective magnetic field wasestablished from the emittance comparison between thebeam profiles with an alkali vapor and without an alkalivapor.
Acknowledgement

The authors also wish their gratitude to the director
Ejiri and staff of the RCNP for their warm hospitality.
References[1] M. Tanaka, M. Fujiwara, S. Nakayama, L. W. Anderson, Phys. Rev. A52 (1995) 392.
[2] R. D. Dubois, and L. H. Toburen, Phys. Rev. A31(1985) 3603.
[3] C. Reynaud, J. Pommier, Vu Ngoc Tuan, and M.
Barat, Phys. Rev. Lett. 43 (1979) 579.
[4] T. Takeuchi, K. Yonehara, Y. Arimoto, T. Yamagata, and M. Tanaka, submitted to Nucl. Instr.
Meth. Section A.

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