Recent works have shown that strongly magnetized plasmas characterized by having a gyrofrequency greater than the plasma frequency exhibit novel transport properties. One example is that the friction force on a test charge shifts, obtaining components perpendicular to its velocity in addition to the typical stopping power component antiparallel to its velocity. Here, we apply a recent generalization of the Boltzmann equation for strongly magnetized plasmas to calculate the ion–electron temperature relaxation rate. Strong magnetization is generally found to increase the temperature relaxation rate perpendicular to the magnetic field and to cause the temperatures parallel and perpendicular to the magnetic field to not relax at equal rates. This, in turn, causes a temperature anisotropy to develop during the equilibration. Strong magnetization also breaks the symmetry of independence of the sign of the charges of the interacting particles on the collision rate, commonly known as the “Barkas effect.” It is found that the combination of oppositely charged interaction and strong magnetization causes the ion–electron parallel temperature relaxation rate to be significantly suppressed, scaling inversely proportional to the magnetic field strength.
REFERENCES
1.
T.
Ott
and
M.
Bonitz
, “
Diffusion in a strongly coupled magnetized plasma
,” Phys. Rev. Lett.
107
, 135003
(2011
).2.
S. D.
Baalrud
and
J.
Daligault
, “
Transport regimes spanning magnetization-coupling phase space
,” Phys. Rev. E
96
, 043202
(2017
).3.
J.
Fajans
and
C.
Surko
, “
Plasma and trap-based techniques for science with antimatter
,” Phys. Plasmas
27
, 030601
(2020
).4.
E. V.
Stenson
,
J.
Horn-Stanja
,
M. R.
Stoneking
, and
T. S.
Pedersen
, “
Debye length and plasma skin depth: Two length scales of interest in the creation and diagnosis of laboratory pair plasmas
,” J. Plasma Phys.
83
, 595830106
(2017
).5.
G. M.
Gorman
,
M. K.
Warrens
,
S. J.
Bradshaw
, and
T. C.
Killian
, “
Laser-induced-fluorescence imaging of a spin-polarized ultracold neutral plasma in a magnetic field
,” Phys. Rev. A
105
, 013108
(2022
).6.
G. M.
Gorman
,
M. K.
Warrens
,
S. J.
Bradshaw
, and
T. C.
Killian
, “
Magnetic confinement of an ultracold neutral plasma
,” Phys. Rev. Lett.
126
, 085002
(2021
).7.
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
).8.
R. T.
Sprenkle
,
S. D.
Bergeson
,
L. G.
Silvestri
, and
M. S.
Murillo
, “
Ultracold neutral plasma expansion in a strong uniform magnetic field
,” Phys. Rev. E
105
, 045201
(2022
).9.
J. M.
Guthrie
and
J. L.
Roberts
, “
Finite-amplitude RF heating rates for magnetized electrons in neutral plasma
,” Phys. Plasmas
28
, 052101
(2021
).10.
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
).11.
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
).12.
N.
Bennett
,
D. R.
Welch
,
G.
Laity
,
D. V.
Rose
, and
M. E.
Cuneo
, “
Magnetized particle transport in multi-MA accelerators
,” Phys. Rev. Accel. Beams
24
, 060401
(2021
).13.
R.
Aymar
,
P.
Barabaschi
, and
Y.
Shimomura
, “
The ITER design
,” Plasma Phys. Controlled Fusion
44
, 519
–565
(2002
).14.
J. H.
Ferziger
and
H. G.
Kaper
, Mathematical Theory of Transport Processes in Gases
(
North-Holland
, 1972
).15.
S.
Ichimaru
, Statistical Plasma Physics, Volume I: Basic Principles
(
CRC Press
, 2004
).16.
L.
Jose
and
S. D.
Baalrud
, “
A generalized boltzmann kinetic theory for strongly magnetized plasmas with application to friction
,” Phys. Plasmas
27
, 112101
(2020
).17.
L.
Jose
and
S. D.
Baalrud
, “
A kinetic model of friction in strongly coupled strongly magnetized plasmas
,” Phys. Plasmas
28
, 072107
(2021
).18.
Y. S.
Derbenev
and
A. N.
Skrinsky
, “
The effect of an accompanying magnetic field on electron cooling
,” Part. Accel.
8
, 235
–243
(1978
).19.
L. I.
Men'shikov
, “
New directions in the theory of electron cooling
,” Phys. Usp.
