In space and astrophysical plasmas, like in planetary magnetospheres, as that of Mercury, energetic electrons are often found near current sheets, which hint at electron acceleration by magnetic reconnection. Unfortunately, electron acceleration by reconnection is not well understood yet, in particular, acceleration by turbulent plasmoid reconnection. We have investigated electron acceleration by turbulent plasmoid reconnection, described by MHD simulations, via test particle calculations. In order to avoid resolving all relevant turbulence scales down to the dissipation scales, a mean-field turbulence model is used to describe the turbulence of sub-grid scales and their effects via a turbulent electromotive force (EMF). The mean-field model describes the turbulent EMF as a function of the mean values of current density, vorticity, magnetic field as well as of the energy, cross-helicity, and residual helicity of the turbulence. We found that, mainly around X-points of turbulent reconnection, strongly enhanced localized EMFs most efficiently accelerated electrons and caused the formation of power-law spectra. Magnetic-field-aligned EMFs, caused by the turbulence, dominate the electron acceleration process. Scaling the acceleration processes to parameters of the Hermean magnetotail, electron energies up to 60 keV can be reached by turbulent plasmoid reconnection through the thermal plasma.

1.
W. H.
Matthaeus
and
S. L.
Lamkin
, “
Rapid magnetic reconnection caused by finite amplitude fluctuations
,”
Phys. Fluids
28
,
303
307
(
1985
).
2.
A.
Lazarian
and
E. T.
Vishniac
, “
Reconnection in a weakly stochastic field
,”
Astrophys. J.
517
,
700
718
(
1999
); e-print arXiv:astro-ph/9811037.
3.
J.
Ambrosiano
,
W. H.
Matthaeus
,
M. L.
Goldstein
, and
D.
Plante
, “
Test particle acceleration in turbulent reconnecting magnetic fields
,”
J. Geophys. Res.
93
,
14383
, (
1988
).
4.
P.
Dmitruk
,
W. H.
Matthaeus
, and
N.
Seenu
, “
Test particle energization by current sheets and nonuniform fields in magnetohydrodynamic turbulence
,”
Astrophys. J.
617
,
667
679
(
2004
).
5.
P.
Petkaki
and
A. L.
MacKinnon
, “
Particle acceleration by fluctuating electric fields at a magnetic field null point
,”
Astron. Astrophys.
472
,
623
632
(
2007
).
6.
P.
Petkaki
and
A. L.
MacKinnon
, “
Acceleration of charged particles by fluctuating and steady electric fields in a X-type magnetic field
,”
Adv. Space Res.
48
,
884
898
(
2011
).
7.
C. A.
Burge
,
P.
Petkaki
, and
A. L.
MacKinnon
, “
Particle acceleration in the presence of weak turbulence at an X-type neutral point
,”
Sol. Phys.
280
,
575
590
(
2012
).
8.
G.
Kowal
,
E. M.
de Gouveia Dal Pino
, and
A.
Lazarian
, “
Particle acceleration in turbulence and weakly stochastic reconnection
,”
Phys. Rev. Lett.
108
,
241102
(
2012
); e-print arXiv:1202.5256 [astro-ph.HE].
9.
A.
Yoshizawa
, “
Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields
,”
Phys. Fluids B
2
,
1589
1600
(
1990
).
10.
N.
Yokoi
and
M.
Hoshino
, “
Flow-turbulence interaction in magnetic reconnection
,”
Phys. Plasmas
18
,
111208
(
2011
); e-print arXiv:1105.6343 [astro-ph.SR].
11.
J.
Birn
,
A. V.
Artemyev
,
D. N.
Baker
,
M.
Echim
,
M.
Hoshino
, and
L. M.
Zelenyi
, “
Particle acceleration in the magnetotail and aurora
,”
Space Sci. Rev.
173
,
49
102
(
2012
).
12.
J. H.
Eraker
and
J. A.
Simpson
, “
Acceleration of charged particles in Mercury's magnetosphere
,”
J. Geophys. Res.
91
,
9973
9993
, (
1986
).
