電磁加速プラズマ流の制御と マッハプローブの特性評価

第7回原研若手研究会

2004年3月19日

電磁加速プラズマ流の制御と

マッハプローブの特性評価

電磁加速プラズマ流の制御と

マッハプローブの特性評価

東北大学 大学院工学研究科

戸張 博之

e-mail : tobari@ecei.tohoku.ac.jp

Keywords

:

Plasma Flow

, Mach Probe, Plasma Acceleration,

Electric Propulsion, MPD Thruster

Outline

Outline

1. Introduction

2. Electric Propulsion

3. Mach Probe Experiment in the HITOP Device

4. Magnetic Nozzle Acceleration of MPDA Plasma

5. Summary

Introduction

Introduction

プラズマの“流れ”と電磁場との相互作用

天体プラズマの物理

プラズマの閉じ込め改善

電気推進機の開発

Image of MUSES-C ion engine

動圧を利用した高ベータ プラズマ閉じ込め

TOHOKU UNIV. 100 102 104 106 102 103 104 105 T h ru s t d e n s it y [N /m 2]

Specific im pulse [sec]

M P D Thruster The rm a l Arcjet C hem ical P P T Ion E n gine Ha ll T hruster

Hall thruster _{MPD thruster}

Thermal arcjet Ion engine

zIonization by electric power

zPower source: solar cell, nuclear reactor zHigh I_sp (≧103_-104_sec)

with small consumption of propellant

zUseful for interplanetary mission

long-term station-keeping manned Mars mission

Chemical Propulsion (CP)

to lift off the earth gravity

zLow I_sp (≦500sec)

Parameters for Thrust Performance U m F = : Thrust

[ ]

Introduction to Electric Propulsion(EP)

Introduction to Electric Propulsion(EP)

Recent Achievement of EP in Japan

Recent Achievement of EP in Japan

Ground test of MPDT

>>May 9, 2003 

The MUSES-C ( Hayabusa ) spacecraft mounting four ECR ion

thrusters was successfully

launched. Asteroid sample return mission is now under progress.

>>March 18, 1995

The MPD thruster onboard the Space Flyer Unit (SFU) was successfully pulse-operated in space with few misfirings.

Outline

Outline

1. Introduction

2. Electric Propulsion

3. Mach Probe Experiment in the HITOP Device

4. Magnetic Nozzle Acceleration of MPDA Plasma

5. Summary

Plasma Flow Measurement

Plasma Flow Measurement

¾Laser Induced Fluorescence (LIF)

¾Visible-Light Spectroscopy (Doppler shift) ¾Mach Probe →簡便で，空間分解能に優れる．

流れに対して異なった方向に捕集面を向け，そのイオン飽和電流値 j_isの信号値の

違いから流速，イオンマッハ数 （ M_i = 流速 / 音速 ）を求める

Theoretical Model of Mach Probe

~up-down~

Theoretical Model of Mach Probe

~up-down~

＜ up-down タイプ＞

Hudis and Ridsky model (1970) 非磁化プラズマ

最初にマッハプローブを提案 

1次元のエネルギー保存より導出 M_i << 1, T_i << T_e

Chung and Hutchinson (1988) 磁化プラズマ 1次元Kinetic model， 粘性の効果を考慮   Hutchinson model (1987) 磁化プラズマ 1-D fluid model，粘性による輸送効果を考慮，M_i < 1 Stangeby model (1984) 磁化プラズマ 1-D fluid model，粘性の効果は無視，M_i < 1 ρ_i< r_p : 磁化プラズマ ρ_i> r_p : 非磁化プラズマ M_c を決めるために… LIFを用いた較正実験：Gunn(2001) 磁化プラズマ中で粘性を考慮したモデ ルとよい一致（実験は M_i < 0.4 ） 非磁化プラズマ中ではモデルが確立さ れていない！！

const.