51
, 645
–680
(2008
).20.
V.
Parkhomchuk
, “
Study of fast electron cooling
,” in Proceedings of the Workshop on Electron Cooling and Related Applications (ECOOL84, 1984)
, edited by
H.
Poth
(
Kernforschungszentrum Karlsruhe GmbH
,
Karlsruhe
, 1984
), pp. 71
–84
.21.
T.
Lafleur
and
S. D.
Baalrud
, “
Transverse force induced by a magnetized wake
,” Plasma Phys. Controlled Fusion
61
, 125004
(2019
).22.
T.
Lafleur
and
S. D.
Baalrud
, “
Friction in a strongly magnetized neutral plasma
,” Plasma Phys. Controlled Fusion
62
, 095003
(2020
).23.
D. J.
Bernstein
,
T.
Lafleur
,
J.
Daligault
, and
S. D.
Baalrud
, “
Friction force in strongly magnetized plasmas
,” Phys. Rev. E
102
, 041201
(2020
).24.
L.
Jose
,
D. J.
Bernstein
, and
S. D.
Baalrud
, “
Barkas effect in strongly magnetized plasmas
,” Phys. Plasmas
29
, 112103
(2022
).25.
M.
Ahmadi
,
B. X. R.
Alves
,
C. J.
Baker
,
W.
Bertsche
,
E.
Butler
,
A.
Capra
,
C.
Carruth
,
C. L.
Cesar
,
M.
Charlton
,
S.
Cohen
,
R.
Collister
,
S.
Eriksson
,
A.
Evans
,
N.
Evetts
,
J.
Fajans
,
T.
Friesen
,
M. C.
Fujiwara
,
D. R.
Gill
,
A.
Gutierrez
,
J. S.
Hangst
,
W. N.
Hardy
,
M. E.
Hayden
,
C. A.
Isaac
,
A.
Ishida
,
M. A.
Johnson
,
S. A.
Jones
,
S.
Jonsell
,
L.
Kurchaninov
,
N.
Madsen
,
M.
Mathers
,
D.
Maxwell
,
J. T. K.
McKenna
,
S.
Menary
,
J. M.
Michan
,
T.
Momose
,
J. J.
Munich
,
P.
Nolan
,
K.
Olchanski
,
A.
Olin
,
P.
Pusa
,
C. Ø.
Rasmussen
,
F.
Robicheaux
,
R. L.
Sacramento
,
M.
Sameed
,
E.
Sarid
,
D. M.
Silveira
,
S.
Stracka
,
G.
Stutter
,
C.
So
,
T. D.
Tharp
,
J. E.
Thompson
,
R. I.
Thompson
,
D. P.
van der Werf
, and
J. S.
Wurtele
, “
Antihydrogen accumulation for fundamental symmetry tests
,” Nat. Commun.
8
, 681
(2017
).26.
C. J.
Baker
,
W.
Bertsche
,
A.
Capra
,
C. L.
Cesar
,
M.
Charlton
,
A. C.
Mathad
,
S.
Eriksson
,
A.
Evans
,
N.
Evetts
,
S.
Fabbri
,
J.
Fajans
,
T.
Friesen
,
M. C.
Fujiwara
,
P.
Grandemange
,
P.
Granum
,
J. S.
Hangst
,
M. E.
Hayden
,
D.
Hodgkinson
,
C. A.
Isaac
,
M. A.
Johnson
,
J. M.
Jones
,
S. A.
Jones
,
S.
Jonsell
,
L.
Kurchaninov
,
N.
Madsen
,
D.
Maxwell
,
J. T. K.
McKenna
,
S.
Menary
,
T.
Momose
,
P.
Mullan
,
K.
Olchanski
,
A.
Olin
,
J.
Peszka
,
A.
Powell
,
P.
Pusa
,
C. Ø.
Rasmussen
,
F.
Robicheaux
,
R. L.
Sacramento
,
M.
Sameed
,
E.
Sarid
,
D. M.
Silveira
,
G.
Stutter
,
C.
So
,
T. D.
Tharp
,
R. I.
Thompson
,
D. P.
van der Werf
, and
J. S.
Wurtele
, “
Sympathetic cooling of positrons to cryogenic temperatures for antihydrogen production
,” Nat. Commun.
12
, 6139
(2021
).27.
W. A.
Bertsche
,
E.
Butler
,
M.
