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

Beam tracing in an accelerating system for plasma jet emitter
Takanori YAMAMOTO, Takeji SAKAE, Takayuki INOUE and Ryuichi UENO
Department of Nuclear Engineering, Kyushu University Fukuoka 812, JAPANAbstract
The plasma jet emitter has been developed as an intense and low divergence beam generator. The emittercan generate about 10 A and several keV energy proton beam, the current density is about 450 mAfcm 2 inthe experiment at TRIUMF, CANADA[l]. This paper
makes a comparison of the experimental data with theresult of the simulation achieved by a newly developed
program for the accelerating lens system of the plasma
jet emitter. The program considers the space charge effect of the beam and the plasma. As the results, a good
agreement can be got between the experiment and thesimulation. One can optimize the lens system by thiscalculation.

Plasm·aexpansion
roomExtractionlens system

Plasma jet emitter

1 Introduction
Fig. 1

In an accelerator, ion sources play an important role
to decide efficiency of generating beam. The plasma jetemitter is a new type of ion source developed by V. I.
Davydenko et al., in Novosibirsk[2], to generate a highcurrent neutral beam for plasma diagnostics in medium
size tokamak. The same type of ion source has been developed in TRIUMF, CANADA for new pulsed optically
pumped polarized H- ion source. For the diagnostics,
the beam needs to have high brightness (about 3 x 108
A/cm 2 rad 2 [3]) and a low divergence (up to 2.0xlo- 2rad). To realize them, a computer simulation is useful
method in designing.
In this work, a simulation is applied to achieve theoptimized designing the accelerating lens for the plasma
jet emitter. A comparison using the experimental dateat TRIUMF is done to investigate the precision of thecalculation.
2 Plasma jet emitterFig 1. shows the schematic drawing of electrodes forthe plasma jet emitter. A pulse plasma is generated ina small vessel (called plasma emitter), which is sandwiched in arc electrodes, by using of a timing controller
for a pulse valve to turn on hydrogen gas, and for pulse
voltage to ignite an arc discharge in the vessel. The pulse
plasma is lead to a vacuum expansion room tllrough anozzle on the plasma emitter. In the room, the plasma isexpanded with no collision and no field unlike the duoplasmatron. The expansion makes cooling of the plasma
as a distance from the anode electrode. The discharge
produces a plasma emission at near the extracting system in having a density of about 10 12 cm- 3 [2] and anelectrode temperature of about 5 eV. At the accelerating
system, particles have almost parallel velocities to thebeam axis because of the cooled plasma temperature.

The schematic drawing of electrodes for theplasma jet emitter.

The plasma surface will be in less disorder than that of
the other ion sources, which makes easer for the simulation model to treat the proton emittion. The plasma
temperature around the surface will be about 5 e V thatis enough small to get a low divergence beam.
Generally to extract the good quality beam from theplasma, a multi slits accel-decel lens system of three orfour electrodes made of molybdenum wires is thoughtup. Especially the multi slit electrodes have a high transmission. In the work, four layers multi slits lens system
is adopted for the plasma jet emitter to extract and accelerate protons from the expanded plasma. The grids
are made of 0.2 mm molybdenum wires. The spacing
between wires is 1.0 mm. The gap between the first(plasma electrode) and second grids is 0.75 mm, thesecond and third grids is 1.9 mm, the third and fourth(ground) is 2.9 mm. In the experiment, a high current
and low divergence beam are found by changing the gridelectrodes voltages each other manually.
3 Method of Simulation of the trajectories

The performance of the lens system is investigated byusing of a computer simulation. The calculation program is developed originally for this work on the baseof the IGUN program[4] with FORTRAN77. It is very
difficult for computers to analyze plasma behavior numerically. Then the simulation adopts a simple mathematical model of the IGUN at the plasma sheath. Itis assumed ions entered to the sheath with a directedenergy of eUi, where Ui is an ion's potential. And electrons are forming an electrostatic shield with an energy
distribution obeyed by Boltzmann's law. The Poisson-168-The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997(a) n = 2.5 e12 em -3

equation is given byyr2 U = _Pi - Pe ,co(1)where(u-Ueup) ,ru;--Pi = en;v u;:=u·Pe = eneexp(2)(UeM)
Ue
Up= Uw + 2ln 1rUim .

Iui

100(a)

50tO.• .

.. . .... ••!•..
,. ... •' •• - /...
••jr.~--(1 - exp ( U ;eUp).s0~/u,+~•-u~##.

'bGs::< -50-100-0.3-0.2!"' ••.••-0.10•

l·~,.

E-£;y Up+ Ui- UXOkV

fields at the lens for a slit in the simulation.
The geometry, given voltages, and the beam current density j = 450 mA/cm2 are put in to thecalculation in two cases of plasma density. (a)The plasma density n = 2.5 x 1012 cm- 3 , (b) isn = 5.0 x 10 12 cm- 3 •(3)

The electron and ion currents to the wall with potential
Uw become balanced. The ion potential Ui and electron
potential Ue are estimated each about Ui ~ Ue ~ 5 eV,then the plasma potential Up is higher than the wall potential Uw by about 16 eV. Uw is the potential of theplasma electrode. Assuming quasi neutrality (ni ~ ne)at the plasma potential U = Up, the right side of an
expression in Eq. (1) can be rewritten byeni .

