Grid-based Vlasov simulations are carried out to re-evaluate the one-dimensional collisionless plasma expansion into vacuum. The grid-based method eliminates the inherent statistical noise in particle-based methods and allows us to extend the solution beyond the self-similar expansion region and resolve small electron timescale wave perturbations. It is shown that the expansion generates both an ion-acoustic rarefaction wave mode and an electron Langmuir wave mode that propagate into the unperturbed plasma upstream. The assumption used in the classical expansion solution that the electrons are an isothermal fluid is accurate within a quasi-neutral, self-similar expansion region but fails in both the upstream and downstream of that region due to electron timescale perturbations.

1.
A.
Gurevich
,
L.
Pariiskaya
, and
L.
Pitaevskii
, “
Self-similar motion of rarefied plasma
,”
Sov. Phys. JETP
22
,
449
454
(
1966
).
2.
J.
Allen
and
J.
Andrews
, “
A note on ion rarefaction waves
,”
J. Plasma Phys.
4
,
187
194
(
1970
).
3.
J.
Crow
,
P.
Auer
, and
J.
Allen
, “
The expansion of a plasma into a vacuum
,”
J. Plasma Phys.
14
,
65
76
(
1975
).
4.
P.
Mora
and
R.
Pellat
, “
Self-similar expansion of a plasma into a vacuum
,”
Phys. Fluids
22
,
2300
2304
(
1979
).
5.
J.
Denavit
, “
Collisionless plasma expansion into a vacuum
,”
Phys. Fluids
22
,
1384
1392
(
1979
).
6.
U.
Samir
,
K.
Wright
, Jr.
, and
N. H.
Stone
, “
The expansion of a plasma into a vacuum: Basic phenomena and processes and applications to space plasma physics
,”
Rev. Geophys.
21
,
1631
1646
, (
1983
).
7.
N.
Singh
,
K.
Wright
, Jr.
,
N.
Stone
,
U.
Samir
, and
K.
Hwang
, “
On the interpretation of measured ion streams in the wake of the shuttle orbiter in terms of plasma expansion processes
,”
J. Geophys. Res.: Space Phys.
94
,
12075
12080
, (
1989
).
8.
J.
Wang
and
D.
Hastings
, “
Ionospheric plasma flow over large high-voltage space platforms. I: Ion-plasma-time scale interactions of a plate at zero angle of attack
,”
Phys. Fluids B
4
,
1597
1614
(
1992
).
9.
J.
Wang
and
D.
Hastings
, “
Ionospheric plasma flow over large high-voltage space platforms. II: The formation and structure of plasma wake
,”
Phys. Fluids B
4
,
1615
1629
(
1992
).
10.
J.
Wang
,
D.
Brinza
, and
M.
Young
, “
Three-dimensional particle simulations of ion propulsion plasma environment for deep space 1
,”
J. Spacecr. Rockets
38
,
433
440
(
2001
).
11.
P.
Mora
, “
Plasma expansion into a vacuum
,”
Phys. Rev. Lett.
90
,
185002
(
2003
).
12.
Y.
Huang
,
Y.
Bi
,
X.
Duan
,
X.
Lan
,
N.
Wang
,
X.
Tang
, and
Y.
He
, “
Self-similar neutral-plasma isothermal expansion into a vacuum
,”
Appl. Phys. Lett.
92
,
031501
(
2008
).
13.
T.
Grismayer
,
P.
Mora
,
J.
Adam
, and
A.
Héron
, “
Electron kinetic effects in plasma expansion and ion acceleration
,”
Phys. Rev. E
77
,
066407
(
2008
).
14.
A. V.
Arefiev
and
B. N.
Breizman
, “
Collisionless plasma expansion into vacuum: Two new twists on an old problem
,”
Phys. Plasmas
16
,
055707
(
2009
).
15.
M.
Merino
,
J.
Mauriño
, and
E.
Ahedo
, “
Kinetic electron model for plasma thruster plumes
,”
Plasma Sources Sci. Technol.
27
,
035013
(
2018
).
16.
Y.
Hu
and
J.
Wang
, “
Expansion of a collisionless hypersonic plasma plume into a vacuum
,”
Phys. Rev. E
98
,
023204
(
2018
).
17.
J.
Wang
and
Y.
Hu
, “
The breakdown of the fluid approximation for electrons in a plasma wake
,”
J. Geophys. Res.: Space Phys.
123
,
8797
8805
, (
2018
).
18.
Y.
Hu
and
J.
Wang
, “
Assessment of electron thermodynamic and fluid approximations for collisionless plasma expansion into a wake
,”
Phys. Plasmas
26
,
023515
(
2019
).
19.
Y.
Hu
and
J.
Wang
, “
Fully kinetic simulations of collisionless, mesothermal plasma emission: Macroscopic plume structure and microscopic electron characteristics
,”
Phys. Plasmas
24
,
033510
(
2017
).
20.
J.
Wang
and
Y.
Hu
, “
On the limitations of hybrid particle-in-cell for ion thruster plume simulations
,”
Phys. Plasmas
26
,
103502
(
2019
).
21.
C.
Cui
,
Y.
Hu
, and
J.
Wang
, “
Direct grid-based Vlasov simulation of collisionless plasma expansion of ion thruster plume
,” AIAA Paper No. 2019-3992.
22.
C.
