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
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1 tobari@ecei.tohoku.ac.jp Keywords : Plasma Flow, Mach Probe, Plasma Acceleration, Electric Propulsion, MPD Thruster
2 Outline 1. Introduction. Electric Propulsion 3. Mach Probe Experiment in the HITOP Device 4. Magnetic Nozzle Acceleration of MPDA Plasma 5. Summary
3 Introduction Image of MUSES-C ion engine Double-Beltrami
![mission long-term station-keeping manned Mars mission Thrust density [N/m ] 10 6 10](/docs-images/82/86373319/images/4-2.jpg "4 10 Thermal Arcjet Chemical PPT Hall Thruster MPD Thruster Ion Engine 10 0 10 10 3")
![10 4 10 5 Hall thruster Specific impulse [sec] MPD thruster Parameters for Thrust](/docs-images/82/86373319/images/4-3.jpg "Performance Thrust : F = mu Specific Impulse : F I sp = = mg U g [ sec] Thermal")
4 Introduction to to Electric Propulsion(EP) Chemical Propulsion (CP) Large thrust density to lift off the earth gravity Low I sp ( 500sec) Electric Propulsion(EP) Ionization by electric power Power source: solar cell, nuclear reactor High I sp ( sec) with small consumption of propellant Useful for interplanetary mission long-term station-keeping manned Mars mission Thrust density [N/m ] Thermal Arcjet Chemical PPT Hall Thruster MPD Thruster Ion Engine Hall thruster Specific impulse [sec] MPD thruster Parameters for Thrust Performance Thrust : F = mu Specific Impulse : F I sp = = mg U g [ sec] Thermal arcjet Ion engine
5 Recent Achievement of of EP in in apan Image of MUSES-C ion engine Ground test of MPDT >>May 9, 003 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. (ref.)
6 Outline 1. Introduction. Electric Propulsion 3. Mach Probe Experiment in the HITOP Device 4. Magnetic Nozzle Acceleration of MPDA Plasma 5. Summary
7 Laser Induced Fluorescence (LIF) Plasma Flow Measurement Visible-Light Spectroscopy (Doppler shift) Mach Probe j is M i = / (a) up-down (b) perp-para
8 Theoretical Model of of Mach Probe ~up-down~ up-down Hudis and Ridsky model (1970) 1 M i << 1, T i << T e Stangeby model (1984) 1-D fluid model M i < 1 Hutchinson model (1987) 1-D fluid model M i < 1 ρ i <r p : ρ i >r p : M c Chung and Hutchinson (1988) 1 Kinetic model LIF Gunn(001) up down = M exp M i c M c : const. M i < 0.4
9 Hutchinson PIC Simulation PIC (v f ) (θ ) Γ( v ) f, π up Mi Γ (v f, θ ) v f : (T e / m i ) 1/ Γ (v f, θ ) : n i (T e / m i ) 1/ Γ = = exp ( v ) f,0 down Mc (example) cosθ (T i / T e =1)
10 Theoretical Model of of Mach Probe ~perp-para~ perp-para perp-tip = κen i γ ete + γ it m i i ( κ : T i / T e ) M i > 1 Mi = en U = i Kuriki and Inutake (1974) M i << 1 = exp M i (ii) Stangeby and Allen(1971) (i),(ii) M i = 1 U = (i) γ γ κ ete + iti mi 1 = exp α Mi ln ( α = κ )
11 HITOP(High density TOhoku Plasma) Device Magnetic Coils Spectrometer Mach Probe Array Segmented End-Plate +0.4 MPDA Laval Nozzle Coil X Plasma X(m) Y Z TMP D Movable Probe TMP 0 1 Z(m) 3 Typical Parameters Cylindrical chamber : length = 3.3 m, inner diameter = 0.8 m Magnetic field : up to 0.1 T Plasma source : MPD Arcjet Ion temperature : 0-40eV Electron temperature : 3-10 ev Plasma density : ~10 15 cm -3 (near the MPDA) Ionization degree : 50-90%
12 MPD(Magneto-Plasma-Dynamic) Arcjet Cross Section of MPDA Fast Acting Valve Gas Flow Gas Reservoir 0.1 (m) Insulator Anode φ 0.03(m) φ 0.01(m) Plasma Cathode 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 cm -3 near the MPD outlet), highly-ionized plasma is produced. X Y Z Principle of Plasma Acceleration (a) Self-Field Acceleration (Anode) j (b) With Externally-Applied Field j (Cathode) (Anode) (Anode) (Cathode) (Anode) θ j z j j z j θ =j r B z F r =j z B θ j r j r B z B z F z =j r B θ F
13 Directional Langmuir probe (DLP) Hutchinson Ion saturation current distribution as a function of θ (cos θ)
