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
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
Introduction
MPD (magneto-plasma-dynamic) arcjet
MPDA is one of advanced plasma thrusters with a
larger thrust for such as a manned Mars mission.
Space laboratory SFU : 4 ton
Self-Field Acceleration
(Anode)
Fz=jrB
j (Cathode)
B
jz
j
Fr=jzB
F
jr
(Anode)
MPDT on-board test
in 1995-1996
On-ground test of MPD
thruster
ISAS, JAXA
TOHOKU UNIV.
HITOP (HIgh density TOhoku Plasma)
( Mach probe )
Length
: 3.3m
Diameter : 0.8m
Axial 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
Typical time variation of MPD-arcjet plasma
Quasi-steady ~ 1msec
He plasma
  0.1g/s
m
Id=7.2kA
B0=0.087T
Various Mach numbers
Ion acoustic Mach number : Mi
1
miU 2
2
U
Mi 

1
Cs
k g T  g T 
2 B e e i i
 Spectrometer (Uz, U, Ti)
 Mach probe, Langmuir probe (Uz, Te, ne)
 Gridded energy analyzer (Ti)
Cs : ion acoustic velocity
Alfvén Mach number : MA
MA 
U
U

VA B
0mi ni
( Ion wave excitation )
VA : Alfvén velocity
( Alfvén wave excitation )
Magnetosonic Mach number : MS
MS 
U
VA2  CS2
TOHOKU UNIV.
Para-perp Mach probe
Ion acoustic Mach number Mi
1
miU 2
2
U
Mi 

1
Cs
k g T  g T 
2 B e e i i
Para-perp Mach probe
 Spectrometer (Uz, U, Ti)
 Mach probe, Langmuir probe (Uz, Te, ne)
 Gridded energy analyzer (Ti)
 Specific heat ratio ( gi and ge )
j||
Mi   
j
 must be calibrated
by use of spectroscopy.
( ion : unmagnetized )
J. Plasma & Fusin Reseach,
81(12005)451-457.
TOHOKU UNIV.
Old experiment on
high-density-plasma injection into multiple mirror
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)
Density
collisional
collisionless
( lc > lii )
( lc < lii )
n= 3.5x1014 to 1. 5x1013 cm-3
In collisional regime, asymmetric
density profile w.r.t. the midplane
of a mirror cell.
Z (cm)
High density plasma injection into multiple mirror
– continued -Density
(uncalibrated)
Current ratio ~ Mach number
Flux density
○ Is Mi at the mirror throat unity ?
○ How large is the specific heat ratio ?
Spectroscopic measurement
Measurement setup
Particle temperature
m c2
T
l1 e (Doppler Broadening)
2k l0
Flow velocities
uz  c
lz sinf
l0
, u  c
l
l0
(Doppler Shift)
Measured spectrum lines
HeI(atom) : 587.762 nm
HeII(ion) : 468.575 nm
TOHOKU UNIV.
Flow characteristics near the exit of MPD arcjet
in uniform external field
He atom
Rotational velocity
[km/s
]
Rotational velocity
[km/s
]
anode
He ion
cathode
[eV
]
Temperature
[eV
]
Temperature
Id = 7.7 kA, dm/dt = 0.06 g/s(He), B0 = 0.1 T
[a.u.]
Line intensity
[a.u.]
Line intensity
TOHOKU UNIV.
20
25
20
15
10
5
HeI(atom)
HeII(ion)
10
M
T [eV]
0
30
0
Flow Energy [eV]
30
z
u [km/sec]
Choked flow in uniform external field
20
Linear increase of ion velocity
Steep increase of Ti
( ion heating : Ti >> Te )
10
0
1
0.8
0.6
0.4
0.2
0
Bernoulli equation
B2 1
g
 U 2 
P  const.
0 2
g 1
Saturation of Mi at unity
(choking)
0
2
4
6
8 10
Discharge Current I [kA]
Why is ion heating and choking ?
What is optimum nozzle for a fast flow ?
d
dm/dt = 0.06g/s(He), B0=1kG (uniform) at Z=4cm
TOHOKU UNIV.
Choked flow in a uniform field (Bz=0.87kG)
Uniform magnetic field
Id = 5.0kA, dm/dt = 0.15g/sec
Miz
Axial profile of ne and MiZ
Mi
Mir
measurement region
gI =5/3 and ge =1 are assumed.
Supersonic flow in a diverging nozzle
Diverging magnetic field
Miz
Axial profile of ne and Mi
Mi
Mir
Id = 5.0kA, dm/dt = 0.15g/sec
measurement region
gI =5/3 and ge =1 are assumed.
Effect of ambient He gas pressure
0.15
0.1
Ambient pressure increases
with time due to neutral atoms
recombined on the end plate.
||
0.05
0
8
6
4
2
0
2
1
i
3
M
J /J