Cui
,
Z.
Huang
,
Y.
Hu
, and
J.
Wang
, “
Grid-based kinetic simulations of collisionless plasma expansion
,” in
The 36th International Electric Propulsion Conference
(
Electric Rocket Propulsion Society
,
2019
), Paper No. IEPC-2019-862.
23.
Y.
Idomura
,
T.-H.
Watanabe
, and
H.
Sugama
, “
Kinetic simulations of turbulent fusion plasmas
,”
C. R. Phys.
7
,
650
669
(
2006
).
24.
A.
Thomas
,
M.
Tzoufras
,
A.
Robinson
,
R.
Kingham
,
C.
Ridgers
,
M.
Sherlock
, and
A.
Bell
, “
A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma
,”
J. Comput. Phys.
231
,
1051
1079
(
2012
).
25.
T.
Umeda
,
T.
Kimura
,
K.
Togano
,
K.
Fukazawa
,
Y.
Matsumoto
,
T.
Miyoshi
,
N.
Terada
,
T. K.
Nakamura
, and
T.
Ogino
, “
Vlasov simulation of the interaction between the solar wind and a dielectric body
,”
Phys. Plasmas
18
,
012908
(
2011
).
26.
M.
Palmroth
,
U.
Ganse
,
Y.
Pfau-Kempf
,
M.
Battarbee
,
L.
Turc
,
T.
Brito
,
M.
Grandin
,
S.
Hoilijoki
,
A.
Sandroos
, and
S.
von Alfthan
, “
Vlasov methods in space physics and astrophysics
,”
Living Rev. Comput. Astrophys.
4
,
1
(
2018
).
27.
K.
Hara
,
I. D.
Boyd
, and
V. I.
Kolobov
, “
One-dimensional hybrid-direct kinetic simulation of the discharge plasma in a Hall thruster
,”
Phys. Plasmas
19
,
113508
(
2012
).
28.
P.
Cagas
,
B.
Srinivasan
, and
A.
Hakim
, “
Continuum kinetic study of magnetized sheaths for use in Hall thrusters
,” in
52nd AIAA/SAE/ASEE Joint Propulsion Conference
(
American Institute of Aeronautics and Astronautics
,
2016
), p.
4619
.
29.
A. L.
Raisanen
,
K.
Hara
, and
I. D.
Boyd
, “
Two-dimensional hybrid-direct kinetic simulation of a Hall thruster discharge plasma
,”
Phys. Plasmas
26
,
123515
(
2019
).
30.
A. R.
Vazsonyi
,
K.
Hara
, and
I. D.
Boyd
, “
Non-monotonic double layers and electron two-stream instabilities resulting from intermittent ion acoustic wave growth
,”
Phys. Plasmas
27
,
112303
(
2020
).
31.
G.
Manfredi
,
S.
Mola
, and
M.
Feix
, “
Rescaling methods and plasma expansions into vacuum
,”
Phys. Fluids B
5
,
388
401
(
1993
).
32.
C.-Z.
Cheng
and
G.
Knorr
, “
The integration of the Vlasov equation in configuration space
,”
J. Comput. Phys.
22
,
330
351
(
1976
).
33.
J. A.
Rossmanith
and
D. C.
Seal
, “
A positivity-preserving high-order semi-Lagrangian discontinuous Galerkin scheme for the Vlasov–Poisson equations
,”
J. Comput. Phys.
230
,
6203
6232
(
2011
).
34.
J. W.
Banks
and
J. A. F.
Hittinger
, “
A new class of nonlinear finite-volume methods for Vlasov simulation
,”
IEEE Trans. Plasma Sci.
38
,
2198
2207
(
2010
).
35.
N. V.
Elkina
and
J.
Büchner
, “
A new conservative unsplit method for the solution of the Vlasov equation
,”
J. Comput. Phys.
213
,
862
875
(
2006
).
36.
J.-M.
Qiu
and
A.
Christlieb
, “
A conservative high order semi-Lagrangian WENO method for the Vlasov equation
,”
J. Comput. Phys.
229
,
1130
1149
(
2010
).
37.
F.
Filbet
,
E.
Sonnendrücker
, and
P.
Bertrand
, “
Conservative numerical schemes for the Vlasov equation
,”
J. Comput. Phys.
172
,
166
187
(
2001
).
38.
T.
Umeda
,
Y.
Nariyuki
, and
D.
Kariya
, “
A non-oscillatory and conservative semi-Lagrangian scheme with fourth-degree polynomial interpolation for solving the Vlasov equation
,”
Comput. Phys. Commun.
183
,
1094
1100
(
2012
).
39.
J.-M.
Qiu
and
C.-W.
Shu
, “
Positivity preserving semi-Lagrangian discontinuous Galerkin formulation: Theoretical analysis and application to the Vlasov–Poisson system
,”
J. Comput. Phys.
230
,
8386
8409
(
2011
).
40.
Y. V.
Medvedev
, “
Ion front in an expanding collisionless plasma
,”
Plasma Phys. Controlled Fusion
53
,
125007
(
2011
).
41.
D. G.
Swanson
,
Plasma Kinetic Theory
(
CRC Press
,
2008
).
42.
Y. V.
Medvedev
, “
Expansion of an ion–ion plasma into a vacuum
,”
Phys. Scr.
69
,
120
(
2004
).
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