14 Hutchinson Hutchinson MPD r p < ρ i 1.5 < T i / T e < 3 Hutchinson T i / T e = (a) M i = 1.3 (U =8km/s, T i =8.6eV, T e =5.3eV) (b) M i = 0.8 (U =19km/s, T i =11eV, T e =6.eV) Good agreement!! cosθ = -1
15 Mach Probe Calibration ~ ~ up - down up down M = exp M i c perp - para ( M i > 1 ) : ( M i < 1 ) : M i = M = exp i 1 = ln M c = 0.40 κ = 0.33
16 M i up - down = M c ln up down (M i > 1) (M i < 1) M M perp - para i i = = 1 ln = ln ( ) M i > 1 ln up down M i < 1 ln ln up down (κ = 0.33 (α = 1.1))
17 up - down perp - para Comparison between exp. and PIC simulation DLP PIC 0.4 < M i < < M i < 1.5
18 Outline 1. Introduction. Electric Propulsion 3. Mach Probe Experiment in the HITOP Device 4. Magnetic Nozzle Acceleration of MPDA Plasma 5. Summary
19 Anomalous ion heating in in the MPDA Plasma u z [km/sec] T [ev] M 30 HeI(atom) 0 HeII(ion) I d =8.6kA, dm/dt=0.06g/s(he), B 0 =1kG(uniform) at Z=4cm T i increases steeply Discharge Current I [ka] d Flow Energy [ev] M u mu i i = = < Cs kb( γ iti + γ ete ) i.e. Thermal energy > Flow energy Why is the Mach number limited? What is the mechanism of the conversion the input energy to the thermal energy? Detailed measurement of j B force field flow field 1
![Spatial Distribution of ofjxb Force B Z [G] Magnetic Field distribution in the Vicinity of MPDA 1000 800 600 400 00 net field strength B Z 0 0 50 100 150 Z [cm] Y [cm] 10 5 0-5 I d =7.](/docs-images/82/86373319/images/20-0.jpg "kA, V d =00V,dm/dt=0.")
20 Spatial Distribution of ofjxb Force B Z [G] Magnetic Field distribution in the Vicinity of MPDA net field strength B Z Z [cm] Y [cm] I d =7.kA, V d =00V,dm/dt=0.1g/s(He), B 0 =870G(uniform) B θ :300[G] X[cm] Z[cm] 30 deformation of magnetic field Spontaneous formation a helicallyconverging magnetic nozzle in the vicinity of MPDA outlet.
21 Spatial Distribution of ofjxb Force Plasma Current Distribution Schematic of the drag force generation MPDA B r j θ B θ j r jxb Force Distribution F F - F + z z Z = jθ Br + jr B θ F z - F z + X [cm] Drag force Accelerating force
22 Energy Balance in in the MPDA Plasma Flow Generalized Bernoulli s Equation Related to the Applied-Field Acceleration** 1 γ P Bθ Bθ BZuθ ( u + u ) + + = const. Z θ Flow energy ~10 8 γ 1 ρ µ Thermal energy ~ ρ µ ρu Self-field energy ~ z MPDA scan lense Y to spectrom eter Laval Nozzle Coil Plasma Additional energy X Z ~10 7 Mi <1 Mi >1 Thermal > Flow. T i / T e ~.. Why? Magnetic nozzle Thermal energy Flow energy Momentum Conversion A M U T ** K.F. Schoenberg et al. ; Phys of Plasmas, 5, p.090 (1998)
23 Magnetic Laval Nozzle Formation scan lense to spectrometer Magnetic Field Line Profile in Vacuum MPDA Laval Nozzle Coil B [T] MPDA X Y Z Nozzle Throat Plasma B LN Z [cm] uniform Laval I d [ka] I LN [ka] Quasi-Steady Discharge ~1ms Time [ms] Z[cm] (a) Discharge Current: I d (b) Nozzle Coil Current: I LN
24 Characteristics in in Magnetic Laval Nozzle Improvement of Acceleration Performance I d = 7.kA, dm/dt = 0.1g/s (He), Nozzle Throat at Z=17cm. The thermal energy is converted to the flow energy by passing through the Laval nozzle and a supersonic plasma flow is achieved. assuming γ i = 5/3
25 Various Behavior in in the Laval Nozzle
26 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 dm M du U ( γ 1) ( 1) + γ M da = M ( M 1) i <1 M i >1 A A 1 da = M 1 A M U dt = T M dρ M = ρ M 1 M da 1 A da A T
27 Comparison with 1-D Isentropic Flow Model
28 Summary MPD DLP MPD
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6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
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1 Physical Chemistry I (Basic Chemical Thermodynamics) [I] [II] [III] [IV] Introduction Energy(The First Law of Thermodynamics) Work Heat Capacity C p and C v Adiabatic Change Exact(=Perfect) Differential
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