Plasmas that are strongly magnetized in the sense that the gyrofrequency exceeds the plasma frequency exhibit novel transport properties that are not well understood. As a representative example, we compute the friction force acting on a massive test charge moving through a strongly coupled and strongly magnetized one-component plasma using a generalized Boltzmann kinetic theory. Recent works studying the weakly coupled regime have shown that strong magnetization leads to a transverse component of the friction force that is perpendicular to both the Lorentz force and velocity of the test charge, in addition to the stopping power component aligned antiparallel to the velocity. Recent molecular dynamics simulations have also shown that strong Coulomb coupling in addition to strong magnetization gives rise to a third component of the friction force in the direction of the Lorentz force. Here, we show that the generalized Boltzmann kinetic theory captures these effects and generally agrees well with the molecular dynamics simulations over a broad range of Coulomb coupling and magnetization strength regimes. The theory is also used to show that the “gyro” component of the friction in the direction of the Lorentz force arises due to asymmetries associated with gyromotion during short-range collisions. Computing the average motion of the test charge through the background plasma, the transverse force is found to strongly influence the trajectory by changing the gyroradius and the gyrofriction force is found to slightly change the gyrofrequency of the test charge resulting in a phase shift.
References
1.
B. R.
Beck
, J.
Fajans
, and J. H.
Malmberg
, “Measurement of collisional anisotropic temperature relaxation in a strongly magnetized pure electron plasma
,” Phys. Rev. Lett.
68
, 317
–320
(1992
).2.
X. L.
Zhang
, R. S.
Fletcher
, S. L.
Rolston
, P. N.
Guzdar
, and M.
Swisdak
, “Ultracold plasma expansion in a magnetic field
,” Phys. Rev. Lett.
100
, 235002
(2008
).3.
J.
Fajans
and C.
Surko
, “Plasma and trap-based techniques for science with antimatter
,” Phys. Plasmas
27
, 030601
(2020
).4.
L. I.
Men'shikov
, “New directions in the theory of electron cooling
,” Phys.-Usp.
51
, 645
–680
(2008
).5.
R.
Aymar
, P.
Barabaschi
, and Y.
Shimomura
, “The ITER design
,” Plasma Phys. Controlled Fusion
44
, 519
–565
(2002
).6.
E.
Thomas
, R. L.
Merlino
, and M.
Rosenberg
, “Magnetized dusty plasmas: The next Frontier for complex plasma research
,” Plasma Phys. Controlled Fusion
54
, 124034
(2012
).7.
A. K.
Harding
and D.
Lai
, “Physics of strongly magnetized neutron stars
,” Rep. Prog. Phys.
69
, 2631
–2708
(2006
).8.
L.
Jose
and S. D.
Baalrud
, “A generalized Boltzmann kinetic theory for strongly magnetized plasmas with application to friction
,” Phys. Plasmas
27
, 112101
(2020
).9.
J. H.
Ferziger
and H. G.
Kaper
, Mathematical Theory of Transport Processes in Gases
(North-Holland
, 1972
).10.
S. D.
Baalrud
and J.
Daligault
, “Effective potential theory for transport coefficients across coupling regimes
,” Phys. Rev. Lett.
110
, 235001
(2013
).11.
S. D.
Baalrud
and J.
Daligault
, “Extending plasma transport theory to strong coupling through the concept of an effective interaction potential
,” Phys. Plasmas
21
, 055707
(2014
).12.
S. D.
Baalrud
and J.
Daligault
, “Transport regimes spanning magnetization-coupling phase space
,” Phys. Rev. E
96
, 043202
(2017
).13.
L. D.
Landau
, “The transport equation in the case of coulomb interactions
,” in Collected Papers of L. D. Landau
, edited by D.
Ter Haar
(Pergamon
, 1965
), pp. 163
–170
.14.
M. N.
Rosenbluth
, W. M.
MacDonald
, and D. L.
Judd
, “Fokker-Planck equation for an inverse-square force
,” Phys. Rev.
107
, 1
–6
(1957
).15.
A.
Lenard
, “On Bogoliubov's kinetic equation for a spatially homogeneous plasma
,” Ann. Phys.
10
, 390
–400
(1960
).16.
R.
Balescu
, “Irreversible processes in ionized gases
,” Phys. Fluids
3
, 52
–63
(1960
).17.
N.
Rostoker
, “Kinetic equation with a constant magnetic field
,” Phys. Fluids
3
, 922
–927
(1960
).18.
S.
Cohen
, E.
Sarid
, and M.
Gedalin
, “Fokker-Planck coefficients for a magnetized ion-electron plasma
,” Phys. Plasmas
25
, 012311
(2018
).19.
D.
Montgomery
, L.
Turner
, and G.
Joyce
, “Fokker-Planck equation for a plasma in a magnetic field
,” Phys. Fluids
17
, 954
–960
(1974
).20.
D. H.
Dubin
, “Parallel velocity diffusion and slowing-down rate from long-range collisions in a magnetized plasma
,” Phys. Plasmas
21
, 052108
(2014
).21.
C.
Dong
, W.
Zhang
, J.
Cao
, and D.