:

exp

M

M

M

J

J













=

Hutchinson PIC Simulation

Hutchinson PIC Simulation

PICコードを用いて，非磁化プラズマ中に球プ ローブがある際，プラズマの流れ ( v_f )に対して ある角度(θ )をもった点に流れ込んでくるイオン フラックス Γ (v_f , θ ) を計算． シミュレーションより得られたモデル式

(

)

( )













=

=

Γ

Γ

_exp

0

,

,

M

M

J

J

v

v

π

Theoretical Model of Mach Probe

~perp-para~

Theoretical Model of Mach Probe

~perp-para~

＜ perp-para タイプ＞ 通常のプローブの理論よりperp-tipのイオン飽和電流 J_⊥は， i i i e e i

m

T

T

en

J

=

κ

γ

+

γ













=

2

exp

M

J

J

κ

γ

γ

M

m

T

T

U

J

J

=

+

=

U

en

J

=

• • •(ii)

Stangeby and Allen(1971)

(i) ,(ii) が M_i = 1 でなめらかに接続す るように下式のようにαを導入 • • • (i) TOHOKU UNIV.

(

α

κ

)

α

ln

exp

=

−













⋅

=

M

J

J

HITOP(High density TOhoku Plasma) Device

HITOP(High density TOhoku Plasma) Device

MPDA Magnetic Coils 2D Movable Probe TMP Plasma 0 1 2 3 Z(m)

Mach Probe Array Spectrometer Segm ented End-Plate Y X Z

X(m)

Cylindrical chamber : length = 3.3 m, inner diameter = 0.8 m

Magnetic field : up to 0.1 T Plasma source : MPD Arcjet

Ion temperature : 20-40eV Electron temperature : 3-10 eV

Plasma density : ~1015_cm-3_{(near the MPDA) Ionization degree : 50-90%}

TOHOKU UNIV.

(b) With Externally-Applied Field

(Anode) (Cathode) j jz jr j F_θ=jrBz B z Bz (Anode)

Principle of Plasma Acceleration

Cross Section of MPDA

Anode Plasm a 0.1 (m ) Ga s Rese rvo ir Ga s Flo w _Cathode φ 0 .0 3 (m ) φ 0 .0 1 (m )

Fast Acting Valve

Y

X Z

In sula to r

MPD(Magneto-Plasma-Dynamic) Arcjet

MPD(Magneto-Plasma-Dynamic) Arcjet

(a) Self-Field Acceleration

(A node) (Cathode) j jz jr j B_θ Fz=jrBθ F Fr=jzBθ (Anode)

The MPDA has a coaxial structure with a center tungsten rod cathode and an annular molybdenum anode.

By use of a fast-acting gas-puff valve, a quasi-steady ( ~1 msec ), high-density

(up to 1015_cm-3 _{near the MPD outlet),}

Hutchinsonモデルの検証実験

Hutchinsonモデルの検証実験

Ion saturation current distribution as a function of θ (cos θ)

Hutchinsonモデルの検証実験

Hutchinsonモデルの検証実験

TOHOKU UNIV. Hutchinsonモデルとの比較

(a) M_i = 1.3 (U =28km/s, T_i =8.6eV, T_e =5.3eV)

(b) M_i = 0.8 (U =19km/s, T_i =11eV, T_e =6.2eV)

実験条件

Mach Probe Calibration

~

_~

Mach Probe Calibration

~

_~

κ i || M J J = ⊥         = ⊥ α exp α | | M_i J J 亜音速流 ( M_i < 1 ) : 超音速流 ( M_i > 1 ) :       ₌₋ κ ln 1 α

κ = 0.33













=

exp

M

M

J

J

M

= 0.40

⊥ ⋅ = J J M_i κ ||













⋅

=

ln

J

J

M

M

(

α

=

−

ln

κ

)













∝

ln

J

J

J

J

























∝













J

J

J

J

ln

ln

M

> 1

M

< 1

up - down タイプ perp - para タイプ

Comparison between exp. and PIC simulation

0.4 < M

< 1.5

DLPによる計測結果

PIC シミュレーションによる結果

0.4 < M

< 1.5 の広い範囲で

良い一致を示した

Outline

Outline

1. Introduction

2. Electric Propulsion

3. Mach Probe Experiment in the HITOP Device

4. Magnetic Nozzle Acceleration of MPDA Plasma

5. Summary

Anomalous ion heating in the MPDA Plasma

Anomalous ion heating in the MPDA Plasma

2 5 0 1 0 2 0 3 0 _{H e I(ato m )} H e II(io n ) u z [km /s e c ] 0 5 1 0 1 5 2 0 F low E n e rgy [ e V ] 0 1 0 2 0 3 0 T [ e V ] 0 0 .2 0 .4 0 .6 0 .8 1 0 2 4 6 8 1 0 M D isch a rg e C urrent I [k A ] I_d=8.6kA, dm/dt=0.06g/s(He), B₀=1kG(uniform) at Z=4cm T_i increases steeply.

