By using particle-in-cell simulations, we study the collision of two plasma flows with one of them carrying a magnetic field. Ion interpenetration results in the formation of a magnetic piston with the magnetic field compression proportional to the density ratio of the colliding plasmas. The counterpropagating ions in the nonmagnetized plasma upstream from the piston excite the ion Weibel instability, which turns into magnetic turbulence. The thickness of the piston increases with time, and it turns into a reverse magnetized shock after less than one ion gyro period. In front of the piston, the time needed to decrease the nonmagnetized ion anisotropy using the magnetic turbulence is much larger than the ion gyroperiod in the piston. Consequently, particles are reflected by the piston, which acts as a wall initiating a transient phase. After several ion periods, the formation of this electromagnetic forward shock is, then, accelerated by the piston, and at large timescale, the dissipation of energy is eventually mediated only by the Weibel turbulence. We report here a new configuration of shocks, where a reverse magnetized and a forward electromagnetic shock coexist separated by a tangential discontinuity. Particle acceleration and heating in the two shock structures and relevance of this scenario of collisionless shock formation to laboratory experiments and astrophysical conditions are discussed.

1.
D. W.
Forslund
and
C. R.
Shonk
, “
Formation and structure of electrostatic collisionless shocks
,”
Phys. Rev. Lett.
25
,
1699
1702
(
1970
).
2.
M. A.
Balikhin
,
M.
Nozdrachev
,
M.
Dunlop
,
V.
Krasnosel'skikh
,
S. N.
Walker
,
H. S. C. K.
Alleyne
,
V.
Formisano
,
M.
Andre
,
A.
Balogh
,
A.
Eriksson
, and
K.
Yearby
, “
Observation of the terrestrial bow shock in quasi-electrostatic subshock regime
,”
J. Geophys. Res.
107
,
SSH 1-1
SSH 1-9
, (
2002
).
3.
M.
Opher
,
J. F.
Drake
,
B.
Zieger
,
M.
Swisdak
, and
G.
Toth
, “
Magnetized jets driven by the sun: The structure of the heliosphere revisited-updates
,”
Phys. Plasmas
23
,
056501
(
2016
).
4.
M. V.
Medvedev
and
A.
Loeb
, “
Generation of magnetic fields in the relativistic shock of gamma-ray burst sources
,”
Astrophys. J.
526
,
697
(
1999
).
5.
Y.
Lyubarsky
and
D.
Eichler
, “
Are gamma-ray burst shocks mediated by the Weibel instability?
,”
Astrophys. J.
647
,
1250
(
2006
).
6.
A.
Marcowith
,
A.
Bret
,
A.
Bykov
,
M. E.
Dieckmann
,
L. O.
Drury
,
B.
Lembège
,
M.
Lemoine
,
G.
Morlino
,
G.
Murphy
,
G.
Pelletier
,
I.
Plotnikov
,
B.
Reville
,
M.
Riquelme
,
L.
Sironi
, and
A. S.
Novo
, “
The microphysics of collisionless shock waves
,”
Rep. Prog. Phys.
79
,
046901
(
2016
).
7.
A. R.
Bell
, “
The acceleration of cosmic rays in shock fronts-I
,”
Mon. Not. R. Astron. Soc.
182
,
147
156
(
1978
).
8.
R. D.
Blandford
and
J. P.
Ostriker
, “
Particle acceleration by astrophysical shocks
,”
Astrophys. J. Lett.
221
,
L29
L32
(
1978
).
9.
E. S.
Weibel
, “
Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution
,”
Phys. Rev. Lett.
2
,
83
84
(
1959
).
10.
A.
Spitkovsky
, “
On the structure of relativistic collisionless shocks in electron-ion plasmas
,”
Astrophys. J. Lett.
673
,
L39
(
2008
).
11.
A.
Spitkovsky
, “
Particle acceleration in relativistic collisionless shocks: Fermi process at last?
,”
Astrophys. J. Lett.
682
,
L5
(
2008
).
12.
H.
Takabe
,
T. N.
Kato
,
Y.
Sakawa
,
Y.
Kuramitsu
,
T.
Morita
,
T.