Li
, “Derivation of the magnetized Balescu-Lenard-Guernsey collision term based on the Fokker-Planck approach
,” Phys. Plasmas
24
, 122120
(2017
).22.
T.
O'Neil
, “Collision operator for a strongly magnetized pure electron plasma
,” Phys. Fluids
26
, 2128
–2135
(1983
).23.
D.
Sigmar
and G.
Joyce
, “Plasma heating by energetic particles
,” Nucl. Fusion
11
, 447
–456
(1971
).24.
T.
Lafleur
and S. D.
Baalrud
, “Transverse force induced by a magnetized wake
,” Plasma Phys. Controlled Fusion
61
, 125004
(2019
).25.
T.
Lafleur
and S. D.
Baalrud
, “Friction in a strongly magnetized neutral plasma
,” Plasma Phys. Controlled Fusion
62
, 095003
(2020
).26.
Ya. S.
Derbenev
and A. N.
Skrinsky
, “The effect of an accompanying magnetic field on electron cooling
,” Part. Accel.
8
, 235
–243
(1978
).27.
V.
Parkhomchuk
, “Study of fast electron cooling
,” in Proceedings of the Workshop on Electron Cooling and Related Applications (ECOOL)
, edited by H.
Poth
(Kernforschungszentrum Karlsruhe GmbH
, Karlsruhe
, 1984
), pp. 71
–84
.28.
D. J.
Bernstein
, T.
Lafleur
, J.
Daligault
, and S. D.
Baalrud
, “Friction force in strongly magnetized plasmas
,” Phys. Rev. E
102
, 041201
(2020
).29.
A. V.
Fedotov
, D. L.
Bruhwiler
, A. O.
Sidorin
, D. T.
Abell
, I.
Ben-Zvi
, R.
Busby
, J. R.
Cary
, and V. N.
Litvinenko
, “Numerical study of the magnetized friction force
,” Phys. Rev. Spec. Top. Accel. Beams
9
, 074401
(2006
).30.
H.
Nersisyan
, C.
Toepffer
, and G.
Zwicknagel
, Interactions between Charged Particles in a Magnetic Field
(Springer-Verlag
, Berlin, Heidelberg
, 2007
).31.
H. B.
Nersisyan
, M.
Walter
, and G.
Zwicknagel
, “Stopping power of ions in a magnetized two-temperature plasma
,” Phys. Rev. E
61
, 7022
–7033
(2000
).32.
H. B.
Nersisyan
, G.
Zwicknagel
, and C.
Toepffer
, “Energy loss of ions in a magnetized plasma: Conformity between linear response and binary collision treatments
,” Phys. Rev. E
67
, 026411
(2003
).33.
H. B.
Nersisyan
and G.
Zwicknagel
, “Binary collisions of charged particles in a magnetic field
,” Phys. Rev. E
79
, 066405
(2009
).34.
C.
Cereceda
, M.
de Peretti
, and C.
Deutsch
, “Stopping power for arbitrary angle between test particle velocity and magnetic field
,” Phys. Plasmas
12
, 022102
(2005
).35.
D. J.
Bernstein
and S. D.
Baalrud
, “Effects of Coulomb coupling on friction in strongly magnetized plasmas
,” Phys. Plasmas
28
, 062101
(2021
).36.
S. D.
Baalrud
and J.
Daligault
, “Mean force kinetic theory: A convergent kinetic theory for weakly and strongly coupled plasmas
,” Phys. Plasmas
26
, 082106
(2019
).37.
J. P.
Hansen
and I. R.
McDonald
, Theory of Simple Liquids: With Applications to Soft Matter
(Academic Press
, 2013
).38.
S. D.
Baalrud
and J.
Daligault
, “Modified Enskog kinetic theory for strongly coupled plasmas
,” Phys. Rev. E
91
, 063107
(2015
).39.
W. H.
Press
, S. A.
Teukolsky
, W. T.
Vetterling
, and B. P.
Flannery
, Numerical Recipes 3rd Edition: The Art of Scientific Computing
(Cambridge University Press
, 2007
).40.
D. J.
Bernstein
, S. D.
Baalrud
, and J.
Daligault
, “Effects of Coulomb coupling on stopping power and a link to macroscopic transport
,” Phys. Plasmas
26
, 082705
(2019
).41.
K. R.
Vidal
and S. D.
Baalrud
, “Extended space and time correlations in strongly magnetized plasmas
,” Phys. Plasmas
28
, 042103
(2021
).42.
D. H. E.
Dubin
, “Test particle diffusion and the failure of integration along unperturbed orbits
,” Phys. Rev. Lett.
79
, 2678
–2681
(1997
).43.
S. D.
Baalrud
and J.
Daligault
, “Effective potential kinetic theory for strongly coupled plasmas
,” AIP Conf. Proc.
1786
, 130001
(2016
).44.
45.
J.
Towns
, T.
Cockerill
, M.
Dahan
, I.
Foster
, K.
Gaither
, A.
Grimshaw
, V.
Hazlewood
, S.
Lathrop
, D.
Lifka
, G. D.
Peterson
, R.
Roskies
, J.
Scott
, and N.
Wilkins-Diehr
, “XSEDE: Accelerating scientific discovery
,” Comput. Sci. Eng.
16
, 62
–74
(2014
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
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