Z
B [T]
Diverging nozzle
×： t= 0.25 ms
■：
0.30 ms
△：
0.35 ms
○：
1.00 ms
0
0
0.5
1
1.5
2
Z [m]
2.5
3
Decrease of Mach number
due to charge exchange
or ionization
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 moment const.
Evaluation of ion specific heat ratio gi by
comparing with isentropic expansion model
dM 2  g 1M 2 dA

M
2 M 2 1 A

5
4

 = const.
g =5 /3
3
2
g =1 .0
g =1 .2
1
0
05
10
15
20
Nozzle ratio RR= A/A1= B1/B
f 2
g
f
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)
 : magnetic moment)
Ion specific heat ratio gi
f 2
g
f
Specific heat ratio g
for ideal gas
( f : degree of freedom )
f=1
f=3
Isothermal
g=3
g = 5/3
g=1
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 gi and ge .
Polytropic exponent
p

Adiabatic
Isothermal
=g
=1
Spatial profiles of Mi in a simple mirror
Supersonic flow in 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
Comparison with Rankine - Hugoniot Relations

n2 U2
g i  1  Mi21


n1 U1 g i  1Mi21  2
2


g

1
M
2
i
i1  2
Mi2 
2g i Mi21  g i  1
Subscripts 1 and 2 indicate quantities
upstream and downstream of shock
region, respectively.
assuming gi = 5/3, ge =1
TOHOKU UNIV.
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 constant
ge = 1
1-D Isentropic Flow Model
MPD plasma flow is modeled by
1D adiabatic flow with a constant
entropy at any cross section
along a flux tube.
 g 1 2 
MA1
M 
2



g 1
2g 1
 const.
1
2
U 2
2 
 M 
  const.
M
g  1
 2
2 
  const.
T  M 
g  1

TOHOKU UNIV.
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  of
compressible media are changed
dM 2  γ  1M 2 dΑ

M
2Μ 2  1 A
dT

γ  1M 2 dA

T
M2 1 A
dU
1 dA
 2
U M 1 A
dρ
M 2 dA
 2
ρ
M 1 A
・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.
Axial profiles of Mi at t = 0.3ms
To evaluate ion specific heat ratio,
gi is varied in 1D isentropic model.
Fitted well
Axial profiles of Mi
（at t = 1.0ms）
To evaluate ion specific heat ratio,
gi is varied in 1D isentropic model.
Fitted
well
Determination of gi
1. Mi = 1 at the Laval nozzle throat.
Mi 
vf
ge 
Ti
g
Te i
1

Te 2
gi  vf ge
Ti

ge = 1)
2. Fitting of Mi to 1D isentropic model.
dM 2  γ  1M 2 dΑ

M
2Μ 2  1 A
Time evolution of gi
Effect of neutral gas or
ionization degree on gi
w/o neutral gas
with neutral gas
Plasma parameters at throat (Z=2.06m)
Id = 5.9 kA ・ ni ~ 6.5×1013 cm-3
・ Ti = 4.8 eV
・ Te = 2.3 eV
Time evolution of gi
Plasma parameter at throat (Z=2.06m)
Id = 5.9 kA
・ ni ~ 6.5×1013 cm-3
・ Ti = 4.8 eV
・ Te = 2.3 eV
Id = 3.8 kA
・ ni ~ 2.5×1013 cm-3
・ Ti = 3.1 eV
・ Te = 2.5 eV
20
25
20
15
10
5
HeI(atom)
HeII(ion)
10
M
T [eV]
0
30
0
Flow Energy [eV]
30
z
u [km/sec]
Choked flow in uniform external field
20
Linear increase of ion velocity
Steep increase of Ti
( ion heating : Ti >> Te )
10
0
1
0.8
0.6
0.4
0.2
0
Bernoulli equation
B2 1
g
 U 2 
P  const.
0 2
g 1
Saturation of Mi at unity
(choking)
0
2
4
6
8 10
Discharge Current I [kA]
Why is ion heating and choking ?
What is optimum nozzle for a fast flow ?
d
dm/dt = 0.06g/s(He), B0=1kG (uniform) at Z=4cm
TOHOKU UNIV.
Strong diamagnetic effect near MPDA exit
B0(external)=870G, He plasma
4
3
2
1
0
-1
-2
-3
-4
4
3
2
1
0
-1
-2
-3
-4
-5
Bz:500(G)
anode
Br:20(G)
cathode
B
j z:250 (A/cm2 )
j r :10 (A/cm2 )
j
05
10 15 20 25 30 35 40
Z (cm)
Converging magnetic nozzle is effectively formed and the
flow is choked in the downjstream uniform field region.
Steady Electromagnetic
Acceleration
in an
MPD Arcjet
Schematic
of flow pattern
near
MPDA
exit
(A) Applied field ( Bz+Br )
Current flow ( jr+jz )
(B) Helical field ( Bz+B )
with a variable-pitch
(C) Ion flow pattern ( uz+u )
TOHOKU UNIV.
Small Laval nozzle near the exit of MPDA
to spectrometer
Magnetic field line in vacuum
scan
lense
Laval Nozzle
Coil
Laval Nozzle
Coil
MPDA
Plasma
MPDA
Y
Z[cm]
X
0
Z
uniform
Laval
B [T]
Nozzle Throat
0.2
20
30
to convert the high ion thermal
energy into a flow energy, leading
to a higher Mach number flow
BLN
0.1
0
0
10
10
20
Z [cm]
B030
TOHOKU UNIV.
Characteristics in a Laval Nozzle
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
TOHOKU UNIV.
Dependence of Acceleration
Performance on Discharge
Current : upstream
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.
TOHOKU UNIV.
Id = 7.2kA, dm/dt = 0.1g/s (He), B0=0.087T
0.2
Mi
Nozzle Throat
downstream
(Z=30.5cm)
20
10
0
0
40
20
1
0.1
0.5
0
0
80
0
10
20
30
Z [cm]
Total energies with and without
the Laval nozzle are nearly equal to
each other.
30
20
0
1.5
Total Energy [eV]
B [T]
0.3
with nozzle
w/o nozzle
flow + thermal
40
0
0
2
4
6
8
10
12
Id [kA]
TOHOKU UNIV.
Flow Energy [eV]
U [km/s]
40
Ti [eV]
Dependence of Acceleration
Performance on Discharge
Current : downstream of nozzle
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
Laval coil
Built-in
coilCoil
Magnetic
Anode
Laval Nozzle
Coil
MPDA
Gas
Z[cm]
0
10
20
30mm
30
Cathode
u||
Mi 
1 ?
CS
u||
MA 
1 ?
VA
Modified Bernoulli
equation
Mms 
u
V C
2
A
2
S
1 ?
B B BZ u
1
g
2
2
 uZ  u 
P

