JAERI-Conf 95-021

PB37
HOLLOW BEAM FORMATION IN THE EXTRACTION REGION OF ECRIS
Y.Batygin, A.Goto and Y.Yano
The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-01, JapanAbstract
Beam optics in the extraction system of an ECR ion
source (ECRIS) are examined both analytically andnumerically, by taking nonlinear effect due to aberrations ofeinzel lens into account. It is shown that this effect cancause hollow beam formation. Simple analytical criteria tokeep the good beam quality in the focusing system aregiven.

integral equals zero because there is no correlation of Px andy. The last integral is proportional to the RMS value oftransverse coordinate <y2>. For most of the beam
distributions Y<y 2> = R/2 where R is a beam radius
comprising around 90% of particles. Finally the RMS valueof canonical momentum is <Pi>= <p?b> + (q Bz R I 4 f
Combining the obtained value of <Px2> with equation (I)the normalized beam emittance E is given by:

1. In trod uctio n

E= 2 R ~Beam quality of a high-intensity heavy-ion
accelerator is mostly defined by the extraction region of theion source ·where nonlinearity due to space charge andfocusing field are significant. At the RIKEN Accelerator
Research Facility an 18-GHz ECR ion source (ECRIS) is
under construction for the heavy-ion linac. This new ECRIS
is expected to produce higher-charge states of heavy-ions sothat the acceleration performance of the linac can be furtherupgraded. The extraction system of this ECRIS consists ofan extraction gap and an einzel lens as shown in Figs.1 and2. After passing the einzel lens, the extracted beam has to befocused onto a spot with a diameter of 10 mm to be matchedwith the following beam transport system. The purpose ofthis study is to examine nonlinear bean1-optics effects of theeinzel lens which can influence the beam profile andemittance shape of the extracted beam.
2. Beam EmittanceIn an ECRIS charged particles are born in a strong
longitudinal magnetic field Bz fulfilling the ECR resonancecondition 2roL=ffiRF where roL =eBzl2me is Larmor's frequencyof electrons and roRF is a microwave frequency. The effective
phase space area occupied by the ensemble of particles is
described by the value of root-mean-square (RMS)
normalized beam emittance defined in canonical-conjugate
coordinates:(1)

where m, x, and Px are a mass, a transversal Cartesian
coordinate and a canonical-conjugate momentum of aparticle, respectively, and c is the speed of light. For·particles in the ECRIS one can put <xPx> = 0. Canonicalmomentum of a particle Px = Px- qAx = Px - qBz y /2 in thelongitudinal magnetic field is a combination of mechanicalmomentum Px and qAx where q is an ion charge and Ax is anx-component of vector potential of the magnetic field . The
RMS value of canonical momentum is given by:

The first integral in eq. (2) describes the thermal spread of
mechanical momentum of charged particles in the ECR
plasma. Therefore, the RMS value of mechanical momentum
is given by <px2> = < Pth 2 > = mkTi where Ti is the ion
temperature and k is Boltzmann's constant. The middle

kTi + [roLR]22cmc2(3)

The formula (3) is usually used for estimation of theemittance of the beam with an ambient magnetic field on thecathode [1]. In the case of the 18-GHz ECRIS the resonant
value of magnetic field is Bz=0.637 T. The normalized beamemittance of, for example, an Ar 5 + beam with the ion
temperature kTi =3eV is E = 2·5·1o-3 Vo.8 10' 10 + 10' 9=3.3·10- 7 n:·m-rad.
3. Numerical Study of Beam Optics
Numerical calculation of particle trajectories in theextraction region was performed with the computer program
BEAMPATH [2]. Particle trajectories obey the equations ofmotion derived from a single particle Hamiltonian in
Cartesian coordinates:(4)
where Uc is a space charge potential of the beam and Uf is apotential of the focusing field. The space charge potential iscalculated from 2D Poisson's equation in Cartesian
coordinates on the mesh 256 x 256. The 2D electrostatic
potentials in the extraction gap and in the einzel lens arecalculated by using the program POISSON.
Numerical study was performed for Ar5 +-ion beamwith current of 100 ef.!A. The following parameters werevaried so as to find the optimal matching conditions for theextracted beam with the beam transport system downstream:
the extraction gap was varied from 3 em to 4 em; the distanceof einzel lens from the extraction hole from 25 em to 35 em;
and the voltage at the central electrode of einzel lens from 10
kV to 14 kV. The results are presented in Table l and in Figs.
1-4.
It is noted that in Fig. 4 the beam forms hollow
structure at the waist point of beam envelope. The same
phenomena were experimentally observed in the highperveance electron guns [ 4] and in the short solenoidelectron lenses with large aberrations [5]. For understanding
more details of these phenomena, let us consider thefollowing analytical model.
4. Hollow Beam Formation
After being extracted from the ECRIS particles pass throughthe focusing lens and then move in a drift space.

