ix-5 磁気ノズルによる遷音速流の生成と 宇宙推進機への応用 ...anode :30mm...
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IX-5 磁気ノズルによる遷音速流の生成と宇宙推進機への応用
Production of a transonic plasma flow in a magnetic nozzle
and its application to space propulsion
IX-5 磁気ノズルによる遷音速流の生成と宇宙推進機への応用
Production of a transonic plasma flow in a magnetic nozzle
and its application to space propulsion
犬竹 正明 Masaaki Inutake
東北大学工学研究科
TOHOKU UNIV.
PF 2006, 1 Dec, 2006, Tsukuba
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OutlineOutline
1. Introduction 2. Experimental devices:
MPD arcjet, spectroscopy and Mach probe3. Plasma flow dynamics in various magnetic channels
Choked flow in a uniform field,Supersonic flow in a diverging field,Shock wave in a simple mirror field,Transonic flow and specific heat ratio γi in a Laval nozzle,Helical-kink instability in a current-carrying plasma jetPlasma detachnent from a magnetic nozzle of a space thruster
5. Summary
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HAYABUSA’s ion engine worked well
Image of HAYABUSA ion engine
Nov 26, 2005 “Hayabusa”spacecraft with four ECR ion engineswas successfully landed on the asteroid “Itokawa””for a sample return mission after 2.5 year flight.
isas.jaxa
Total weight 500kg, Xe gas 60kg,
If chemical, propellant 500kg !
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Self-field acceleration
Plasma thruster with a larger thrust for a manned Mars mission
MPD (Magneto-Plasma-Dynamic) ArcjetMPD (Magneto-Plasma-Dynamic) Arcjet
(Anode)
(Cathode)j jz
jrj
BθFz=jrBθ
FFr=jzBθ
(Anode)On-ground test of MPD thruster
ISAS, JAXA
MPDT on-board test in 1995-1996
Space laboratory SFU : 4 ton
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Electromagnetic Acceleration
(a) Self-field acceleration
(b) With external field
Blowing + Swirling (rotation)
Pumping ( pinch)
to improve the performance and to suppress electrode erosion
+ Hall acceleration
(In the present experiments)
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MPD Arcjet
( Mach probe )
Quasi-steady pulse ~ 1msHighly-ionized ~ 50 - 90%Density ~ 1018 - 1021 ( m-3)Ion temperature Ti ~ 20 - 40 eVElectron Te ~ 3 - 10 eV
Cathode : 10mmφAnode :30mmφ
Length : 3.3mDiameter : 0.8mAxial Bz : ~0.1 T
HITOP (HIgh density TOhoku Plasma) Device
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Spectrum lines
00
,sinλλ
λφλ θ
θΔ
=Δ
= cucu zz
Flow Velocities
Particle Temperature
e10
2
2λ
λΔ=
ck
mT (Doppler Broadening)
(Doppler Shift)
HeI(atom) : 587.762 nmHeII(ion) : 468.575 nm
Spectroscopic measurements near the MPD exit
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Ion acoustic Mach number : Mi
( )iieeB
i
si
TTk
Um
CUM
γ+γ==
21
21 2
Alfvén Mach number : MA
iiA
A
nmB
UVUM
0μ
==
Magnetosonic Mach number : MS
22SA
SCV
UM+
=
(VA : Alfvén velocity)
Mach probe in the downstream region
κ is calibrated by use of spectroscopy. γI and γe are assumed.
⊥
⋅=jj
Mi||κ
Ando et al., J. Plasma & Fusin Reseach,81 (12005) 451-457.
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Uniform field near the MPDA
3. Plasma flow dynamics in various magnetic channelsChoked flow in a uniform field,Supersonic flow in a diverging field,Shock wave in a simple mirror field,Transonic flow and specific heat ratio γi in a Laval nozzle,Helical-kink instability in a current-carrying plasma jetPlasma detachnent from a magnetic nozzle of a space thruster
Gradually divergingfield in the down stream region
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Flow characteristics near the exit of MPD arcjet in uniform external field
Flow characteristics near the exit of MPD arcjet in uniform external field
Id = 7.7 kA, dm/dt = 0.06 g/s(He), B0 = 0.1 T
Temperature
Line intensity
Temperature
Line intensity
[km
/s]
[eV]
[a.u
.]