Kadono
,
K.
Shigemori
,
K.
Otani
,
H.
Nagatomo
,
T.
Norimatsu
,
S.
Dono
,
T.
Endo
,
K.
Miyanishi
,
T.
Kimura
,
A.
Shiroshita
,
N.
Ozaki
,
R.
Kodama
,
S.
Fujioka
,
H.
Nishimura
,
D.
Salzman
,
B.
Loupias
,
C.
Gregory
,
M.
Koenig
,
J. N.
Waugh
,
N. C.
Woolsey
,
D.
Kato
,
Y.
Li-T
,
Q.-L.
Dong
,
S.-J.
Wang
,
Y.
Zhang
,
J.
Zhao
,
F.
Wang-L
,
H.
Wei-G
,
J.-R.
Shi
,
G.
Zhao
,
J.
Zhang-Y
,
T.-S.
Wen
,
W.-H.
Zhang
,
X.
Hu
,
S.-Y.
Liu
,
Y. K.
Ding
,
L.
Zhang
,
Y.-J.
Tang
,
B.-H.
Zhang
,
Z.-J.
Zheng
,
Z.-M.
Sheng
, and
J.
Zhang
, “
High-Mach number collisionless shock and photo-ionized non-LTE plasma for laboratory astrophysics with intense lasers
,”
Plasma Phys. Controlled Fusion
50
,
124057
(
2008
).
13.
H.
Ahmed
,
M. E.
Dieckmann
,
L.
Romagnani
,
D.
Doria
,
G.
Sarri
,
M.
Cerchez
,
E.
Ianni
,
I.
Kourakis
,
A. L.
Giesecke
,
M.
Notley
,
R.
Prasad
,
K.
Quinn
,
O.
Willi
, and
M.
Borghesi
, “
Time-resolved characterization of the formation of a collisionless shock
,”
Phys. Rev. Lett.
110
,
205001
(
2013
).
14.
D. B.
Schaeffer
,
W.
Fox
,
D.
Haberberger
,
G.
Fiksel
,
A.
Bhattacharjee
,
D. H.
Barnak
,
S. X.
Hu
,
K.
Germaschewski
, and
R. K.
Follett
, “
High-Mach number, laser-driven magnetized collisionless shocks
,”
Phys. Plasmas
24
,
122702
(
2017
).
15.
W.
Fox
,
G.
Fiksel
,
A. A. B. P. Y.
Chang
,
K.
Germaschewski
,
S. X.
Hu
, and
P. M.
Nilson
, “
Filamentation instability of counterstreaming laser-driven plasmas
,”
Phys. Rev. Lett.
111
,
225002
(
2013
).
16.
C. M.
Huntington
,
F.
Fiuza
,
J. S.
Ross
,
A.
Zylstra
,
R. P.
Drake
,
D.
Froula
,
G.
Gregori
,
N. L.
Kugland
,
C.
Kuranz
,
M.
Levy
,
C. K.
Li
,
J.
Meinecke
,
T.
Morita
,
R.
Petrasso
,
C.
Plechaty
,
B. A.
Remington
,
D. D.
Ryutov
,
Y.
Sakawa
, and
A. A. S. H. S.
Park
, “
Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows
,”
Nat. Phys.
11
,
173
176
(
2015
).
17.
C. M.
Huntington
,
M. J. E.
Manuel
,
J. S.
Ross
,
S. C.
Wilks
,
F.
Fiuza
,
H. G.
Rinderknecht
,
H. S.
Park
,
G.
Gregori
,
D. P.
Higginson
,
J.
Park
,
B. B.
Pollock
,
B. A.
Remington
,
D. D.
Ryutov
,
C.
Ruyer
,
Y.
Sakawa
,
H.
Sio
,
A.
Spitkovsky
,
G. F.
Swadling
,
H.
Takabe
, and
A. B.
Zylstra
, “
Magnetic field production via the Weibel instability in interpenetrating plasma flows
,”
Phys. Plasmas
24
,
041410
(
2017
).
18.
C. K.
Li
,
V. T.
Tikhonchuk
,
Q.
Moreno
,
H.
Sio
,
E.
