Proceedings of International Forum for Green Asia 2017
Special issue of Evergreen - Joint Journal of Novel Carbon Resource Sciences & Green Asia Strategy

P-03

Energy Balance Development for RF-induced Plasma Breakdown in QUEST
R. YONEDA1 and K. HANADA2
1Interdisciplinary Graduate School of Engineering, Kyushu University
2
Research Institute of Applied Mechanics, Kyushu University
Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan,Abstract
Plasma breakdown by radio frequency (RF) is a common method to plasma devices. In theQUEST spherical tokamak, we employ electron cyclotron resonance heating (ECRH) to initiate
plasma, which is RF injection in EC frequency range (2.45, 8.2 and 28GHz). Illustration of RFinduced plasma breakdown requires particle and energy balance equation together for detailed
description. In this study, we discuss the development of energy balance equation to investigate
experimental observations of RF-induced breakdown in QUEST.
space for CS is technically limited andoperation without CS is the important issue.
CS-less design can directly contribute toenhancing its compactness and costeffectiveness. For this purpose, non-inductive
plasma current start-up experiments withECRH have been demonstrated in STs withexternal vertical field Bv: MAST, CDX-U,
LATE TST-2 and QUEST. Experiments onCDX-U and DIII-D show a parameter scan ofplasma current Ip with different Bv, RF power
and neutral pressure. In the experiments, Ip
changes proportionally to RF power,
inversely to neutral pressure and Bv. They
also present that confined electrons in open
field are important in breakdown phase. This
indicates magnetic configuration andstrength of Bv play essential roles in RFinduced breakdown. In QUEST, theimportance of incubated electrons due tomagnetic configuration has been also
confirmed by experiments and a modelingthat lifetime of electrons highly contributes tobreakdown occurrence [4]. In the modelingpreviously developed only solves particle
balance equations in time. Therefore, in thisstudy, we discuss development of energybalance equations to include RF power
dependence.

1. Introduction
When electric field is applied topartially ionized gas, electrons areaccelerated and collide with neutrals forfurther ionizations. Repetition of this process
yields current, and plasma discharge isachieved. In tokamak operations, breakdownof plasma is the first step of the plasma buildup. Here, the definition of breakdown is thecondition that plasma discharge is achieved
and sustained. The conventional way toobtain breakdown in tokamak is to apply
toroidal electric field E by changing coilcurrent of center solenoid (CS) in time, which
accelerates electrons. This method is called
inductive breakdown. Breakdown conditions
for inductive plasma start-up have been
intensively investigated because it was one
critical issue for ITER design [1]. It is welldescribed that the minimum E for inductive
breakdown is governed by prefill gas
pressure and connection length. ITER plan
employs multi-pole field null configuration
and additional radio RF power injection tosupport inductive breakdown by preionization, because of the difficulty to supply
sufficient E[2]. Intensive studies hadpromoted in many devices to obtain reliablebreakdown with ECRH [3].Consequently,
there remain no technical problems to realizea reliable breakdown in ITER with ECRHassist [1]. Besides, in spherical tokamaks(STs) with low aspect ratio of plasma, the2. Particle and Energy Balance Equations

The model we developed in this paper isbased on the Townsend avalanche theory. In8Proceedings of International Forum for Green Asia 2017
Special issue of Evergreen - Joint Journal of Novel Carbon Resource Sciences & Green Asia Strategy

P-03
𝑖𝑘𝑗𝑘
is reaction rate for reaction i between jand k, np is population density. The first termof the right hand side of the equation stands
for the production of particles and the second
is the loss term represented by 𝜏loss.
Energy balance equations accompaniedwith particle balance [6] is written as,

this model, plasma breakdown is achieved
when the ionization rate of neutral hydrogenatoms and molecules caused by electron
impact exceeds the loss rate of electrons.
Therefore, we can simply express the relation
between electron production and loss as,
𝑑𝑛e−1−1)= 𝑛e (𝜏ion− 𝜏loss
𝑑𝑡

3 𝑑𝑛𝑝 𝑇𝑝𝑖𝑖𝑖
= ∑ ∑ 𝜖𝑗𝑘𝑝
𝐸𝑗𝑘𝑝
𝑘𝑗𝑘
𝑛𝑗 𝑛𝑘
2 𝑑𝑡

−1−1
where 𝜏ionis the ionization rate and 𝜏loss
is the loss rate. Hence, electron density is,𝑗<𝑘 𝑖+ ∑ 𝐸𝑗𝑝 𝑘𝑗el 𝑛𝑗 𝑛𝑝 + 𝑃RF,𝑝 ,𝑗−1−1)𝑡],𝑛e = 𝑛e0 exp[(𝜏ion− 𝜏loss𝑖where 𝑇𝑝 is Maxwellian temperature, 𝐸𝑗𝑘𝑝
the corresponding energy change forinvolved populations. 𝑘𝑗el is the elastic
collision reaction and 𝑃RF,𝑝 is the RF power
coupled to plasma. In the equation, the firstterm in the right hand side stands for inelastic
collisions and the second for elastic collisions.

where ne0 is the initial density of electrons.
−1For ionization rate 𝜏ion, it is usually referred
as Townsend first coefficient α. We propose a
different approach to evaluate RF-induced
breakdown by building up a model thatderives α in time as a result of overall
reactions such as ionization, recombinationand excitation. Following the database of thereactions [5], the model developed solves
particle balance equations in time. The
particle balance equation [6] is described as
below,𝑑𝑛𝑝
𝑑𝑡

𝑛𝑝

𝑖𝑖
= ∑𝑗<𝑘 ∑𝑖 𝜖𝑗𝑘𝑝
𝑘𝑗𝑘
𝑛𝑗 𝑛𝑘 − 𝜏loss

3. Simulation Results and Discussion

Firstly, in Fig.1, we demonstrated asimulation by ignoring elastic collisions forsimplicity. We assumed that power
absorption to plasma occurs a cylindrical EC
resonance layer, which is reasonable for RFinduced breakdown in tokamak magnetic
configurations. Electron density andtemperature become steady after the rapid
increase at 1ms. These observations are
consistent with experimental results.
Description in detail will be given in thepresentation.

,Particle Density [m^-3]𝑖where, 𝜖𝑗𝑘𝑝
is the number of lost or gained,
1017(a)

1016

e1015
1014

0.002

Electron Temperature Te [eV]

Reference
1. R. Toschi, IAEA-CN-53/F-I-2 225 (1991).
2. J. Stober, Nucl. Fusion 51, 83031 (2011).
3. V. Erckmann, Plasma Phys. Control. Fusion
36, 1869 (1994).
4. R. Yoneda, PHYSICS OF PLASMAS 24,062513 (2017).
5. J. R.K. Janev, ELEMENTARY
PROCESSES IN HYDROGEN-HELIUM
PLASMAS (Springer-Verlag, Berlin, 1987).
6. T. Wauters, Plasma Phys. Control. Fusion
53, 125003 (2011)

1013
0.004

0.006

0.008

0.010

0.008

0.010

Time [sec]

(b)
4030
20
100.002

0.004

0.006

Time [sec]Figure 1. Modeling results of particle andenergy balance equations. (a) Hydrogenparticle density and (b) electron
temperature in time.

9