Charlton
, and
N.
Madsen
, “
Physics with antihydrogen
,” J. Phys. B: At., Mol. Opt. Phys.
48
, 232001
(2015
).28.
S.
Ichimaru
and
M. N.
Rosenbluth
, “
Relaxation processes in plasmas with magnetic field. temperature relaxations
,” Phys. Fluids
13
, 2778
–2789
(1970
).29.
H. B.
Nersisyan
,
C.
Deutsch
, and
A. K.
Das
, “
Number-conserving linear-response study of low-velocity ion stopping in a collisional magnetized classical plasma
,” Phys. Rev. E
83
, 036403
(2011
).30.
T.
Kihara
,
Y.
Midzuno
,
K.
Sakuma
, and
T.
Shizume
, “
Ion-electron relaxation of plasmas in a magnetic field, II
,” J. Phys. Soc. Jpn.
15
, 684
–687
(1960
).31.
T.
Kihara
and
Y.
Midzuno
, “
Irreversible processes in plasmas in a strong magnetic field
,” Rev. Mod. Phys.
32
, 722
–730
(1960
).32.
C.
Dong
,
H.
Ren
,
H.
Cai
, and
D.
Li
, “
Effects of magnetic field on anisotropic temperature relaxation
,” Phys. Plasmas
20
, 032512
(2013
).33.
C.
Dong
,
H.
Ren
,
H.
Cai
, and
D.
Li
, “
Temperature relaxation in a magnetized plasma
,” Phys. Plasmas
20
, 102518
(2013
).34.
T.
Kihara
, “
Ion-electron relaxation of plasmas in a strong magnetic field. I
,” J. Phys. Soc. Jpn.
14
, 1751
–1754
(1959
).35.
V.
Silin
, “
On relaxation of electron and ion temperatures of fully ionized plasma in a strong magnetic field
,” Sov. Phys. JETP
16
, 1281
(1963
).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.
S. D.
Baalrud
and
J.
Daligault
, “
Effective potential theory for transport coefficients across coupling regimes
,” Phys. Rev. Lett.
110
, 235001
(2013
).38.
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
).39.
D. J.
Bernstein
and
S. D.
Baalrud
, “
Method to determine the electron–ion temperature relaxation rate from test particle distributions
,” Phys. Plasmas
29
, 072705
(2022
).40.
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
).41.
J. P.
Hansen
and
I. R.
McDonald
, Theory of Simple Liquids: With Applications to Soft Matter
(
Academic Press
, 2013
).42.
G. P.
Lepage
, “
Adaptive multidimensional integration: Vegas enhanced
,” J. Comput. Phys.
439
, 110386
(2021
).43.
44.
E.
Hairer
,
S. P.
Norsett
, and
G.
Wanner
, “
Runge-Kutta and extrapolation methods
,” in Solving Ordinary Differential Equations I: Nonstiff Problems
(
Springer
,
Berlin Heidelberg
, 1993
), pp. 129
–353
.45.
N. R.
Shaffer
and
S. D.
Baalrud
, “
The Barkas effect in plasma transport
,” Phys. Plasmas
26
, 032110
(2019
).46.
S. D.
Baalrud
and
J.
Daligault
, “
Temperature anisotropy relaxation of the one-component plasma
,” Contrib. Plasma Phys.
57
, 238
–251
(2017
).47.
D. H.
Dubin
, “
Parallel velocity diffusion and slowing-down rate from long-range collisions in a magnetized plasma
,” Phys. Plasmas
21
, 052108
(2014
).48.
D. H. E.
Dubin
, “
Test particle diffusion and the failure of integration along unperturbed orbits
,” Phys. Rev. Lett.
79
, 2678
–2681
(1997
).49.
T.
Ott
,
M.
Bonitz
,
P.
Hartmann
, and
Z.
Donkó
, “
Spontaneous generation of temperature anisotropy in a strongly coupled magnetized plasma
,” Phys. Rev. E
95
, 013209
(2017
).50.
B.
Scheiner
and
S. D.
Baalrud
, “
Viscosity of the magnetized strongly coupled one-component plasma
,” Phys. Rev. E
102
, 063202
(2020
).51.
H.
Kählert
and
M.
Bonitz
, “
Dynamic structure factor of the magnetized one-component plasma: Crossover from weak to strong coupling
,” Phys. Rev. Res.
4
, 013197
(2022
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