13.
T. P.
Armstrong
,
S. M.
Krimigis
, and
L. J.
Lanzerotti
, “
A reinterpretation of the reported energetic particle fluxes in the vicinity of Mercury
,”
J. Geophys. Res.
80
,
4015
4017
, (
1975
).
14.
E.
Kirsch
and
A. K.
Richter
, “
Possible detection of low energy ions and electrons from planet Mercury by the HELIOS spacecraft
,”
Ann. Geophys.
3
,
13
18
(
1985
).
15.
G. C.
Ho
,
S. M.
Krimigis
,
R. E.
Gold
,
D. N.
Baker
,
J. A.
Slavin
,
B. J.
Anderson
,
H.
Korth
,
R. D.
Starr
,
D. J.
Lawrence
,
R. L.
McNutt
, and
S. C.
Solomon
, “
MESSENGER observations of transient bursts of energetic electrons in Mercury's magnetosphere
,”
Science
333
,
1865
1868
(
2011
).
16.
G. C.
Ho
,
S. M.
Krimigis
,
R. E.
Gold
,
D. N.
Baker
,
B. J.
Anderson
,
H.
Korth
,
J. A.
Slavin
,
R. L.
McNutt
, Jr.
,
R. M.
Winslow
, and
S. C.
Solomon
, “
Spatial distribution and spectral characteristics of energetic electrons in Mercury's magnetosphere
,”
J. Geophys. Res.: Space Phys.
117
,
A00M04
, (
2012
).
17.
D. J.
Lawrence
,
B. J.
Anderson
,
D. N.
Baker
,
W. C.
Feldman
,
G. C.
Ho
,
H.
Korth
,
R. L.
McNutt
,
P. N.
Peplowski
,
S. C.
Solomon
,
R. D.
Starr
,
J. D.
Vandegriff
, and
R. M.
Winslow
, “
Comprehensive survey of energetic electron events in Mercury's magnetosphere with data from the MESSENGER gamma-ray and neutron spectrometer
,”
J. Geophys. Res.: Space Phys.
120
,
2851
2876
, (
2015
).
18.
D. N.
Baker
,
R. M.
Dewey
,
D. J.
Lawrence
,
J. O.
Goldsten
,
P. N.
Peplowski
,
H.
Korth
,
J. A.
Slavin
,
S. M.
Krimigis
,
B. J.
Anderson
,
G. C.
Ho
,
R. L.
McNutt
,
J. M.
Raines
,
D.
Schriver
, and
S. C.
Solomon
, “
Intense energetic electron flux enhancements in Mercury's magnetosphere: An integrated view with high-resolution observations from MESSENGER
,”
J. Geophys. Res.: Space Phys.
121
,
2171
2184
, (
2016
).
19.
D. C.
Delcourt
,
K.
Seki
,
N.
Terada
, and
Y.
Miyoshi
, “
Electron dynamics during substorm dipolarization in Mercury's magnetosphere
,”
Ann. Geophys.
23
,
3389
3398
(
2005
).
20.
L. M.
Zelenyi
,
J. G.
Lominadze
, and
A. L.
Taktakishvili
, “
Generation of the energetic proton and electron bursts in planetary magnetotails
,”
J. Geophys. Res.
95
,
3883
3891
, (
1990
).
21.
L.
Zelenyi
,
M.
Oka
,
H.
Malova
,
M.
Fujimoto
,
D.
Delcourt
, and
W.
Baumjohann
, “
Particle acceleration in Mercury's magnetosphere
,”
Space Sci. Rev.
132
,
593
609
(
2007
).
22.
J.
Büchner
,
P.
Kilian
,
P.
Muñoz
,
F.
Spanier
,
F.
Widmer
,
X.
Zhou
, and
N.
Jain
, “
Kinetic simulations of electron acceleration at mercury
,” in
Magnetic Fields in the Solar System
, edited by
H.
Luehr
,
J.
Wicht
,
S.
Gilder
, and
M.
Holschneider
(
Astrophysics and Space Science Library, Springer
,
Cham
,
2018
), Chap. 8, pp.
