Electric fields are commonplace in plasmas and affect transport by driving currents and, in some cases, instabilities. The necessary condition for instability in collisionless plasmas is commonly understood to be described by the Penrose criterion, which quantifies a sufficient relative drift between different populations of particles that must be present for wave amplification via inverse Landau damping. For example, electric fields generate drifts between electrons and ions that can excite the ion-acoustic instability. Here, we use particle-in-cell simulations and linear stability analysis to show that the electric field can drive a fundamentally different type of kinetic instability, named the electron-field instability. This instability excites electron plasma waves with wavelengths 30 λ D e, has a growth rate that is proportional to the electric field strength, and does not require a relative drift between electrons and ions. The Penrose criterion does not apply when accounting for the electric field. The large value of the observed frequency, near the electron plasma frequency, further distinguishes it from the standard ion-acoustic instability, which oscillates near the ion plasma frequency. The ubiquity of macroscopic electric fields in quasineutral plasmas suggests that this instability is possible in a host of systems, including low-temperature and space plasmas. In fact, damping from neutral collisions in such systems is often not enough to completely damp the instability, adding to the robustness of the instability across plasma conditions.

1.
M. A.
Lieberman
and
A. J.
Lichtenberg
,
Principles of Plasma Discharges and Materials Processing
, 2nd ed. (
Wiley-Interscience
,
Hoboken, NJ
,
2005
).
2.
V. A.
Lisovskiy
,
K. P.
Artushenko
, and
V. D.
Yegorenkov
, “
Reduced electric field in the positive column of the glow discharge in argon
,”
Vacuum
122
,
75
81
(
2015
).
3.
S.
Nijdam
,
J.
Teunissen
, and
U.
Ebert
, “
The physics of streamer discharge phenomena
,”
Plasma Sources Sci. Technol.
29
(
10
),
103001
(
2020
).
4.
G. T.
Marklund
, “
Electric fields and plasma processes in the auroral downward current region, below, within, and above the acceleration region
,”
Space Sci. Rev.
142
(
1–4
),
1
21
(
2009
).
5.
V.
Rozhansky
,
E.
Kaveeva
,
I.
Senichenkov
,
E.
Sytova
,
I.
Veselova
,
S.
Voskoboynikov
, and
D.
Coster
, “
Electric fields and currents in the detached regime of a tokamak
,”
Contrib. Plasma Phys.
58
(
6–8
),
540
546
(
2018
).
6.
P.
Foukal
and
S.
Hinata
, “
Electric fields in the solar atmosphere: A review
,”
Sol. Phys.
132
(
2
),
307
334
(
1991
).
7.
T.
Lafleur
,
S. D.
Baalrud
, and
P.
Chabert
, “
Characteristics and transport effects of the electron drift instability in Hall-effect thrusters
,”
Plasma Sources Sci. Technol.
26
(
2
),
024008
(
2017
).
8.
S. M.
Hamberger
, “
Experimental studies of electrostatic fluctuations in a turbulently heated plasma
,”
Phys. Fluids
15
(
5
),
825
(
1972
).
9.
B.
Coppi
, “
Anomalous plasma resistivity at low electric fields
,”
Phys. Fluids
14
(
1
),
134
(
1971
).
10.
G. F.
Reiter
, “
Instability of the steady state of a plasma in a uniform electric field
,”
Phys. Fluids
10
(
4
),
703
(
1967
).
11.
O.
Penrose
, “
Electrostatic instabilities of a uniform non-Maxwellian plasma
,”
Phys. Fluids
3
(
2
),
258
(
1960
).
12.
D. A.
Gurnett
and
A.
Bhattacharjee
,
Introduction to Plasma Physics: With Space, Laboratory and Astrophysical Applications
, 2nd ed. (
Cambridge University Press
,
Cambridge
,
2017
).
13.
B. D.
Fried
,
M.
Gell-Mann
,
J. D.
Jackson
, and
H. W.
Wyld
, “
Longitudinal plasma oscillations in an electric field
,”
J. Nucl. Energy, Part C
1
(
4
),
190
198
(
1960
).
14.
B. D.
Fried
and
G. J.
Culler
, “
Plasma oscillations in an external electric field
,”
Phys. Fluids
6
(
8
),
1128
1138
(
1963
).
