25G06
Measurement of Plasma Flow Velocity in a Fast-flowing Plasma
高速プラズマ流でのプラズマ流速測定
Kohei Okawa, Naohiro Takahashi, Yuko Hashima, Hiroshi Watanabe, Yuki Izawa,Nozomi Tanaka and Akira Ando
大川 耕平，高橋 直大，橋間 裕子，渡部 博，伊澤 裕紀，田中のぞみ，安藤晃

Department of Electrical Engineering, Graduate School of Engineering, Tohoku University
6-6-05, Aoba-yama, Aoba, Sendai 980-8579, Japan
東北大学工学研究科 〒980-8579 仙台市青葉区荒巻字青葉6-6-05
The plasma flow velocity is one of the important parameters to understand the plasma flow characteristics
and evaluation of thrust performance in electric propulsion. In this research, we measured the plasma flow
velocity by the time of flight (TOF) method using Langmuir probes and Mach probes. Ion saturation
currents were measured simultaneously by two probes set at separated positions. The plasma flow velocity
was evaluated by time difference between the two signals. Effect of the distance between the two probes
was examined.

1. Introduction
We have investigated fast-flowing plasma withvarious magnetic nozzle configurations [1-3]. Machnumber was measured directly by Mach probes inthe plasma and large increase of Mach number wasobserved in an expanding magnetic nozzle
configuration. The thermal energy of the plasma
flow is expected to convert into kinetic energy bypassing through the divergent magnetic nozzle.
Although plasma flow velocity can be estimated by
the measurement of Mach number and temperature,
direct measurement of plasma flow velocity isimportant for the researches of the fast-flowing
plasma.
An electric propulsion system is suitable forlong-term mission in space with its higher specificimpulse [4]. Magneto-Plasma-Dynamic (MPD)
thruster is one of the promising candidates for thehigh power thruster utilizing electric propulsion
system. In order to evaluate the thrust performance,measurement of plasma parameters such as flow
velocity is important. With a divergent magnetic
field applied on a MPD thruster, the flow velocity isexpected to increase by additional acceleration
forces [5].
We have measured ion saturation currents at
different axial positions shot by shot and averaged
axial flow velocity was evaluated by the time delayof initial phase of the discharge [6]. In this research,
the time of flight (TOF) method was utilized using
two probes separated 5-20 cm apart to each other.
The estimation method and comparison with theprevious method are presented.

device in Tohoku University (see Fig. 1). The MPD
thruster was attached on an end port of HITOP
device, and operated with a variety of gases. Figure
2 shows the schematic of the MPD thruster. A
magnetic coil is set near the exit of the MPD
thruster to generate an additional magnetic field.
Uniform magnetic field of 50 mT and additional
field were applied in the experiments as shown inFig.3, which forms a divergent magnetic nozzle.
A fixed Langmuir probe and a movable Machprobe are set separately with a short distance on theaxis of the plasma flow. We can evaluate the plasma
flow velocity by the time of flight (TOF) methodfrom the time lag of two ion saturation current

Fig.1. Schematic of the HITOP device

Magnetic coil
Gas
Inlet
Cathode
0.1m

2. Experimental procedure
Experiments were performed by the HITOP

Anode

Fig.2. Schematic of the MPD thruster

20.0

U [km/s]

0.6

B [T]B0 = 0.05 T
Bzp = 0.1 T

0.4

Bzp = 0.2 T
Bzp = 0.3 T

0.20-0.2

15.0

Previous result
dZ = 20 cm
dZ = 15 cm
dZ = 10 cm
dZ = 5cm

10.0
5.0
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.000.2

0.4

I [kA]Z [m]signals measured by the two probes. The time lag
can be estimated using the cross-correlation
function,,(1)12 ( )   g1 ( x)g 2 ( x   )dx
where g1, g2 are the ion saturation currents. Thetime lag equals to  where the cross-correlation
function becomes maximum. The velocity is
calculated from the time lag and probe separation
distance.
3. Results and discussions
Figure 4 shows the dependence of a plasma flow
velocity U on the discharge current Id. Here thedistance of two probes dZ was changed. We haveevaluated the plasma flow velocity previously fromthe initial delay of the discharge measured atseveral axial positions [6]. The results from Eq. (1)were slightly smaller than the previous results.
Previous estimation of plasma flow velocity isprobably affected by relatively fast particles in thedischarge. Fast particles attain to probes faster thanbulk particles and contribute to an initial rise of ion
saturation currents. The measured results in thisstudy were slightly scattered but the flow velocity
can be estimated within +-3km/s. The error can be
reduced by sampling more number of data points ina shot.
Figure 5 shows the dependence of U on Id in
various divergent magnetic configurations in Ar
plasma. U increased as the increase of Id and Bzp.
This was caused by the increase of Lorentz force
which drives the plasma flow axially. When thedivergent magnetic nozzle was not applied, theplasma flow velocity increased and limited to about
8.7 km/s, that is the Alfvén critical velocity [7].
With an applied magnetic field the plasma flow
velocity increased beyond the critical velocity. The
plasma flow velocity increased with the divergent

dFig.4. The plasma flow velocity U as a function of thedischarge current Id. dZ is the distance between
two probes.

50.0
40.0U [km/s]

Fig.3. A uniformed magnetic field B0 and an
additional magnetic field Bzp by the small coilBzp = 0 T
Bzp = 0.1 T
Bzp = 0.2 T

30.0

Bzp = 0.3 T

20.0
10.0
0.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0

I [kA]
dFig.5. The dependence of U on Id in various additional
magnetic fields in Fig.3. Ar plasma.

magnetic nozzle intensity.
4. Conclusion
The plasma flow velocity in a MPD thruster wasevaluated by the TOF method using a crosscorrelation function. The plasma flow velocity wasevaluated in several separation distances between
two probes. The plasma flow velocity increased
with the increase of discharge current and thedivergent magnetic nozzle intensity.
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