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磁気ノズルを通過する遷音速流

プラズマ科学のフロンティアチュートリアル講演　　　　　　 NIFS. Aug. 3, 2007. 高速プラズマ流の生成とその応用　－その２－. 磁気ノズルを通過する遷音速流. 犬竹　正明. 東北大学名誉教授 , 電気通信研究所客員教授. Outline. Introduction Establishment of Mach probe measurement by comparing with spectroscopic measurements Plasma flow dynamics in various magnetic channels

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磁気ノズルを通過する遷音速流

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  1. プラズマ科学のフロンティアチュートリアル講演　　　　　　NIFS. Aug. 3, 2007 高速プラズマ流の生成とその応用　－その２－ 磁気ノズルを通過する遷音速流 犬竹　正明 東北大学名誉教授, 電気通信研究所客員教授

  2. Outline • Introduction • Establishment of Mach probe measurement • by comparing with spectroscopic measurements • Plasma flow dynamics in various magnetic channels • Choked flow in a uniform field, • Supersonic flow and shock in a simple mirror field. • Transonic flow in a magnetic Laval nozzle. • Evaluation of ion specific heat ratio gi • estimated from a spatial variation of Mi • Optimization of a magnetic nozzle for MPD thruster • Summary

  3. MPD (magneto-plasma-dynamic) arcjet Space laboratory SFU : 4 ton Self-Field Acceleration On-ground test of MPD thruster TOHOKU UNIV. Introduction MPDA is one of advanced plasma thrusters with a larger thrust for such as a manned Mars mission. MPDT on-board test in 1995-1996 ISAS, JAXA

  4. HITOP (HIgh density TOhoku Plasma) ( Mach probe ) Length : 3.3mDiameter : 0.8mAxial Bz : ～0.1 T Cathode : 10mmf Anode ：30mmf MPD Arcjet Quasi-steady pulse ~ 1ms Highly-ionized ~ 50-90% Density ~ 1018 - 1021 ( m-3) Ion temperature Ti ~ 20 - 40 eV Electron Te ~ 3 - 10 eV

  5. Typical time variation of MPD-arcjet plasma Quasi-steady ~ 1msec He plasma Id=7.2kA B0=0.087T

  6. Various Mach numbers TOHOKU UNIV. Ion acoustic Mach number : Mi • Spectrometer (Uz, Uq, Ti) • Mach probe, Langmuir probe (Uz, Te, ne) • Gridded energy analyzer (Ti) Cs : ion acoustic velocity Alfvén Mach number : MA ( Ion wave excitation ) VA : Alfvén velocity ( Alfvén wave excitation ) Magnetosonic Mach number : MS

  7. Para-perp Mach probe TOHOKU UNIV. Ion acoustic Mach number Mi • Spectrometer (Uz, Uq, Ti) • Mach probe, Langmuir probe (Uz, Te, ne) • Gridded energy analyzer (Ti) • Specific heat ratio ( giand ge ) Para-perp Mach probe k must be calibrated by use of spectroscopy. J. Plasma & Fusin Reseach, 81(12005)451-457. ( ion : unmagnetized )

  8. Phys. Lett. A78(1980)143. Pulsed MPD arcjet A. Komori, M. Inutake, R. Hatakeyama, N. Sato Magnetic field movable probes Vertical lines show mirror throat. lc : cell length = 10 cm lii : ion-ion mean fee path N : 10 cells Rm : mirror ratio 1.0 and 1.5 Z (cm) collisional collisionless ( lc > lii) ( lc < lii) n= 3.5x1014 to1. 5x1013cm-3 Incollisional regime, asymmetric density profile w.r.t. the midplane of a mirror cell. Z (cm) Old experiment on high-density-plasma injection into multiple mirror Density

  9. High density plasma injection into multiple mirror – continued -- Density (uncalibrated) Current ratio ~ Mach number Fluxdensity ○Is Mi at the mirror throat unity ? ○How large is the specific heat ratio?

  10. Spectroscopic measurement TOHOKU UNIV. Measurement setup Particle temperature (Doppler Broadening) Flow velocities (Doppler Shift) Measured spectrum lines HeI(atom) : 587.762 nm HeII(ion) : 468.575 nm

  11. Flow characteristics near the exit of MPD arcjet in uniform external field anode Rotational velocity Rotational velocity [km/s] [km/s] cathode Temperature Temperature [eV] [eV] Line intensity Line intensity [a.u.] [a.u.] TOHOKU UNIV. He atom He ion Id = 7.7 kA, dm/dt = 0.06 g/s(He), B0 = 0.1 T

  12. Choked flow in uniform external field TOHOKU UNIV. Bernoulli equation Linear increase of ion velocity Steep increase of Ti ( ion heating : Ti >> Te ) Saturation of Mi at unity (choking) Why is ion heating and choking ? What is optimum nozzle for a fast flow ? dm/dt = 0.06g/s(He), B0=1kG (uniform) at Z=4cm