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JAERI-Conf 95-021

E(.) 0x0510152030354045050

10204030

5060z,emz, em

Fig. 2. Particle traject01ies in the extraction region of theECR ion source: extraction gap 4cm, lens voltage 12.5kV, position of lens center 30.4 em, coefficient Ca. R 2 =0.3.

Fig. 1 Particle trajectories in the extraction region of theECR ion source: extraction gap 4cm, lens voltage 14
kV, position of lens center 25 em, coefficient Ca. R2 =0.15.

1.5 c-.--,--,--,-....,--,
1 t----1----rl:

Eo.5

(.)

0~

E
u_

-1 ~1--+~~+--r_,-1 ~-t-9:..,..:..P.+-+--l-1.5 LI..LL.LLLJ..u...I..LL.LL.U..U.J..U.Ju..J..LLU..U-1.5 -1 -0.5 0 0.5 1 1.5

X 10. 3xa..

-0.5~.,-1.5 U..U..L.Lu.U..U..LLUU..U.U..U..U.U.LU.J-1.5 -1 -0.5 0 0.5 1 1.5x, em

0-0.05-0.1 E--+'"""'F--+--+-+--J-0.15 E---1--+-1-+--r_,-0.2 t:Lu.LI..u.U..U"'-L.LU..W...LLu.U.U.1.U.J-1.5 -1 -0.5 0 0.5 1 1.5x,em-0.5 ~+-"--t]0-0.15 E-"1"'-+-+---+---+--l-0. 2 b..u..Ll..Lu.U.........LLu..uJ..u.u.l..u..<u.JxJO

I

1.:-0.1 5 E---1--+---11-+--r_,-0.2 t:L.LJ...L.Lu.U..U..LU.Jl.u..LU..U.u..I..L.LU.J-1.5 -1 -0.5 0 0.5 1 1.5x,emx,em

Fig. 3. Cross sections of the beam (top) and phasespace projections of particles (bottom) at z= 14 em(left column) and at z=51 em (right column) for theextraction system presented in Fig. 1. RMS emittance
growth is Ef/E0 =1.15.

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0.2 .,.-----,-..-.,.---,--,--,
0.2 1""'"".--r-.--.--......--,
0.15 E---+--+-+--+-=&--1
o.15 r-+----11----t--+-+----l0.1 E---+--+--1--:
o.1 r-+----11----t--+-+----l0.05 E---1--+--:
o.o5 r-+----11----1:~ 0 E---1---+'t---1----1 ~0-0.05-0.05-0.1 E---+.;i;e;lil"'-+--+-1---1-0.1 E--+----1-+---+-+---l0.5-1.5 U..U........,_LLL.l.L.L.UL.LI..L...........LLLL.....,_..U-1.5 -1 -0.5 0 0.5 I I.5x, em
X-1.5 -I -0.5 0-1 f--t-----f___;,+--+-t---1-1 t---t----"1'"9>-1.5 t:I..LJ...LI..u..Li.l..J.LL.LJl.u..LU..U.u..I..L.I.J..LJ-1.5 -1 -0.5 0 0.5 1 1.5x, em
X 10.30.2 .,.-----,--,--,---,-.,---,
0.15 E---+----1-+---+-+---l
0.1 E---+----1-+---:
0.05 E--+---+-o>.

......_..

-0.5 1----+--:Tf~.... _,,, ....,

-0.5

o.5-3

0.2 .,.---,---,-,-..,---,--,
0.15 E--+----1-+--+---:-t---1
0. 1 E--+----f-+-,.jp~t---1~

0. 05 E--1-----f--:

0 E---1---J.
-0.05-0.1 E-+..;;n~+--+-1----1-0.15 r--+--+-t--t--+--1-0.2 t:u..&..LLLJ.L.LlJu..u...U..U.LLLJ.L.LlJLU..U-1.5 -1 -0.5 0 0.5 I 1.5x,emFig. 4. Cross sections of the beam (top) and phasespace projections of particles (bottom) at Z=lfi em (leftcolumn) and at z = 60 em (right column) for theextraction system presented in Fig. 2. RMS emittance
growth is EfiEo = 1.3.