[km
/s]
[eV]
[a.u
.]
Rotational velocityanode
cathode
Rotational velocity
He atom He ion
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Saturation of Mi in a Uniform External Field Saturation of Mi in a Uniform External Field
25
0
10
20
30 HeI(atom)HeII(ion)
u z[k
m/s
ec]
0
5101520
Flow
Ene
rgy
[eV
]0
10
20
30
T [e
V]
00.20.40.60.8
1
0 2 4 6 8 10
M
Discharge Current Id [kA]
• Steep increase of ion temperature( ion heating : Ti >> Te )
dm/dt = 0.06g/s(He), B0=1kG (uniform) at Z=4cm
• Saturation of Mi at unity( the flow is choked )
• Linear increase of flow velocity
const.μBP
1γγρU
21
0
2θ2
Z =+−+
Bernoulli’s equation
( Bθ is proportional to Id )
∝∝
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Choked flow in a uniform field (Bz=0.87kG)
Miz
Miθ
Mir
Id = 5.0kA, dm/dt = 0.15g/sec
Uniform magnetic field
Axial profile of ne and MiZ
measurement region
γI =5/3 and γe =1 are assumed.
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Supersonic flow in a diverging field
Miz
Miθ
Mir
Id = 5.0kA, dm/dt = 0.15g/sec
Diverging magnetic field
Axial profile of ne and Mi
measurement region
γI =5/3 and γe =1 are assumed.
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Shock wave near the mirror midplane
Mi = 1 ?
Shock Wave and Transonic Flow in a Laval nozzle
Shock thickness = 20~30cm
transonic flowLaval nozzle
lc= 150cm > λii ~ 20cmc/ωpi ~10cm
Mirror cell Shock
Transonic flowin a Laval nozzle
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throatShock region
Mach probe data
Langmuirprobe
Langmuirprobe
Electrostaticenergyanalyzer
Te is almost constant γe = 1
γe = 1γi =5/3
Axial profiles of plasma parameters
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( )( ) A
dΑ1Μ2M1γ2
MdM
2
2
−−+
=
AdA1M
1UdU
2 −=
( )AdA
1MM1γ
TdT
2
2
−−
−=
AdA1M
Mρdρ
2
2
−−=
・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.
When the nozzle wall varies gradually,
Mach number M, flow velocity U, temperature T and mass density ρ of compressible media are changed
1-D isentropic flow in a Laval nozzle1-D isentropic flow in a Laval nozzle
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Evaluation of ion specific heat ratio γi
Fitted well
Axial profiles of Mi is best-fitted to1-D isentropic model.
t = 0.3ms
It was confirmed that Mi = 1 at the throat. ( Sonic Black Hole)
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The flow is choked in the downstream uniform field region.
B0 (external)=870G, He plasma
Near the MPDA exit a converging magnetic nozzle is effectively formed due to strong diamagnetic effect.
Near the MPDA exit a converging magnetic nozzle is effectively formed due to strong diamagnetic effect.
-3-2-101234
-4
-3-2-10123 Bz:500 (G)
Br:20 (G)
4
-4
anode
cathode
-5 0 5 10 15 20 25 30 35 40Z (cm)
j :10 (A/cm )r2
j :250 (A/cm )z2
B
j
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Plasma Rotation and Potential formation
Rotational velocity increases with the increase of applied-field strength.
