24P137-P
Monte-Carlo Simulation of glow discharges in magnetic field
粒子モンテカルロ法による磁場中グロー放電の挙動解析
Yuuichi ASAHI, Hiroaki Tsutsui, Shunji Tsuji-Iio and Ryuichi Shimada
朝比 祐一, 筒井 広明、飯尾 俊二、嶋田 隆一
Tokyo Institute of Technology
2-12-1-N1-11, Ookayama, Meguro-ku,
東京工業大学 〒152-8850 東京都目黒区大岡山2-12-1-N1-11
A Monte-Carlo based simulation code is applied to glow-discharge, especially high frequency glowdischarge (HF-GD), in magnetic fields. Both electric and magnetic fields are provided externally and are
not adjusted self-consistently. We have tried to examine the pre-breakdown phenomena and found that theorbiting electrons would play an important role in the uniformity of HF-GD plasma in magnetic fields.

1. Introduction
It is well-known that the wall surface
conditions of fusion devices are directly related toplasma performance. Thus, from the operational
point of view, it is quite important to keep thewall surfaces clean. The way to clean up the wall
surfaces is often regarded as wall conditioning ordischarge cleaning, wherein plasma is used toremove impurities from wall surfaces. In ITER,
the next generation experimental fusion reactor,
the wall conditioning method would be very
limited due to the presence of strong magnetic
fields. High frequency glow discharge cleaning(HF-GDC) is one of the candidates for wallconditioning in superconducting devices, likeITER. Although, it has been shown that HF-GDC
works well in some superconducting devices [1,2], including EAST and HT-7, the performance ofHF-GDC in other devices is unclear. Furthermore,
the basic mechanism of HF-GDC in magnetic
fields has not been explained theoretically yet.
Therefore, to apply this technique to ITER, wehave to reveal the basic mechanism of HF-GD
and evaluate its future performance in ITER.
2. Background
Glow discharge is the most common plasma
and is widely used for many purposes including
glow discharge cleaning (GDC) of tokamak wall
surfaces. It is sometimes used within magnetic
fields, e.g. Penning discharges, and its
characteristics in magnetic fields are well examined.
However, when it comes to strong magnetic fields,
plasma become very unstable and sometimes
cannot ignite. Unfortunately, this is the case inGDC in future superconducting devices whereinmagnetic fields are always present. By contrast, it isreported that HF-GD plasma within magnetic fields
is uniform and stable. HF-GD plasma also shows

similar characteristics with those of GD plasma
without magnetic fields [1].
3. Objectives
The objectives of this study are to reveal
the basic mechanism of HF-GD and to make areasonable model for it. First of all, we focusedon the pre-breakdown phase, since it is much easier toanalyze and it would be attributed to the shape of plasma.

4. Methodology
In order to simulate the glow discharge at thevery beginning, we traced the trajectory of fastelectrons emitted from wall surfaces and introduced
collision effects based on Monte-Carlo method. For
simplicity, we choose Ar gas as background andassume that following atomic processes aredominant in inelastic collisions and ignored others.
Ionization: e  Ar  e  Ar   e
Excitation: e  Ar  e  Ar *Thus, in our case we accounted for N = 3 collisional
events (elastic collision, excitation, ionization) byusing Nanbu method [3]. Firstly, we generate arandom number U (0, 1) and obtain the integer iform i = [NU+1], where [ ] is Gauss’s symbol. Thenthe reaction probability for the specified reaction is
calculated at every time step.
Pi  N Ar c i ( )t , i  1, N (1)where N Ar is the number density of Ar gas,c is the electron speed,  is the energy ofelectron, and  i is the cross section of i-thevent.
Secondly, we generate another random
number U  (0, 1) and check whether U  satisfies
U   (i / N )  Pi or U   (i / N )  Pi . In the former
case, i-th collision occurs while the latter case

causes no collision.
5. Summary
The experiments in EAST showed that
HF-GD plasma becomes more uniform at lower
filling pressure [1]. This means that the mechanismof its uniformity can become clear at lower pressure,which then indicates that collision-less electron
trajectories are important. Firstly, we carried out
simulation to examine the collision-less electron
trajectory in magnetic and/or electric field. The
impact of electric field can be found in the different
electron trajectories with and without electric field(See Fig.1 (a) and (b)). The electric field is calculated
from the electric potential shown in Fig. 1 and themagnetic field only includes the toroidal component
without any ripples.

energetic electrons can only exist near the electrode.
By contrast, with alternating electric field, a part ofaccelerated electrons can survive and continue
circular motion with higher energy (see Fig. 3).

Fig. 3. Time evolution of single electron energy

6. Future works
We are planning to introduce collisions ofions and examine their behavior. The second step isto add the self-consistent effect to our model with
PIC method.

Fig. 1 electric potential
The impact of electric field can be found in the different
electron trajectories with and without electric field (SeeFig.2 (a) and (b)).

Fig. 2. A particle trajectory in Bt = 1.0 [T], (a)without E, (b) with E (f = const., U = 2 [kV]),and (c) with E (f = 100 [kHz], U = 2 [kV])Without electric field, electrons continue thecircular motion inside the torus (see Fig. 2 (a)),
whereas electrons under electric field fall into theelectrode as shown in Fig. 2 (b, c). Secondly, we
calculated the energy change of an electron fordifferent frequencies. For constant electric field,
electrons are always accelerated toward theelectrode. Thus when they are approaching to theelectrode their speed will increase, but they willsoon be in touch with electrode. Therefore,

References[1] J. Li et al, Wall conditioning towards the utilization
inITER,
J.
Nucl.
Mater(2010),
doi:10.1016/j.jnucmat.2010.10.048[2] M. Shimada et al, Wall conditioning on ITER, J.
Nucl.
Mater(2010),
doi:10.1016/j.jnucmat.2010.11.085[3] K. Nanbu, Jpn. J. Appl. Phys., vol. 33, pp.4752 4753 , 1994.