(

)

γ

γ

¶ Why is the Mach number limited?

¶ What is the mechanism of the

conversion the input energy to the thermal energy?

Detailed measurement of ¾ j×B force field

¾ flow field

Spatial Distribution of jxB Force

Spatial Distribution of jxB Force

5 0 -5 ₀ 1 0 2 0 3 0 -1 0 -5 0 5 10 Z [cm ] X [cm ] Y [c m ] B_θ:300[G ] 0 200 400 600 800 1000 0 50 100 150 B Z [G ] Z [cm] ∆B Z

net field strength

I_d=7.2kA, V_d=200V,dm/dt=0.1g/s(He), B₀=870G(uniform)

TOHOKU UNIV.

Magnetic Field distribution in the Vicinity of MPDA

deformation of magnetic field

Spontaneous formation a

helically-converging magnetic nozzle in the

Spatial Distribution of jxB Force

Spatial Distribution of jxB Force

X [cm] M PDA B_θ jr

Fz

+

Fz

B

j

B

j

F

=

−

+

F

_F

Drag force

Schematic of the drag force generation

Energy Balance in the MPDA Plasma Flow

Energy Balance in the MPDA Plasma Flow

P la sm a Y X _Z M P D A sc an to s p ec trom e ter len s e Laval Nozzle Coil Generalized Bernoulli’s Equation Related

to the Applied-Field Acceleration**

(

)

Thermal > Flow. T_i / T_e ~ 2. …. Why?

Flow energy Magnetic nozzle

Thermal energy

Momentum Conversion

Magnetic Laval Nozzle Formation

Magnetic Laval Nozzle Formation

0 10 20 30

Z[cm ]

M PDA Laval Nozzle Coil 0 2 4 6 8 I d [k A ] 0 1 2 0 0.5 1 1.5 2 I LN [k A ] Time [m s] (a) Discharge Current: I_d (b) Nozzle Coil Current: I_LN Quasi-Steady Discharge ~1ms Plasm a Y X _Z M PDA s ca n

to spe ctro m ete r

le ns e 0 0.1 0.2 uniform Laval 0 10 20 30 B [ T ] Z [cm ] B_LN Nozzle Throat

Characteristics in Magnetic Laval Nozzle

Characteristics in Magnetic Laval Nozzle

TOHOKU UNIV. Improvement of Acceleration Performance

I_d = 7.2kA, dm/dt = 0.1g/s (He), Nozzle Throat at Z=17cm.

assuming γ_i = 5/3 The thermal energy is converted to the

flow energy by passing through the Laval

nozzle and a supersonic plasma flow is

Various Behavior in the Laval Nozzle

1-D Isentropic Flow Model

1-D Isentropic Flow Model

The MPD plasma flow is modeled

by

a one-dimensional adiabatic

flow with a constant entropy

at any

cross section along a flux tube.

U Nozzle Throat _A

(

)

(

)

(

)

A

dA

M

M

d

A

dA

M

M

T

dT

A

dA

M

U

dU

A

dA

M

M

M

dM

1

1

1

1

1

1

2

1

2

−

=

−

−

=

−

=

−

−

+

=

ρ

ρ

γ

γ

_M

<1

M

>1

A

M

U

T

Comparison with 1-D Isentropic Flow Model

Summary

Summary

¾

DLPを用いたマッハプローブの較正実験

¾

MPDアークジェットプラズマ中の電磁場計測

¾

磁気ラバールノズルによるプラズマ加速

東北大学におけるMPDアークジェットを用いた高ベータ・高速プラズマ流

の生成と制御に関する最近の研究結果を紹介した．

高ベータ・高速プラズマ流の制御

アドバンスト核融合，宇宙ジェットの構造解明

および電気推進機開発への貢献