15.
R.
Kompaneets
,
Y. O.
Tyshetskiy
, and
S. V.
Vladimirov
, “
Ion response in a weakly ionized plasma with ion flow
,”
Phys. Plasmas
20
(
4
),
042108
(
2013
).
16.
R.
Kompaneets
,
A. V.
Ivlev
,
S. V.
Vladimirov
, and
G. E.
Morfill
, “
Instability of ion kinetic waves in a weakly ionized plasma
,”
Phys. Rev. E
85
(
2
),
026412
(
2012
).
17.
A. N.
Kryshtal
, “
Bernstein-wave instability in a collisional plasma with a quasistatic electric field
,”
J. Plasma Phys.
60
(
3
),
469
484
(
1998
).
18.
T. E.
Sheridan
and
S. D.
Baalrud
, “
Time-dependent Tonks-Langmuir model is unstable
,”
Phys. Rev. E
96
(
5
),
053201
(
2017
).
19.
C. K.
Birdsall
and
A. B.
Langdon
,
Plasma Physics via Computer Simulation
(
CRC Press
,
2018
).
20.
B.
Scheiner
and
P. J.
Adrian
, “
Why the particle-in-cell method captures instability enhanced collisions
,”
Phys. Plasmas
26
(
3
),
034501
(
2019
).
21.
H.
Timko
,
P. S.
Crozier
,
M. M.
Hopkins
,
K.
Matyash
, and
R.
Schneider
, “
Why perform code-to-code comparisons: A vacuum arc discharge simulation case study
,”
Contrib. Plasma Phys.
52
(
4
),
295
308
(
2012
).
22.
R.
Courant
,
K.
Friedrichs
, and
H.
Lewy
, “
On the partial difference equations of mathematical physics
,”
IBM J. Res. Dev.
11
(
2
),
215
234
(
1967
).
23.
D. R.
Nicholson
and
D. R.
Nicholson
,
Introduction to Plasma Theory
(
Wiley
,
New York
,
1983
), Vol. 1.
24.
M.
Hayashi
, “
Recommended values of transport cross sections for elastic collisions and total collision cross section for electrons in atomic and molecular gases
,”
Technical Report No. IPPJ-AM-19
, (
Institute of Plasma Physics, Nagoya Institute of Technology
,
1981
).
25.
C.
Yuan
,
A. A.
Kudryavtsev
, and
V. I.
Demidov
,
Introduction to the Kinetics of Glow Discharges
(
Morgan & Claypool Publishers
,
2018
).
26.
U.
Ebert
,
S.
Nijdam
,
C.
Li
,
A.
Luque
,
T.
Briels
, and
E.
van Veldhuizen
, “
Review of recent results on streamer discharges and discussion of their relevance for sprites and lightning
,”
J. Geophys. Res.: Space Phys.
115
(
A7
),
A00E43
(
2010
).
27.
P.
Varma
,
S. P.
Mishra
,
G.
Ahirwar
, and
M. S.
Tiwari
, “
Effect of parallel electric field on Alfven wave in thermal magnetoplasma
,”
Planet. Space Sci.
55
(
1–2
),
174
180
(
2007
).
28.
V. V.
Plyusnin
,
J. A. C.
Cabral
,
H.
Figueiredo
, and
C. A. F.
Varandas
, “
Runaway effects at the plasma boundary in ISTTOK
,”
J. Nucl. Mater.
313
,
1052
1055
(
2003
).
29.
T.
Tang
,
L.
Zeng
,
Z. Y.
Qiu
,
S. Y.
Lin
,
Y. W.
Sun
,
G. Y.
Wei
,
X.
Zhu
,
D. L.
Chen
,
Y.
Huang
,
Y. M.
Duan
et al, “
Observation of electrostatic fluctuations driven by runaway electrons in east disruptions
,”
Nucl. Fusion
63
(
6
),
066034
(
2023
).
30.
V. V.
Parail
and
O. P.
Pogutse
, “
The kinetic theory of runaway electron beam instability in a tokamak
,”
Nucl. Fusion
18
(
3
),
303
(
1978
).
31.
G.
Nicolis
and
P.
Sels
, “
Variational study of the runaway instability in a two-component plasma
,”
Phys. Fluids
10
(
2
),
414
417
(
1967
).
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