23P171-B
Numerical Studies of Ponderomotive Acceleration and Ion Cyclotron
Resonance: Application to Next Generation Electric Thrusters
ポンデロモーティブ加速とイオンサイクロトロン共鳴の数値解析:
次世代電気推進の開発に向けて
F. Otsuka1, T. Hada1, T. Ichihara1, S. Shinohara2, T. Matsuoka3, T. Tanikawa4
大塚史子1,	 羽田亨1,	 市原拓1,	 篠原俊二郎2,	 松岡健之3,	 谷川隆夫4	 
1

2

ESST, Kyushu University, Kasuga, Fukuoka, 816-8580, Japan
Inst. Eng., Tokyo University of Agriculture and Technology, Koganei, Tokyo 184-8588, Japan
3
Japan Aerospace Exploration Agency, Sagamihara, Kanagawa 252-5210, Japan
4
RIST, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan	 1
九州大学大学院 総合理工学研究院 〒816-8580	  春日市春日公園 6-1
2
東京農工大学大学院	 工学研究院〒184-8588	  小金井市中町	 2-24-16
3
宇宙航空研究開発機構	  〒252-5210	  相模原市中央区由野台 3-1-1
4
東海大学 総合科学技術研究所	  〒259-1292	  平塚市北金目	 4-1-1

We have examined particle acceleration by external electromagnetic RF (Radio Frequency) field by means of test
particle simulations, and applied this concept to the development of next generation electric thrusters, as a part of theHEAT (Helicon Electrodeless Advanced Thrusters) project. When a localized transverse electromagnetic field and adivergent background magnetic field are considered as external electromagnetic fields, two acceleration processes
coexist: the ponderomotive acceleration and the ion cyclotron resonance. Based on a model that includes ion-neutral
collisions and ion wall-loss, we estimate the thrust as a function of external field parameters.

1. Introduction‘Electrodeless’ plasma thruster is a promising
candidate for the next generation electric thrusters,
and has been extensively studied worldwide. In
particular, research and development of theelectrodeless thruster using helicon plasma sourceis the main target of the HEAT (HeliconElectrodelessAdvancedThrusters)
project(overview of the project will be presented in thisconference [1]). As a part of the project, we report
here one type of the plasma acceleration schemes,i.e., the ponderomotive and the ion cyclotron
resonance (PA/ICR) acceleration.
The ponderomotive force arises from a spatial
gradient of an electromagnetic field energy density.
The schematic picture of the PA/ICR scheme isshown in Fig. 1. Electrodes are placed outside theplasma region, so that the erosion of the electrodes
can be avoided. A background magnetic field isoriented mainly along the z-axis and a linearlypolarized transverse RF electric field is applied withits magnitude E(z) given as a Gaussian pulse. The
ponderomotive pseudopotential is then written as,!=

q2
E 2 (z)4m " 2 # $(z) 2 ,(1)

where ω is the RF wave frequency, and m, q, andΩ are the ion mass, charge, and the gyro-frequency,respectively. If Ω is uniform in z, Φ is symmetricFig.1. Schematic picture of PA/ICR schemewith respect to z, and so the ponderomotive force is
oppositely directed on the two sides of the potential.
On the other hand, if Ω is given in such a way thatit decreases along the z-axis and the resonance point
coincides with the peak of E(z), the sign of Φ isreversed at the peak and the ponderomotive force
becomes uni-directional, so that an ion can obtain
net energy as it passes through the potential [2]. We
apply this concept to the plasma thruster.
In the above configuration, the ICR acceleration
co-exists, i.e., the perpendicular ion heating
followed by the energy conversion fromperpendicular to parallel direction by the mirroringeffect. A well-known application of the ICR to theplasma thruster is the Variable Specific Impulse
Magnetoplasma Rocket (VASIMR) [3]. In thispresentation, we discuss ion acceleration due to thePA combined with the ICR mechanism. The effectsof ion wall-loss and ion-neutral collisions areincluded.

