This short note presents concise semi-analytical expressions for electron temperature and potential in unsteady dilute cold plasma flows. The analysis is based on the detailed fluid model for electrons. Ionizations and normalized electron number density gradients are neglected, and the transport properties are assumed as local constants. Flow is unsteady and Maxwell's equations are adopted in the analysis. With these treatments, the partial differential equations for unsteady electron temperature and potential degenerate as ordinary differential equations. Along an electron streamline, two simple formulas for unsteady electron temperature and plasma potential are obtained. These formulas offer some insights, for example, the electron temperature and plasma potential distributions along an electron streamline include two exponential functions: one for spatial distance along a streamline and the other for time.

1.
C. K.
Birdsall
and
A. B.
Langdon
,
Plasma Physics via Computer Simulation
(
Institute of Physics
,
1991
).
2.
F. F.
Chen
,
Introduction to Plasma Physics and Controlled Fusion
, 2nd ed. (
Springer
,
Haryana, India
,
2006
).
3.
I. D.
Boyd
and
J. T.
Yim
, “
Modelling of the near field plume of a Hall thruster
,”
J. Appl. Phys.
95
,
4575
4584
(
2004
).
4.
S.
Simon
,
A.
Bobwetter
,
T.
Bagdonat
,
U.
Motschamnn
, and
K.
Glassmier
, “
Plasma environment of Titan: A 3D hybrid simulation study
,”
Ann. Geophys.
24
,
1113
1135
(
2006
).
5.
G. A.
Bird
,
Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(
Clarendon Press
,
1994
).
6.
R.
Sentis
,
D.
Paillard
,
C.
Baranger
, and
P.
Seytor
, “
Modeling and numerical simulation of plasma flows with two-fluid mixing
,”
Eur. J. Mech. B
30
,
252
1258
(
2011
).
7.
D. M.
Bond
,
V.
Wheatley
, and
R.
Samtaney
, “
Plasma flow simulation using the two-fluid model
,” in Proceedings of the
20th Australasian Fluid Mechanics Conference
, Perth, Australia (
2016
).
8.
V. V.
Aristov
,
Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows
(
Kluwer Academic
,
2001
), ISBN 1-4020-0388-9.
9.
D.
Cooke
and
I.
Katz
, “
TSS-1R electron currents: Magnetic limited collection from a heated presheath
,”
Geophys. Res. Lett.
25
,
753
756
, (
1998
).
10.
L.
Pekker
and
N.
Hussary
, “
Effect of boundary conditions on the heat flux to the wall in two-temperature modeling of ‘thermal’ plasmas
,”
J. Phys. D: Appl. Phys.
47
,
455202
(
2014
).
11.
F.
Wei
,
H. X.
Wang
,
A. B.
Murphy
,
W. P.
Sun
, and
Y.
Liu
, “
Numerical modelling of the nonequilibrium expansion process of argon plasma flow through a nozzle
,”
J. Phys. D: Appl. Phys.
46
,
505205
(
2013
).
12.
M.
Mitcher
and
C. H.
Kruger
,
Partially Ionized Gases
(
Wiley
,
1973
).
13.
N. L.
Aleksandrov
,
S. V.
Kidysheva
,
M. M.
Nudnova
, and
A. Y.
Starikovskii
, “
Mechanism of altru-fast heating in a non-equilibrium weakly ionized air discharge plasma in high electric fields
,”
J. Phys. D: Appl. Phys.
43
,
255201
(
2010
).
14.
C.
Cai
and
D.
Cooke
, “
A simple model for electron temperature in dilute plasma flows
,”
Phys. Plasma
23
,
103513
(
2016
).
15.
C.
Cai
, “
Numerical investigations on plasma plume flows from a cluster of electric propulsion devices
,”
Aerosp. Sci. Technol.
41
,
134
143
(
2014
).
You do not currently have access to this content.