  13. Choked flow in a uniform field (Bz=0.87kG) Id = 5.0kA, dm/dt = 0.15g/sec Uniform magnetic field Miz Axial profile of ne and MiZ Miq Mir gI =5/3 and ge =1 are assumed. measurement region

  14. Supersonic flow in a diverging nozzle Diverging magnetic field Miz Axial profile of ne and Mi Miq Mir Id = 5.0kA, dm/dt = 0.15g/sec gI =5/3 and ge =1 are assumed. measurement region

  15. Effect of ambient He gas pressure Ambient pressure increases with time due to neutral atoms recombined on the end plate. ×： t= 0.25 ms ■：　 0.30 ms △：　 0.35 ms ○：　 1.00 ms Decrease of Mach number due to charge exchange or ionization

  16. Evaluation of specific heat ratio Isentropic flow model Dynamics of a plasma flow in a diverging magnetic channel. Variation of ion Mach number depends on ion specific heat ratio gi . Kinetic model magnetic momentm=const.

  17. Evaluation of ion specific heat ratio gi by comparing with isentropic expansion model f : degree of freedom f = 1 g = 3 f = 2 g = 2 f = 3 g = 5/3 = 1.7 gi is around 1.2 (depending on Z position or pressure) ge is 1.0(isothermal) Nozzle ratio R = A/A1= B1/B (m : magnetic moment)

  18. Ion specific heat ratio gi f= 1 g = 3 f = 3 g = 5/3 g = 1 G = 1 Isothermal Isothermal G = g Adiabatic Specific heat ratio g for ideal gas ( f : degree of freedom ) Specific heat ratio for plasmas ・ Degree of freedom is expected to increase due to excitation or ionization processes. ・ Precise measurement of Mi, Ti, and Te profiles is necessary to evaluate the values of giand ge . Polytropic exponent

  19. Spatial profiles of Mi in a simple mirror Supersonic flowin diverging field diverging field supersonic Shock wave formation near the mirror midplane.Transonic flow from subsonic to supersonic in a Laval nozzle. Laval nozzle mirror transonic flow Mi= 1 ? lc=150cm > lii= 20cm Shock :thckness = 20~30cm

  20. Comparison with Rankine - Hugoniot Relations TOHOKU UNIV. Subscripts 1 and 2 indicate quantities upstream and downstream of shock region, respectively. assuming gi = 5/3, ge =1

  21. Axial profiles of plasma parameters Shock region throat Langmuir probe Electrostatic energy analyzer Mach probe data ge = 1 gi=5/3 Langmuir probe Te is almost constantge = 1

  22. 1-D Isentropic Flow Model TOHOKU UNIV. MPD plasma flow is modeled by 1D adiabatic flow with a constant entropy at any cross section along a flux tube.

  23. 1-D isentropic flow in a Laval nozzle When the nozzle wall varies gradually, Mach number M, flow velocity U, temperature T and mass density r of compressible media are changed ・Mach number M increases when a plasma passes through a Laval nozzle. ・Mach number M becomes unity at the nozzle throat. ・The value of ion specific heat ratio influences spatial evaluation of a Mach number.

  24. Axial profiles of Mi at t = 0.3ms To evaluate ion specific heat ratio, gi is varied in 1D isentropic model. Fitted well

  25. Fitted well Axial profiles of Mi　　　（at t = 1.0ms） To evaluate ion specific heat ratio, gi is varied in 1D isentropic model.

  26. Determination ofgi 1. Mi = 1 at the Laval nozzle throat. (ge = 1) 2. Fitting of Mi to 1D isentropic model.

  27. w/o neutral gas with neutral gas Time evolution ofgi Effect of neutral gas or ionization degree on gi Plasma parameters at throat (Z=2.06m) ・ni ~ 6.5×1013 cm-3 ・ Ti = 4.8 eV ・ Te = 2.3 eV Id = 5.9 kA

  28. Time evolution ofgi Plasma parameter at throat (Z=2.06m) Id = 5.9 kA Id = 3.8 kA ・ni ~ 6.5×1013 cm-3 ・ Ti = 4.8 eV ・ Te = 2.3 eV ・ ni ~ 2.5×1013 cm-3 ・ Ti = 3.1 eV ・ Te = 2.5 eV

  29. Choked flow in uniform external field TOHOKU UNIV. Bernoulli equation Linear increase of ion velocity Steep increase of Ti ( ion heating : Ti >> Te ) Saturation of Mi at unity (choking) Why is ion heating and choking ? What is optimum nozzle for a fast flow ? dm/dt = 0.06g/s(He), B0=1kG (uniform) at Z=4cm

  30. B0(external)=870G, He plasma Strong diamagnetic effect near MPDA exit B j Converging magnetic nozzle is effectively formed and the flow is choked in the downjstream uniform field region.