D'Humières
,
X.
Ribeyre
,
P.
Korneev
,
S.
Atzeni
,
R.
Betti
,
A.
Birkel
,
E. M.
Campbell
,
R. K.
Follett
,
J. A.
Frenje
,
S. X.
Hu
,
M.
Koenig
,
Y.
Sakawa
,
T. C.
Sangster
,
F. H.
Seguin
,
H.
Takabe
,
S.
Zhang
, and
R. D.
Petrasso
, “
Collisionless shocks driven by supersonic plasma flows with self-generated magnetic fields
,”
Phys. Rev. Lett.
123
,
055002
(
2019
).
19.
M. E.
Dieckmann
,
D.
Folini
,
I.
Hotz
,
A.
Nordman
,
P.
Dell'Acqua
,
A.
Ynnerman
, and
R.
Walder
, “
Structure of a collisionless pair jet in a magnetized electron-proton plasma: Flow-aligned magnetic field
,”
Astron. Astrophys.
621
,
A142
(
2019
).
20.
P.
Hartigan
, “
The visibility of the Mach disk and the bow shock of a stellar jet
,”
Astrophys. J.
339
,
987
(
1989
).
21.
S.
Matsukiyo
and
M.
Scholer
, “
Modified two-stream instability in the foot of high Mach number quasi-perpendicular shocks
,”
J. Geophys. Res.
108
,
010080
, (
2003
).
22.
H.
Sakemi
,
M.
Machida
,
T.
Akahori
,
H.
Nakanishi
,
H.
Akamatsu
,
K.
Kurahara
, and
J.
Farnes
, “
Magnetic field analysis of the bow and terminal shock of the ss433 jet
,”
Publ. Astron. Soc. Jpn.
70
,
27
(
2018
).
23.
Y.
Sentoku
and
A. J.
Kemp
, “
Numerical methods for particle simulations at extreme densities and temperatures: Weighted particles, relativistic collisions and reduced currents
,”
J. Comput. Phys.
227
,
6846
6861
(
2008
).
24.
C.
Birdsall
and
A.
Langdon
,
Plasma Physics Via Computer Simulation
, Series in Plasma Physics and Fluid Dynamics (
Taylor & Francis
,
2004
).
25.
D. D.
Ryutov
,
N. L.
Kugland
,
H. S.
Park
,
C.
Plechaty
,
B. A.
Remington
, and
J. S.
Ross
, “
Basic scalings for collisionless-shock experiments in a plasma without pre-imposed magnetic field
,”
Plasma Phys. Controlled Fusion
54
,
105021
(
2012
).
26.
S. G.
Bochkarev
,
E.
d'Humières
,
P.
Korneev
,
V. Y.
Bychenkov
, and
V. T.
Tikhonchuk
, “
The role of electron heating in electromagnetic collisionless shock formation
,”
High Energy Density Phys.
17
,
175
182
(
2015
).
27.
A. M.
Bykov
and
R. A.
Treumann
, “
Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks
,”
Astron. Astrophys. Rev.
19
,
42
(
2011
).
28.
R. Z.
Sagdeev
,
D. A.
Usikov
, and
G. M.
Zaslavsky
,
Nonlinear Physics -From the Pendulum to Turbulence and Chaos
(
Harwood Academic Publishers
,
1988
).
29.
T. D.
Arber
,
K.
Bennett
,
C. S.
Brady
,
A.
Lawrence-Douglas
,
M. G.
Ramsay
,
N. J.
Sircombe
,
P.
Gillies
,
R. G.
Evans
,
H.
Schmitz
, and
A. R. A. B. C. P.
Ridgers
, “
Contemporary particle-in-cell approach to laser-plasma modelling
,”
Plasma Phys. Controlled Fusion
57
,
113001
(
2015
).
30.
The choice of this code for these simulations is explained by an efficient 1D3V parallelization of EPOCH.
31.
C.
Ruyer
,
L.
Gremillet
,
A.
Debayle
, and
G.
Bonnaud
, “
Nonlinear dynamics of the ion Weibel-filamentation instability: An analytical model for the evolution of the plasma and spectral properties
,”
Phys. Plasmas
22
,
032102
(
2015
).
