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

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

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 !

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

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)

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

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

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.

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

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

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 )

∝∝

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.

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.

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

throatShock region

Mach probe data

Langmuirprobe

Langmuirprobe

Electrostaticenergyanalyzer

Te is almost constant　　　　 　γe = 1

γe = 1γi =5/3

Axial profiles of plasma parameters

( )( ) 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

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)

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

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]

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

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

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.

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 ?

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

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

(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