  31. Schematic of flow pattern near MPDA exit

  32. Small Laval nozzle near the exit of MPDA TOHOKU UNIV. Magnetic field line in vacuum Laval Nozzle Coil to convert the high ion thermal energy into a flow energy, leading to a higher Mach number flow B0

  33. Characteristics in a Laval Nozzle TOHOKU UNIV. Improvement of Acceleration Performance ●: w/o nozzle ●: with nozzle Id = 7.2kA, dm/dt = 0.1g/s (He), Nozzle Throat at Z=17cm, B0=0.087T. ●: w/o nozzle ●: with nozzle The thermal energy is converted to the flow energy by passing through the Laval nozzle and a supersonic plasma flow is achieved. assuming gi = 5/3

  34. Dependence of Acceleration Performance on Discharge Current : upstream TOHOKU UNIV. Id = 7.2kA, dm/dt = 0.1g/s (He), B0=0.087T When the converging nozzle ratio is inappropriate, the plasma parameters in the subsonic region upstream of the throat are self-adjusted so as to satisfy the sonic condition at the throat.

  35. Dependence of Acceleration Performance on Discharge Current : downstream of nozzle TOHOKU UNIV. Id = 7.2kA, dm/dt = 0.1g/s (He), B0=0.087T flow + thermal Total energies with and without the Laval nozzle are nearly equal to each other.

  36. Laval coil Built-in coil New nozzle coil for MPD arcjet to optimize the Lorentz force acceleration Present Coil with uniform field or Laval nozzle Built-in Coil with stronger field of 0.5~1.0T ? ? ? Modified Bernoulli equation ?

  37. Direct measurement of ion acoustic wave Velocity of ion acoustic wave ion acoustic wave excitation CSchanges with gi Ti =5, Te =2.5 (eV) • The change in gi can be confirmed by measuring velocity of ion acoustic wave. • The ion acoustic wave is excited in a flowing plasma.

  38. Measurement of Wave Dispersion Relation TOHOKU UNIV. Alfven wave measurement in uniform magnetic field Wave dispersion excited by R-H antenna agrees well with SAW in w/wci<1.5 and coincides with CAW in w/wci>2. Wave by L-H well corresponds to CAW in the whole range of frequency.

  39. Dependence on Curvature of Magnetic Field Lines TOHOKU UNIV. The instability appears even in uniform or diverging magnetic field without any bad curvature of the magnetic field line. The instability seems to be related to the current flowing in the plasma.

  40. Measurement of current flowing in the plasma Multi-channel Magnetic Probe Array Iz measurement by magnetic probe array

  41. 高速プラズマジェットのヘリカルーキンク不安定性の同定高速プラズマジェットのヘリカルーキンク不安定性の同定

  42. Density profile of the collimated helical jet The jet is not so much diffused even with a large helical axis rotation. Analogous to astrophysical jet ?

  43. Astronomical Jet Active Galactic Nuclei (AGN) Radio Jet MHD simulation of the AGN jet Large scale jet is formed from a small core region and twisted structure (wiggles) is observed. The twisted structure is formed in a jet rotating azimuthally by helical-kink instability. M.Nakamura,et.al., New Astronomy, 6 (2001) 61. D.L.Meier, et.al., Science, 291(2001)84.

  44. Astronomical jet and accretion disc

  45. Summary TOHOKU UNIV. (1) In a uniform field applied on MPDA, ion Mach number Mi is limited at unity (choked flow), due to an effective converging nozzle formed by strong diamagnetic effect. (2) In a diverging nozzle, ion thermal energy is converted to flow energy, resulting in a supersonic flow with Mi up to 2-3. (3) Near the midplane of a simple mirror, shockwave is observed. The jump agrees well with Rankine-Hugoniot relations. The shock thickness is nearly equal to ion-ion mean free path. (4) In a Laval nozzle, a re-accelerated transonic flow is observed. Spatial variation of Mi is best-fitted to that predicted from 1D isentropic model. gi = 1.2 – 2.0, depending on neutral atom density and ge = 1. Sonic condition Mi = 1 is confirmed at the throat. (4) Near the exit of applied-field MPD arcjet,helical flow across helical field with a variable pitch is observed. Ion thermal energy is converted to a flow energy through a small-scaleLaval nozzle. Optimum nozzle shape will be found.

  46. 国際熱核融合実験装置(ITER)～発電実証にむけての大きな一歩～国際熱核融合実験装置(ITER)～発電実証にむけての大きな一歩～ Tore Supra Tore Supra ITER ITER 2005年6月　カダラッシュ（フランス）に決定！ 2005年6月　カダラッシュ（フランス）に決定！ 0102030(m) ITERのねらい: 実際の燃料（重水素，三重水素）を用いて核融合反応を長時間持続し，投入エネルギーの10倍以上のエネルギー（核融合出力）を発生させる． 日本，欧州，ロシア，米国，中国，韓国が参加 日本の建設候補地は六ヶ所村（上）だったが・・・ JAEA

  47. Introduction

  48. プラズマ核融合学会誌2007年1月号～5月号 講座「高速プラズマ流と衝撃波の研究事始め」

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