25G07
Measurement of the Specific Heat Ratio of Ions in Plasma
with Various Rare Gases
Yuko Hashima, Naohiro Takahashi, Kohei Okawa, Hiroshi Watanabe, Yuki Izawa,Nozomi Tanaka and Akira Ando,,,,,,
Department of Electrical Engineering, Graduate School of Engineering, Tohoku University
6-6-05, Aramakiji, Aoba-ku, Sendai 980-8579, Japan980-8579
6-6-05
We have experimentally evaluated the specific heat ratio of ions γi in plasmas by comparing the behavior
in a magnetic nozzle with the isentropic flow model. Axial profiles of ion Mach number Mi were measured
in a fast-flowing plasma passing through a Laval type magnetic nozzle. The γi was derived from Mi at thenozzle throat and behavior of Mi in the nozzle. The γi in He, Ne and Ar plasmas were evaluated.

Fig.1. Schematic of HITOP device. The position ofZ = 0 corresponds to the cathode tip positionof the MPDA.

0.1

0.05

o

2. Experimental Apparatus and Procedure
Figure 1 shows a schematic of the HITOP (HIghdensity TOhoku Plasma) device. We use a MPDA(MagnetoPlasmaDynamic Arcjet) as a plasmasource. Plasma is exhausted from the MPDA with
Mach number of nearly unity [2,3]. In this study,
divergent and convergent magnetic nozzle
configurations were used as shown in Fig.2. The
maximum magnetic field was 0.065 T and magnetic
throat was formed at Z = 2.2 m, where the Laval
type nozzle was formed. Various gases of He, Ne,
Ar and Kr were used in the experiments.
The plasma parameters were measured by a
Mach probe (a three direction probe) and athree-grid energy analyzer (Faraday cup) for themeasurements of ion energy distribution. All
diagnostic tools were set on a two dimensional
movable stage in the chamber. The parameters weremeasured from Z = 0.8 m to 2.6 m.
The plasma passes through the divergent region(Z = 1-1.5 m), where Mach number Mi increases [4].
When it comes into converging cross section region
at Z = 1.5 m to 2.2m, collisional shock wave occurs
and Mach number of plasma flow suddenly

B (T)1. Introduction
The specific heat ratio γ is one of the importantparameters specifying thermodynamic behavior ofmedia. In processes of gas compression orexpansion, the pressure p and the volume V obey
the polytropic relation, pV γ = const. . Generally, γ
is derived as γ = (f + 2)/f, where f is the degree offreedom. The specific heat ratio with γ = 5/3 isfrequently postulated in energetic relations ofmono-atomic plasmas. In plasmas many processesof ionization and electron excitation make thederivation of γ difficult.
We have experimentally determined the specificheat ratio of ions γi by using isentropic relations.
When the nozzle cross section gradually changes,
physical quantities of passing plasma flow vary
according to the isentropic relations [1]. The γi wasevaluated by comparing the ion Mach number Mi
with the relations.

001Z(m)23Fig.2 The axial magnetic field configuration used in theexperiment. Purple area corresponds to theoccurrence of shock wave, and light blue line
corresponds to nozzle throat of the Laval nozzle.

decreased. The subsonic flow passes through aLaval nozzle near Z = 2.2 m, and Mach number
increases from subsonic to supersonic according to
the isentropic flow model as expressed in Eq.(1).
2dM i 2 + (γ i − 1) M i dS,(1)=2M
2( M i − 1) SHere, S is the cross section of the magnetic nozzle.
3. Experimental Results
We have evaluated γi by the following twomethods. The first method is comparison between
experimental value and isentropic flow model(Eq.(1)). Figure 3 shows axial profiles of Mi in
helium plasma assuming as (a) γi = 1.0, (b) γi = 5/3and (c) γi = 2.0. The Mi is obtained from Machprobe measurements [5-7]. Experimental results
were compared with the theoretical curves, and thespecific heat ratio was close to 1.0 rather than 5/3.
The second method is based on the assumptionthat Mi becomes unity at the throat of the Laval
nozzle. The specific heat ratio is expressed by the(a)isentropic flow (γ =1.0)

3iexperimental value (γ =1.0)

following equation,

γi =(Te 2vf −γeTi) .

(2)

Here, γi and γe are ion and electron specific heatratio and Ti and Te are ion and electron temperature,
respectively. The vf is expressed as(3)v f = U / γ eTe / mi .
Here, U is flow velocity and mi is ion mass of theplasma. We obtained the ion specific heat ratio ofhelium plasma as 1.1 by assuming electron specificheat ratio as unity. The obtained specific heat ratios
were consistent with each other, and much smaller
than 5/3.
We have evaluated γi in other rare gases andobtained different values from that of helium
plasma. The γi of neon and argon plasmas werearound 1.6 and 2.0, respectively. There are someprocesses to make the γi lower in plasmas, such as
electron-ion collisions, charge-exchange collisions,ionization and excitation processes. We havemeasured the specific heat ratio in different densityof plasmas and evaluated mean free paths in thesereactions in plasma.

iMi

210(b)

01Z(m)

23

isentropic flow (γ =5/3)

3iexperimental value (γ =5/3)iMi

210(c)

01Z(m)

23

isentropic flow (γ =2.0)i3experimental value (γ =2.0)iMi21001Z(m)23Fig.3 Axial profile of Mi in helium gas (closed circles).
Solid line represents theoretical curve calculated
from Eq.(1) by assuming (a) γi = 1.0 (b) γi = 5/3(c) γi = 2.0.

4. Summary
The ion specific heat ratios of plasmas wereevaluated by comparing with the isentropic flow
model by using two methods. The obtained values
showed good agreement to each other, and they
were smaller than 5/3 in helium plasma. The γi isdifferent in other rare gas plasmas. The effects ofcollisions on the specific heat ratio wereinvestigated and detail discussions are necessary
further.
References[1] M. Inutake, A. Ando, K. Hattori, H. Tobari and T.
Yagai: J. Plasma Fusion Res. 78 (2002) 1352.
[2] M. Inutake and A. Ando: Plasma Phys. Control.
Fusion 49, (2007) A121.
[3] H. Tobari, A. Ando, M. Inutake, and K. Hattori:
Physics of Plasmas, 14 (2007) 093507.
[4] A. Ando, T. Hagiwara, T. Komagome, K. Hattori andM. Inutake: Plasma and Fusion Research. 3, (2008)
S1018[5] A. Ando, T. K. Watanabe, T. Makita, H. Tobari andK. Hattori: Contributions to Plasma Phys., 46 (2006)
335.
[6] A. Ando, T. S. Watanabe, T. K. Watanabe, H. Tobari,K. Hattori and M. Inutake: J. Plasma and FusionRes., 81 (2005) 451.
[7] A. Ando, H. Tobari, M. Shibata, H. Isobe, K. Hattori,
H. Higaki and M. Inutake: Trans. of Fusion Scienceand Tech., 51 (2007) 217.