JAERI-Conf 95-021

PA11
PLASMA JET EMITTER: SIMULATION MODEL
FOR THE PLASMA IN A SMALL ION SOURCEKenzo OGAWA, Takeji SAKAE, Takanori YAMAMOTO,Yusuke UOZUMI, Akihiro NOIITOMI and Masaru MATOBA
Department of Nuclear Engineering, Kyushu University
Fukuoka 812, JapanAbstract
A program that simulates a small ion source plasma
in the cylindrical coordinate system is developed. In thiscomputation, technique of Particle-in-Cell is used. Theprogram includes the electromagnetic field of three dimensions, the process of the ionization by electron's collision,a discharge electric current and so on. Comparing theresults of the calculation for ion source plasma usirig thisprogram with experimental results for PIG ion source, weget good agreement for the electronic temperature, theelectron and the ion density. As a result of this calculartion, we will be able to analyze the plasma jet emitter thathas cylindrical discharge tube with axial magnetic field byconsidering the collision mechanism and the examinationof the initial condition.
1 Introduction
In an accelerator, an ion source plays an importantrole to decide efficiency of acceleration, brightness and/orintensity of the extracted ion beam. To optimize a quality
and a utilization rate of the extracted beam, the characteristics of the source should be investigated by using
simulation technique as well as experimental work.
In this work, we pay attention to small ion sources
which have a cylindrical discharge tube with axial magnetic field. This type of ion source includes the plasma
jet emitter and PIG type ion source. For the first step,
we have calculated the PIG ion source plasma, becauseof its simplicity. Our purpose is to establish the methodof simulation and suggest.a model for explaining physicalphenomena in the small plasma space.
Plasma in the cylindrical discharge tube withaxial magnetic field
Figure 1 shows scheme of our ion source. Discharge
processes in the cylindrical discharge tube with axial magnetic field are as follows. Electrons extracted from thecathode surface are accelerated by the electric field between anode and cathode. Then electrons interact withneutral particles and ionize them. The electrons have excessive energy, so electrons go forward after interactingwith the neutral particles. Then electrons drift toward toanother side of cathode, they are accelerated by the reverse electric field and return to the discharge space. In
this way, ionization chain is continued.
This process is continued until the electron energy isless than ionization energy of neutral particle. These electrons drift to the anode. Ions produced by this ionization
are attracted to cathode and knock the cathode: Then thecathode releases secondary electrons. They repeat above
processes. As a result of this effect of amplification, thedischarge reaches to the anode and discharge current becomes the value that is decided by the internal resistantof circuit. Characteristic of this ion source is that it has asmall discharge space, because of spiral motion of electronby the axial electromagnetic field.

I - - - - 1...
,.__ _ _ _ 25

unit (mm)Fig.l Scheme of the cylindrical discharge tube with axial
magnetic field.
zaxis

23

Modeling of the cylindrical discharge tube
with axial magnetic field
This system has a symmetrical geometry about ther- (}plane and the z axis (r 0). From this geometricalfeature, the following assumptions are made in this work.

=Fig.2 Coordinates of calculation area.
Same phenomena occur in both sides of r - (} plane. The
electromagnetic field in the discharge space is uniform to
the direction of (}. Therefore we use the r- z coordinate inorder to minimize the simulation space (see Fig.2). Actual
geometry between the cathode and anode is more complex,
but in this calculation we simplify this geometry as shown
Fig.2.
We make assumptions about the interactions between
charged particles and the walls as follows. Electrons areabsorbed at the anode. When ions collide with the anode,
they are elastically scattered. Ions are absorbed at thecathode. There is no interaction between the cathode andelectrons.
4 Method of simulation
Basic equations and some conditions used for simulartion are as follows.

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JAERI-Conf 95-021

200

- ..

0~

-200

Accumulation ofelectric field data by
successive method

-400
~-600

i\\\ \l\i\1\

16-800a.. -1000--1200--1400---1600

Not achieve toequilibrium state=~

time= 0 (sec)· time= 8.01 X108(uc)\time= 1.60X107(sec)time= 2.67 X1Ci 7(sec)

-1800
0515

102025Zaxis(mm)Fig.3 Flow-chart of the simulation.