ExB drift is not dominant in the plasma rotation
BEV BE ∝×Q
eizZi ppp ;BjBjrp
runm +==−+
∂∂
− θθθ 0
2
( ) ( ) 011 =∂
∂−−+η=−+ θθθθ r
pen
BjBjen
jBuBuE ezZrzZr
The uθ increases linearly with the plasma radius in the core region
⇒ rigid rotation
Generalized Ohm’s law (radial component)
Equation of motion for a rotating plasma
0
5
10
15
20
0 500 1000
He atomHe ion
u θ [k
m/s
]
Applied Field B0 [G]
0
5Fl
ow e
nerg
y [e
V]
1
-15-10
-505
1015 B0=0.05[T]
B0=0.1[T]
-3 -2 -1 0 1 2 3
u θ[k
m/s
]
AnodeCathode
X [cm]
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TOHOKU UNIV.
(A) Applied field ( Bz+Br ) Current flow ( jr+jz )
(B) Helical field ( Bz+Bθ )
with a variable-pitch
(C) Ion flow pattern ( uz+uθ )
Steady Electromagnetic Acceleration in an MPD ArcjetSchematic of flow patterns near the MPDA exit
Jr flows across B( not force-free)
Ui flows across B( UxB: back emf, Hall term)
( ) ( ) 011 =∂
∂−−+η=−+ θθθθ r
pen
BjBjen
jBuBuE ezZrzZr
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Instabilities in an MPD Plasma FlowInstabilities in an MPD Plasma FlowPlasma behavior in axial direction
From the phase difference of azimuthal and axial probe array signal, the plasma has twisted structure and it rotates in the same direction of the twist.
TOHOKU UNIV.
Schematic helically-twisted plasma column
Collimated Helical Jet from an MPD Arcjet
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Dependence on Curvature of Magnetic Field LinesDependence on Curvature of Magnetic Field Lines
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.
TOHOKU UNIV.
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Density profile of the collimated helical jetDensity profile of the collimated helical jet
The jet is not so much diffused even with a large helical axis rotation.
Analogous to astrophysical jet ?
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Ref: D.L.Meier, et.al., Science, 291(2001)84.
Active Galactic Nuclei (AGN) Radio Jet
Ref: M.Nakamura,et.al., New Astronomy, 6 (2001) 61.
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.
Astrophysical JetAstrophysical Jet
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SummarySummary
(1) Mechanism of electro-magnetic acceleration :
Self-field MPDA : Bernoulli equation ? Partly yes
Applied-field MPDA : modified Bernoulli equation ? Not yet
(2) Mach number limitation and ion heating near MPDA exit:
Choked flow in the effectively converging nozzle due to strong diamagnetic effect of a high beta plasma ? Yes
Shock heating or adiabatic compression heating ? Not yet
const.=+−
+0
22
121
μγγρ θBPUZ
( ) const.=−+−
++z
ZZ u
uBBBPuu00
222
121
μμγγρ θθθθ
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(3) Energy conversion through a magnetic nozzle :
Isentropic conversion from subsonic to supersonic flow possible ? Yes
How high is the specific heat ratio γi ?
γi = 2.0 - 1.2 depending on the ionization degree
(4) Higher velocity by ICRF wave heating : (not shown)
Alfvén wave one-path heating of a fast flowing plasma possible ? Yes
Perp-para particle energy conversion according to magnetic moment μ = const. ? Yes
(5) Helical-kink instability and its control: yes
(6) Plasma detachment from a magnetic filed line : (in future)
Can super-Alfvénic flow tear away the field line ?
Steadily or intermittently ? Charge separation ?
IX-5 磁気ノズルによる遷音速流の生成と�宇宙推進機への応用 �Production of a transonic plasma flow �in a magnetic nozzle �and its application to space pOutlineMPD (Magneto-Plasma-Dynamic) ArcjetFlow characteristics near the exit of MPD arcjet � in uniform external fieldSaturation of Mi in a Uniform External Field Choked flow in a uniform field (Bz=0.87kG)Supersonic flow in a diverging fieldShock Wave and Transonic Flow in a Laval nozzle�Axial profiles of plasma parametersEvaluation of ion specific heat ratio gi Dependence on Curvature of Magnetic Field LinesDensity profile of the collimated helical jetSummary