201
240
.
23.
J. A.
Slavin
,
M. H.
Acuna
,
B. J.
Anderson
,
D. N.
Baker
,
M.
Benna
,
S. A.
Boardsen
,
G.
Gloeckler
,
R. E.
Gold
,
G. C.
Ho
,
H.
Korth
,
S. M.
Krimigis
,
R. L.
McNutt
,
J. M.
Raines
,
M.
Sarantos
,
D.
Schriver
,
S. C.
Solomon
,
P.
Travnicek
, and
T. H.
Zurbuchen
, “
MESSENGER observations of magnetic reconnection in Mercury's magnetosphere
,”
Science
324
,
606
610
(
2009
).
24.
G. A.
DiBraccio
,
J. A.
Slavin
,
S. M.
Imber
,
D. J.
Gershman
,
J. M.
Raines
,
C. M.
Jackman
,
S. A.
Boardsen
,
B. J.
Anderson
,
H.
Korth
,
T. H.
Zurbuchen
,
R. L.
McNutt
, and
S. C.
Solomon
, “
MESSENGER observations of flux ropes in Mercury's magnetotail
,”
Planet. Space Sci.
115
,
77
89
(
2015
).
25.
W. J.
Sun
,
S. Y.
Fu
,
J. A.
Slavin
,
J. M.
Raines
,
Q. G.
Zong
,
G. K.
Poh
, and
T. H.
Zurbuchen
, “
Spatial distribution of Mercury's flux ropes and reconnection fronts: MESSENGER observations
,”
J. Geophys. Res.: Space Phys.
121
,
7590
7607
, (
2016
).
26.
N. F.
Loureiro
,
A. A.
Schekochihin
, and
S. C.
Cowley
, “
Instability of current sheets and formation of plasmoid chains
,”
Phys. Plasmas
14
,
100703
(
2007
); e-print arXiv:astro-ph/0703631.
27.
D. A.
Uzdensky
,
N. F.
Loureiro
, and
A. A.
Schekochihin
, “
Fast magnetic reconnection in the plasmoid-dominated regime
,”
Phys. Rev. Lett.
105
,
235002
(
2010
); e-print arXiv:1008.3330 [astro-ph.SR].
28.
M.
Hoshino
,
A.
Nishida
,
T.
Yamamoto
, and
S.
Kokubun
, “
Turbulent magnetic field in the distant magnetotail: Bottom-up process of plasmoid formation?
,”
Geophys. Res. Lett.
21
,
2935
2938
, (
1994
).
29.
M.
Karlický
, “
Series of high-frequency slowly drifting structures mapping the flare magnetic field reconnection
,”
Astron. Astrophys.
417
,
325
332
(
2004
).
30.
M.
Bárta
,
J.
Büchner
,
M.
Karlický
, and
J.
Skála
, “
Spontaneous current-layer fragmentation and cascading reconnection in solar flares. I. Model and analysis
,”
Astrophys. J.
737
,
24
(
2011
); e-print arXiv:1011.4035 [astro-ph.SR].
31.
M.
Karlický
,
M.
Bárta
, and
D.
Nickeler
, “
Fragmentation during merging of plasmoids in the magnetic field reconnection
,”
Astron. Astrophys.
541
,
A86
(
2012
).
32.
F.
Widmer
,
J.
Büchner
, and
N.
Yokoi
, “
Characterizing plasmoid reconnection by turbulence dynamics
,”
Phys. Plasmas
23
,
092304
(
2016
).
33.
J. F.
Drake
,
M.
Swisdak
,
H.
Che
, and
M. A.
Shay
, “
Electron acceleration from contracting magnetic islands during reconnection
,”
Nature (London)
443
,
553
556
(
2006
).
34.
J. F.
Drake
,
M.
Swisdak
, and
R.
Fermo
, “
The power-law spectra of energetic particles during multi-island magnetic reconnection
,”
Astrophys. J., Lett.
763
,
L5
(
2013
); e-print arXiv:1210.4830 [astro-ph.SR].