Fig.4 The change of time of the potential distribution on
the central axis.

avmat = q (E+ v x B) ,\72<I> = _f!.

E'(1)
(2)
Cl)

0VxE

~103 ~-----~-----+---~~----~-----i-------·-----~

(3)

c..

~ 10 2 ~-----+-·------+-·-----i---­E

where m is the mass, v the velocity, q the electric charge,

E the electric field, B the magnetic field, c the light velocity, J the current density, E the dielectric coefficient, tthe time, p the charge density, <I> electric potential. Theseequations are translated to the finite-difference equations
and numerically solved.
To develop the simulation code, we use a PIC (Particlein Cell) method. This code uses Leap-Flog method [2] tocalculate Eq.(1). Though this simulation is done in r- z
plane, (r, z, Vr, w, vz) are used as the parameters of particles. Because this calculation is carried out in the threedimensional electromagnetic field.
The potential distribution is divided into two cases.
(a) The potential distribution by impressing voltage on
the cathode without electric charge density.
(b) The potential distribution with electric charge density(not impressing voltage on the cathode).
In the computation, the case (a) data is used as thebasic potential distribution data by electrode and the case(b) data is used as the potential distribution data for expressing the spatial electric charge effect. Finally, thewhole potential distribution is computed by piling up thesedata.
The discharge current is estimated by only considering the number of ionization events; ionization phenomena
play significant roles in the present simulation. The number of ions and electron which are generated per unit time
is assumed so as to be equivalent to be experimentallyobtained result[ 1].
In this work, to simplify this model we use only thehydrogen ions and elections. This calculation is carriedout by using spur particles which represent huge numberof these particles, because many particles exist in the discharge space. Cathode potential is -1.8 kV, axial magnetic
field is 0.09 T. Figure 3 shows the flow chart of the simulation. This computation is continued until the numberof particles reach to equilibrium value.
Results and discussion
The Fi~ure 4 shows the potential distribution along
the z axis lr = 0 mm). Fluctuations of the potential
are seen all over the discharge space. The steep potential
5::lz

101 b-------i-------~---··--10° ~~~~~~~~~~~~~~~~
10" 3 10" 2 10" 1 1d' 10 1Energy (eV)Fig.5 The distribution of the electron energy.
gradient which is located in the ion sheath is seen near
the cathode (z = 26 ~ 28mm). This is characteristic
phenomenon in the plasma.
Figures 5 and 6 show energy distribution of electron
and hydrogen ion, respectively. Both distributions havemaximum value near 0 eV and exponentially decrease t~ward high energy. The average energy of the electrons is5.67 eV. That of the hydrogen ions is 3.74 eV. These results are slightly higher than the values of experimental
report[1] because the electrons are caught and accelerated
by the fluctuation of the potentiaL
Both number densities of electron and hydrogen ion
are around 1012 cm- 3 and these values are approximately
equal to the experimental values[1].
6 Conclusion
In this work, a simple model for the simulation of theplasma in the cylindrical discharge tube with axial magnetic field was established. The results of this calculationagreed well with the experimental results[1]. From theseresults, this model could be useful for studying the plasma
in the cylindrical discharge tube with axial magnetic field.
The simulation of the plasma could be done more accurately by examining the width of llt, the number of thesuper particle and the boundary condition of the Maxwellequation. Furthermore, we will be able to analyze theplasma jet emitter by considering the collision mechanisms
and the initial condition of particles.

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106

eV

105
~~ 104
Illc.

0 103
l5.c
E~1Q2

10110°~~~~~~~~~~~~~~~

10"310"210"110°101

1Q210S

104

Energy (eV)Fig.6 The distribution of the hydrogen ion energy.

References[1] Fumiaki Noda, Kyushu University, The master theses: Study of small PIG ion source for super conductive
cyclotron (1994)[2] C.K. Birdsall: Plasma Physics via Computer Simulation, Mac Graw Hill (1985)-54-