 const. ?
2
g 1
0
0uz


2
Direct measurement of ion acoustic wave
Velocity of ion acoustic wave
Cs 
k B g e Te  g i Ti 
mi
ion acoustic wave excitation
CS changes 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.
Measurement of Wave Dispersion Relation
Alfven wave measurement in uniform magnetic field
0
Z
5
MPDA
Y
RF-antenna
Z
magnetic probe
ww
ci
4
X
M =0.13
CAW
A
R-H
L-H
3
2
1
SAW
0
Wave dispersion excited by R-H antenna
agrees well with SAW in w/wci<1.5 and
coincides with CAW in w/wci>2.
0
1
2
3
4
k||c/wpi
Wave by L-H well corresponds to CAW in
the whole range of frequency.
TOHOKU UNIV.
5
Dependence 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.
Measurement of current flowing in the plasma
Multi-channel Magnetic Probe
Array
Multi-channel Micro Magnetic Probe
Micro-tip magnetic
SUS pipe
MPD
Anode
Current Iz
Endplate
MPD
Cathode
(O.D. 15mmf)
Ceramic sleeve
390mm
Iz measurement by magnetic probe array
1000mm
Connector
SW2
SW1
Crooss sectional view
-5
Twisted pair
Case
2
NS = 2.3 x 10 Turn
10mm
Tip inductor
4.5mm
Br Bq Bz
Ceramic sleeve
(O.D. 5mmf I.D. 3mmf)
Ch1 tip-set
Ch2 tip-set
Magnetic probe tip :
Micro-Tip Inductor used for inductrial applications
Features... 1. Good reproducibility
2. Cheap
3. Good signal responce even in a high
frequency region
Vacuum
Magnetic Chamber
probe
Instabilities
Instabilitiesin
inan
anMPD
MPDPlasma
PlasmaFlow
Flow
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
Plasma behavior in axial direction
Schematic helically-twisted plasma column
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.
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 ?
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 helicalkink instability.
D.L.Meier, et.al., Science, 291(2001)84.
M.Nakamura,et.al., New Astronomy, 6 (2001) 61.
Astronomical
Jet
and
Accretion
Astronomical
and
disc
Astronomicaljet
Jet
andaccretion
AccretionDisc
Disc
supersonic jet and shock front
AGN jet (Cyg A)
magnetic
channel
Acretion disc
Close
binary system (SS433)
ActiveGalaxy　NGC4261
Summary
(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, shock wave 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-scale
Laval nozzle. Optimum nozzle shape will be found.
TOHOKU UNIV.
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～
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
ITER
ITER
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
Tore Supra
2005年6月
2005年6月
カダラッシュ（フランス）に決
カダラッシュ（フランス）に決
定！
定！
0
JAEA
10
20
30
日本の建設候補地は六ヶ所村（上）だったが・・・
Introduction
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」

Download File

Recent Advances in Understanding of Diamond Wire Swing

Nov. 11th (Tue.) Nov. 12th (Wed.)

5 - 原子力委員会

Consideration of Baffle cooling scheme