35.
M.
Oka
,
T.-D.
Phan
,
S.
Krucker
,
M.
Fujimoto
, and
I.
Shinohara
, “
Electron acceleration by multi-island coalescence
,”
Astrophys. J.
714
,
915
926
(
2010
); e-print arXiv:1004.1154 [astro-ph.SR].
36.
K. G.
Tanaka
,
M.
Fujimoto
,
S. V.
Badman
, and
I.
Shinohara
, “
Dynamic magnetic island coalescence and associated electron acceleration
,”
Phys. Plasmas
18
,
022903
(
2011
).
37.
X.
Zhou
,
J.
Büchner
,
M.
Bárta
,
W.
Gan
, and
S.
Liu
, “
Electron acceleration by cascading reconnection in the solar corona. I. Magnetic gradient and curvature drift effects
,”
Astrophys. J.
815
,
6
(
2015
); e-print arXiv:1504.06486 [astro-ph.SR].
38.
S. E.
Guidoni
,
C. R.
DeVore
,
J. T.
Karpen
, and
B. J.
Lynch
, “
Magnetic-island contraction and particle acceleration in simulated eruptive solar flares
,”
Astrophys. J.
820
,
60
(
2016
); e-print arXiv:1603.01309 [astro-ph.SR].
39.
D.
Borovikov
,
V.
Tenishev
,
T. I.
Gombosi
,
S. E.
Guidoni
,
C. R.
DeVore
,
J. T.
Karpen
, and
S. K.
Antiochos
, “
Electron acceleration in contracting magnetic islands during solar flares
,”
Astrophys. J.
835
,
48
(
2017
).
40.
W.
Schmidt
, “
Large eddy simulations in astrophysics
,”
Living Rev. Comput. Astrophys.
1
,
2
(
2015
); e-print arXiv:1404.2483.
41.
J.
Skála
,
F.
Baruffa
,
J.
Büchner
, and
M.
Rampp
, “
The 3D MHD code GOEMHD3 for astrophysical plasmas with large Reynolds numbers. Code description, verification, and computational performance
,”
Astron. Astrophys.
580
,
A48
(
2015
).
42.
F.
Widmer
,
J.
Büchner
, and
N.
Yokoi
, “
Sub-grid-scale description of turbulent magnetic reconnection in magnetohydrodynamics
,”
Phys. Plasmas
23
,
042311
(
2016
); e-print arXiv:1511.04347 [physics.plasm-ph].
43.
M.
Fujimoto
,
W.
Baumjohann
,
K.
Kabin
,
R.
Nakamura
,
J. A.
Slavin
,
N.
Terada
, and
L.
Zelenyi
, “
Hermean magnetosphere-solar wind interaction
,”
Space Sci. Rev.
132
,
529
550
(
2007
).
44.
F.
Krause
and
K.-H.
Rädler
,
Mean-Field Magnetohydrodynamics and Dynamo Theory
(
Pergamon Press Ltd
.,
Berlin
,
1980
).
45.
N.
Yokoi
,
D.
Schmitt
,
V.
Pipin
, and
F.
Hamba
, “
A new simple dynamo model for stellar activity cycle
,”
Astrophys. J.
824
,
67
(
2016
); e-print arXiv:1601.06348 [astro-ph.SR].
46.
N.
Yokoi
, “
Cross helicity and related dynamo
,”
Geophys. Astrophys. Fluid Dyn.
107
,
114
184
(
2013
); e-print arXiv:1306.6348 [astro-ph.SR].
47.
F.
Hamba
, “
One-dimensional calculation of a turbulent dynamo model for reversed field pinches
,”
Phys. Fluids B
2
,
3064
3073
(
1990
).
48.
F.
Hamba
, “
Turbulent dynamo effect and cross helicity in magnetohydrodynamic flows
,”
Phys. Fluids
4
,
441
450
(
1992
).
49.
K.
Higashimori
,
N.
Yokoi
, and
M.
Hoshino
, “
Explosive turbulent magnetic reconnection
,”
Phys. Rev. Lett.