32.
R. C.
Davidson
,
D. A.
Hammer
,
I.
Haber
, and
C. E.
Wagner
, “
Nonlinear development of electromagnetic instabilities in anisotropic plasmas
,”
Phys. Fluids
15
,
317
333
(
1972
).
33.
C.
Ruyer
,
L.
Gremillet
,
G.
Bonnaud
, and
C.
Riconda
, “
Analytical predictions of field and plasma dynamics during nonlinear Weibel-mediated flow collisions
,”
Phys. Rev. Lett.
117
,
065001
(
2016
).
34.
C.
Ruyer
,
L.
Gremillet
,
G.
Bonnaud
, and
C.
Riconda
, “
A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks
,”
Phys. Plasmas
24
,
041409
(
2017
).
35.
W.
Marshall
, “
The structure of magneto-hydrodynamic shock waves
,”
Proc. R. Soc. London, Ser. A
233
,
367
376
(
1955
).
36.
Q.
Moreno
,
M. E.
Dieckmann
,
X.
Ribeyre
,
V. T.
Tikhonchuk
,
D.
Folini
,
R.
Walder
, and
E.
d'Humieres
, “
Failed self-reformation of a sub-critical fast magnetosonic shock in collisionless plasma
,”
Plasma Res. Express
1
,
035001
(
2019
).
37.
S.
Matsukiyo
and
M.
Scholer
, “
Simulations of pickup ion mediated quasi-perpendicular shocks: Implications for the heliospheric termination shock
,”
J. Geophys. Res.
119
,
2388
2399
, (
2014
).
38.
P.
Korneev
,
E.
d'Humières
, and
V. T.
Tikhonchuk
, “
Collisionless plasma interpenetration in a strong magnetic field for laboratory astrophysics experiments
,”
Phys. Plasmas
21
,
022117
(
2014
).
39.
A. L.
Verdon
,
I. H.
Cairns
,
D. B.
Melrose
, and
P. A.
Robinson
, “
Warm electromagnetic lower hybrid wave dispersion relation
,”
Phys. Plasmas
16
,
052105
(
2009
).
40.
M. E.
Dieckmann
,
Q.
Moreno
,
D.
Doria
,
L.
Romagnani
,
G.
Sarri
,
D.
Folini
,
R.
Walder
,
A.
Bret
,
E.
d'Humieres
, and
M.
Borghesi
, “
Expansion of a radially symmetric blast shell into a uniformly magnetized plasma
,”
Phys. Plasmas
25
,
052108
(
2018
).
41.
F. M.
Rieger
,
V.
Bosch-Ramon
, and
P.
Duffy
, “
Fermi acceleration in astrophysical jets
,”
Astrophys. Space Sci.
309
,
119
125
(
2007
).
42.
A.
Bret
and
M. E.
Dieckmann
, “
How large can the electron to proton mass ratio be in particle-in-cell simulations of unstable systems?
,”
Phys. Plasmas
17
,
032109
(
2010
).
43.
Y.
Matsumoto
,
T.
Amano
,
T. N.
Kato
, and
M.
Hoshino
, “
Stochastic electron acceleration during spontaneous turbulent reconnection in a strong shock wave
,”
Science
347
,
974
978
(
2015
).
44.
Y.
Matsumoto
,
T.
Amano
,
T. N.
Kato
, and
M.
Hoshino
, “
Electron surfing and drift accelerations in a Weibel-dominated high-Mach-number shock
,”
Phys. Rev. Lett.
119
,
105101
(
2017
).
45.
R. P.
Drake
, “
The design of laboratory experiments to produce collisionless shocks of cosmic relevance
,”
Phys. Plasmas
7
,
4690
4698
(
2000
).
46.
R. A.
Treumann
, “
Fundamentals of collisionless shocks for astrophysical application, 1. Non-relativistic shocks
,”
Astron. Astrophys. Rev.
17
,
409
535
(
2009
).
47.
J. D.
Huba
,
NRL Plasma Formulary
(
Naval Research Laboratory
,
2009
).
You do not currently have access to this content.