JAERI-Conf 95-021

4.......

3.5-5i'..

3in ~IF ro ile'1.5
1r"""- r-0.500.2v

3\20\v

41\.... 2.5a..

r-1 ra1 1 ·roTI le~-11 C:ll ·ruTI

0.4 0.6 0.8'~!"-~

1- -r- r--..

I li+i· II C '"f llo

101.2l";o,..

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

r, em

r, em

Fig. 5. Beam profile conservation in weak nonlinear field Ca. R2 = 0.15 (left) and hollow beam
formation in strong nonlinear field Ca R2 = 0.3 (right), calculated from formula (7).
For particles born in the magnetic field of ECRIS the valueof azimuthal component of canonical momentum
Pe = (112) q Bz ?o is conserved. The electric field of theeinzel lens provides focusing effect which can be describedby a linear term as well as higher order terms. The radial
equation of motion of a particle in this region is given by

After passing through the thin lens initially parallel
particles with radial displacement r0 are converged withslope ·of r~ =- ( l +Cur~) r 0 /f, where f is a focal length ofthe lens and Ca; is a spherical aberration coefficient. The
equation of motion (5) can be integrated in drift space toobtain the relationship between the initial and the final
radii of particle:

where 't (= z/f) is a dimensionless drift distance and 11 (=roLt) is a dimensionless time of particle drift. To find the·beam density redistribution, let us take it into account thatthe number of particles dN inside a thin ring (r, r+dr) is kept
constant during the drift of the beam, and hence the particle
density p(r)=dN/(2n:rdr) at any z is connected with theinitial density p(r0 ) by the equation p (r) ch.2 = p (ro) ~, orFrom this relationship changing of the beam profile
is observed when a spherical abenation is significant. Thelinear focusing lens (Ca;=O) conserves the beam profile andchanges only sizes of the beam. Nonlinear component ofelectrostatic field increases focusing of particles incomparison with the linear component only [6]. It results
in a beam profile with a inore particle-populated boundary
than the central region (see Fig. 5).
This hollow beam formation is accompanied byemittance growth of the beam. In the case considered theeffective RMS emittance can increase by 1.3 times (see fig.
4). Such effect of the nonlinearity on beam intensity

Table I. Parameters of 100 eJ.LA Ar 5+ ion beam in theextraction region of the 18-GHz ECRIS.
Extract.
gap,
emCenter of Beam
Lens
voltage, of lens, waist,emem
kV

Waist Emittanceradius, growth,£fifoem------------------------------------------------------l.l
1.6
34
344
3
44

1012.5'13l3
l3
1430.4
30.4
30.4
30.4
35.5
2559
60
56
60
48

0.5
0.6
0.4
0.5
0.5

1.3l.l1.3
1.4l.lredistribution can be controlled by the product of sphericalabenation coefficient and square of beam radius Ca. R 2.
Analysis of the formula (7) shows that the beam profile isconserved if Ca;R 2 < 0.2 . For the lens considered Ca; = 0.1
cm-2, and hence the beam radius R in the lens should be
kept smaller than 1.4 em. The numerical calculations
confirm this limitation to keep the quality of the beam (seeFigs. 1-4).
5. Conclusions
Nonlinear effect associated with the hollow beamprofile formation in the extraction region of ECRIS wasexamined through both the numerical particle tracking andthe analytical treatment. Simple formula has been derived
to estimate the significance of spherical abenations on thebeam profile redistribution. This study is important in thedesign of the low-energy part of heavy-ion accelerators.
6. References[1]. I.Ben-Zvi, Proceedings of the PAC95, Washington
D.C., (1993), 2962.
[2]. Y.Batygin, Proceedings of the EPAC92, Berlin,(1992), 822.
[3]. J.Kim, J.Whealton and G.Schiling, J. Appl. Phys.
49 (2) (1978), 517.
[4]. M.Reiser, "Theory and Design of Charged Particle
Beams", Wiley, New York, 1994.
[5]. P.Loschialpo et.al., J. Appl. Phys., 57, (1985),10.
[6). J.D.Lawson, "The Physics of Charged Pmticle
Beams", Clarendon Press, Oxford, 1977.

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