110
,
255001
(
2013
); e-print arXiv:1305.6695 [astro-ph.EP].
50.
F.
Krause
and
K.-H.
Raedler
,
Mean-Field Magnetohydrodynamics And Dynamo Theory
(
Pergamon Press Ltd
.,
Berlin
,
1980
).
51.
P. G.
Watson
,
S.
Oughton
, and
I. J. D.
Craig
, “
The impact of small-scale turbulence on laminar magnetic reconnection
,”
Phys. Plasmas
14
,
032301
(
2007
).
52.
B.
Vreman
,
B.
Geurts
, and
H.
Kuerten
, “
Realizability conditions for the turbulent stress tensor in large-eddy simulation
,”
J. Fluid Mech.
278
,
351
362
(
1994
).
53.
R.
Du Vachat
, “
Realizability inequalities in turbulent flows
,”
Phys. Fluids
20
,
551
556
(
1977
).
54.
J.
Büchner
and
L. M.
Zelenyi
, “
Regular and chaotic charged particle motion in magnetotail like field reversals. I - Basic theory of trapped motion
,”
J. Geophys. Res.
94
,
11821
11842
, (
1989
).
55.
J.
Büchner
and
L. M.
Zelenyi
, “
Regular and chaotic particle motion in sheared magnetic field reversals
,”
Adv. Space Res.
11
,
177
182
(
1991
).
56.
T. G.
Northrop
,
The Adiabatic Motion of Charged Particles
(
Interscience Publishers
,
1963
).
57.
X.
Zhou
,
J.
Büchner
,
M.
Bárta
,
W.
Gan
, and
S.
Liu
, “
Electron acceleration by cascading reconnection in the solar corona. II. Resistive electric field effects
,”
Astrophys. J.
827
,
94
(
2016
).
58.
M.
Gordovskyy
,
P. K.
Browning
, and
G. E.
Vekstein
, “
Particle acceleration in a transient magnetic reconnection event
,”
Astron. Astrophys.
519
,
A21
(
2010
).
59.
L.-P.
Yang
,
L.-H.
Wang
,
J.-S.
He
,
C.-Y.
Tu
,
S.-H.
Zhang
,
L.
Zhang
, and
X.-S.
Feng
, “
Numerical simulation of superhalo electrons generated by magnetic reconnection in the solar wind source region
,”
Res. Astron. Astrophys.
15
,
348
(
2015
); e-print arXiv:1406.4233 [astro-ph.SR].
60.
R.
Turkmani
,
P. J.
Cargill
,
K.
Galsgaard
,
L.
Vlahos
, and
H.
Isliker
, “
Particle acceleration in stochastic current sheets in stressed coronal active regions
,”
Astron. Astrophys.
449
,
749
757
(
2006
).
61.
M.
Gordovskyy
,
P. K.
Browning
, and
G. E.
Vekstein
, “
Particle acceleration in fragmenting periodic reconnecting current sheets in solar flares
,”
Astrophys. J.
720
,
1603
1611
(
2010
).
62.
D.
Schriver
,
P. M.
Trávníček
,
B. J.
Anderson
,
M.
Ashour-Abdalla
,
D. N.
Baker
,
M.
Benna
,
S. A.
Boardsen
,
R. E.
Gold
,
P.
Hellinger
,
G. C.
Ho
,
H.
Korth
,
S. M.
Krimigis
,
R. L.
McNutt
,
J. M.
Raines
,
R. L.
Richard
,
J. A.
Slavin
,
S. C.
Solomon
,
R. D.
Starr
, and
T. H.
Zurbuchen
, “
Quasi-trapped ion and electron populations at Mercury
,”
Geophys. Res. Lett.
38
,
L23103
, (
2011
).
63.
B. M.
Walsh
,
A. S.
Ryou
,
D. G.
Sibeck
, and
I. I.
Alexeev
, “
Energetic particle dynamics in Mercury's magnetosphere
,”
J. Geophys. Res.: Space Phys.
118
,
1992
1999
, (
2013
).
You do not currently have access to this content.