(a)vz[km/s]

8resonancepoint

6parallelacceleration

420050100z[cm](b)

150200Magnetic Mirror¡!! [eV]

64PA

20ICR-20246¡[eV]

8310210110010-110234567 8 9100234E0 [V/m]Fig.3. Thrust vs. Electric field intensity

The energy gain for vb=400 m/s is larger than thatfor vb=1600 m/s, since slower particle can staylonger time near the resonance point, leading tolarge energy gain by the ICR and the PA. The ratioof the energy gain by the PA to the ICR is typicallyaround 1/3.
Figure 3 estimates the thrust, F=(1-σ)(nπR2mvz)vz,
as a function of E0, where σ is a rate of theabsorbed to the initial macro-particles, n is the ion
number density (=1018/m3), R is the plasma radius(=0.03 m), and vz is the exhaust velocity at z=2 m.
Different groups of runs with and without thewall-loss and the ion-neutral collisions are shown.
Theoretical estimate is given by Δε//=Δε ⊥~(πq2E02/2m)(LB/ωvb), assuming the energy gain by
the ICR only [2]. The parameters are vb=400 m/s
and the others are the same as in Fig. 2 except E0.
When the wall-loss and the collisions are bothincluded, the thrust saturates at a constant level as
E0 is increased. A shielding effect of the external
electric field will be also discussed in this presentation. A proof of principle experiment of this scheme
has been launched recently at Tokai University.
Acknowledgments
This work has been supported by the Grants-in
Aid for Scientific Research under Contract No. (S)21226019 from the Japan Society for the Promotionof Science.

10
8

without wall-loss and without collisions
with wall-loss and without collisions
with wall-loss and with collisions
Theory410

Thrust [mN]

2. Numerical Model and Results
We have performed test particle simulations basedon the configuration described above. The external
field parameters are the gradient scale length alongz for the divergent magnetic field, LB, the width of
the Gaussian pulse for the electric field, LE, and themaximum intensity of the electric field, E0. Ion
species is assumed to be argon. The magnitude of
the magnetic field at the resonance is 400 G, so thatω ~ 9.6 104/s. A cylinder with 20 cm diameter forz < 1 m and no bounded space for 1 m < z < 2 m areassumed for a vacuum chamber and an exhaust
region, respectively. The absorbing boundary
conditions at the wall are used. For the ion-neutral
collisions, we use the Monte-Carlo model [4]. It is
assumed that the neutral particles are always at rest
and that the particle scattering is isotropic.
Figure 2 shows a typical example of (a) the ion
trajectory and (b) the energy evolution for two
different initial particle velocities. Here, ε// and ε⊥	 are the parallel and the perpendicular ion energy
components, respectively. The parameters used are
LB = 1 m, LE = 0.4 m, and E0 = 30 V/m. In this run,the wall-loss and the collisions are not considered.
In (a), the particles are gradually accelerated along z,
as they pass through the resonance point at 0.5 m.
In (b), the particles gain energies, ε⊥and ε//, by theICR and the PA, respectively, and then the energy
conversion from ε⊥to ε// occurs by the mirroring.

10Fig.2. Typical ion orbits for initial axial velocities, vb=
400 and 1,600 m/s, shown by the solid and the dashedlines, respectively.

References[1] H. Nishida, S. Shinohara, T. Tanikawa, T. Hada, I.
Funaki et al.: proceeding of Plasma 2011 (thisconference), Kanazawa, 22-25 Nov., 2011[2] I.Y. Dodin, N.J. Fisch, and J.M. Rax: Phys. Plasmas,
11 (2004) 5046.
[3] E.A. Bering III, F.R. Chang Diaz, J.P. Squire, T.W.
Glover, et al.: Phys. Plasmas 17 (2010) 043509.
[4] V. Vahedi and M. Surendra: Comput. Physics.
Commun. 87 (1995) 179.