-0.8kV

Fig. :,1 The protons beam trajectories and the electric

The plasma potential Up is calculated by

Pe)
Pi (-co 1 - Pi =

5.3kV

6kV

(4)

Raius [mm]

0.1

0.2

0.3

0.2

0.3100(b)The electrical field around the plasma surface and thelens can be solved ·by using of the relaxation methodwith small meshes (10 Jl.m). For one relaxation's step,in the case that a potential at a lattice is greater thanthe plasma electrode potential, the potential is calculated from the Poisson Equation with the right-handside expression of Eq. (4). In other cases, a chargeof the lattice point is estimated by the total charge inthe lattice square. The electron compensation effect isassumed that the beam current density decreases to ahalf roughly. The calculation to solve the renewal Poisson equation is repeated until the solution has enoughsmall convergence.
4 Results and discussion
The simulation is performed on the condition of theexperimental data. In one case of the condition, the lensgeometry is set to the same as the experiment. The beam
current density j is set to 450 mA/cm2 • The plasma
electrode voltage is 6.0 kV, second is 5.3 kV, third is-0.8 kV, and fourth is ground. This condition makes
one of the largest current beams in the experiment. Theplasma density is an adjustable parameter in this calculation. The results for two cases of the plasma density
are given, the case (a) for plasma density n = 2.5 x 10 12cm- 3 , (b) for n = 5.0 x 10 12 cm- 3 . These order of..
..
I50]'

e.......

0,
..
..

~'bG

~

-50

-100

-0.3

-0.2

-0.1

0

Raius [mm]0.1

Fig. 3 The emittance diagram on the exit (fourth) elec-trode. The condition is the same as Fig. 2,the density about 10 12 cm- 3 is proper because of theexperiment[2]. The electric fields, the proton beam trajectories, the beam emittance, and the plasma surface
position are the outputs of the program.
Fig. 2 shows the calculation results of proton trajectories. The beam is bundled up almost in this electrical field. The beam trajectory depends hardly on theplasma density. The high plasma density has a tendency
to generate a thin beam for a slit. Fig. 3shows the emittance diagram on the fourth electrode (ground) for a slitin the condition of Fig. 2. The divergence is enoughsmall, under 50 mrad each other.

-169-The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

6.04

-. .

6,....,>~'-'...c 5.92

]

~

5.88
5.84
5.8
-0.2

Fig. 4"'\..
'\I elect1 bde I\"'' \\.

5.96

Q)

jl..

~~tion. In the expansion of the pulsed plasma, changing ofthe density will not much influence the beam divergence.
Therefore, this simulation program for static plasma canestimate the performance of the extracted beam.

\'\

5 Conclusion\~The simulation can make almost the same results offocusing as the experiment. The beam emittance can beestimated by the simulation. It is suggested that eachconditions can be optimized by using the calculation on
the assumption of the fixed parameters for other conditions.

•' ~\- • • ·- 1.0e+12 [cm-3 ]------- 2.5e+l2 [cm-3 ]5.0e+12 [cm-3 ]I-0.1'\..,

~

\\I

00.1
Distance[mm]0.2Acknowledgements

0.3

The potentials along the center of the beam axis
for one slit around plasma electrode (first) in threecases of plasma density. The "electrode" in thisfigure is a projection of the plasma electrode potential. The distance 0. mm is defined as a centerof the plasma electrode in the horizontal axis.

Fig. 4 shows the potentials along the center of thebeam axis for one slit around plasma electrode in casesof the plasma density 1.0 x 10 12 , 2.5 x 10 12 , and 5.0 x 10 12
cm- 3 . The plasma potential Up is 6.015 keV from Eq.
(3). The position of plasma sheath moves to downstream over the plasma electrode as the plasma density increases. As the simulation result, the position ofplasma sheath depends on the plasma density. But thebeam divergence has a little dependence on the posi-The authors would like to acknowledge V. I. Davydenko for his advises and A. N.Zelenski for his explanation of the experiment at TRIUMF.
References[1] A. N.Zelenski et al., "Pulsed optically pumped polarized H- ion source development", Rev. Sci. Instrum. 67(3), March 199.6, 378.
[2] V.I. Davydenko et al., "Reception of precise highintensity ionic and atomic beams", Sov. Phys.
Dokl. 28(8). August 1983, 687.
[3] Yu. I. Belchenko et al., "Ion sources at Novosibirsk Institute of Nuclear Physics (invited)", Rev.
Sci. lustrum. 61(1). January 1990, 1359.
[4] R. Becker et al., "IGUN-A program for the simulation of positive ion extraction including magneticfields", Rev. Sci. lustrum. 63( 4), April1992, 2756.

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