Non-Maxwellian electron velocity space distribution functions (EVDFs) are useful signatures of plasma conditions and non-local consequences of collisionless magnetic reconnection. In the past, EVDFs were obtained mainly for antiparallel reconnection and under the influence of weak guide-fields in the direction perpendicular to the reconnection plane. EVDFs are, however, not well known, yet, for oblique (or component-) reconnection in case and in dependence on stronger guide-magnetic fields and for the exhaust (outflow) region of reconnection away from the diffusion region. In view of the multi-spacecraft Magnetospheric Multiscale Mission (MMS), we derived the non-Maxwellian EVDFs of collisionless magnetic reconnection in dependence on the guide-field strength bg from small () to very strong (bg = 8) guide-fields, taking into account the feedback of the self-generated turbulence. For this sake, we carried out 2.5D fully kinetic Particle-in-Cell simulations using the ACRONYM code. We obtained anisotropic EVDFs and electron beams propagating along the separatrices as well as in the exhaust region of reconnection. The beams are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field. The beams propagate in the direction opposite to the background electrons and cause instabilities. We also obtained the guide-field dependence of the relative electron-beam drift speed, threshold, and properties of the resulting streaming instabilities including the strongly non-linear saturation of the self-generated plasma turbulence. This turbulence and its non-linear feedback cause non-adiabatic parallel electron acceleration. We further obtained the resulting EVDFs due to the non-linear feedback of the saturated self-generated turbulence near the separatrices and in the exhaust region of reconnection in dependence on the guide field strength. We found that the influence of the self-generated plasma turbulence leads well beyond the limits of the quasi-linear approximation to the creation of phase space holes and an isotropizing pitch-angle scattering. EVDFs obtained by this way can be used for diagnosing collisionless reconnection by using the multi-spacecraft observations carried out by the MMS mission.
References
1.
J.
Büchner
and W.
Daughton
, “Basic theory of collisionless reconnection
,” in Reconnection of Magnetic Fields: Magnetohydrodynamics Collisionless Theory and Observations
, edited by J.
Birn
and E. R.
Priest
(Cambridge University Press
, 2007
), Chap. 3
, pp. 87
–166
.2.
M.
Yamada
, R. M.
Kulsrud
, and H.
Ji
, “Magnetic reconnection
,” Rev. Mod. Phys.
82
, 603
–664
(2010
).3.
E. G.
Zweibel
and M.
Yamada
, “Magnetic reconnection in astrophysical and laboratory plasmas
,” Annu. Rev. Astron. Astrophys.
47
, 291
–332
(2009
).4.
R. A.
Treumann
and W.
Baumjohann
, “Collisionless magnetic reconnection in space plasmas
,” Front. Phys.
1
, 31
(2013
).5.
W.
Gonzalez
and E.
Parker
, Magnetic Reconnection
, Astrophysics and Space Science Library (Springer International Publishing
, 2016
).6.
J. L.
Burch
, T. E.
Moore
, R. B.
Torbert
, and B. L.
Giles
, “Magnetospheric multiscale overview and science objectives
,” Space Sci. Rev.
199
, 5
–21
(2016
).7.
M.
Hoshino
, K.
Hiraide
, and T.
Mukai
, “Strong electron heating and non-Maxwellian behavior in magnetic reconnection
,” Earth Planets Space
53
, 627
–634
(2001
).8.
K.
Fujimoto
and R. D.
Sydora
, “Particle description of the electron diffusion region in collisionless magnetic reconnection
,” Phys. Plasmas
16
, 112309
(2009
).9.
A.
Divin
, S.
Markidis
, G.
Lapenta
, V. S.
Semenov
, N. V.
Erkaev
, and H. K.
Biernat
, “Model of electron pressure anisotropy in the electron diffusion region of collisionless magnetic reconnection
,” Phys. Plasmas
17
, 122102
(2010
).10.
J.
Ng
, J.
Egedal
, A.
Le
, W.
Daughton
, and L.-J.
Chen
, “Kinetic structure of the electron diffusion region in antiparallel magnetic reconnection
,” Phys. Rev. Lett.
106
, 065002
(2011
).11.
N.
Bessho
and A.
Bhattacharjee
, “Instability of the current sheet in the Earth's magnetotail with normal magnetic field
,” Phys. Plasmas
21
, 102905
(2014
).12.
J. R.
Shuster
, L. L.-J.
Chen
, W. S.
Daughton
, L. C.
Lee
, K. H.
Lee
, N.
Bessho
, R. B.
Torbert
, G.
Li
, and M. R.
Argall
, “Highly structured electron anisotropy in collisionless reconnection exhausts
,” Geophys. Res. Lett.
41
, 5389
–5395
, doi: (2014
).13.
J. R.
Shuster
, L.-J.
Chen
, M.
Hesse
, M. R.
Argall
, W.
Daughton
, R. B.
Torbert
, and N.
Bessho
, “Spatiotemporal evolution of electron characteristics in the electron diffusion region of magnetic reconnection: Implications for acceleration and heating
,” Geophys. Res. Lett.
42
, 2586
–2593
, doi: (2015
).14.
J.
Egedal
, W.
Daughton
, A.
Le
, and A. L.
Borg
, “Double layer electric fields aiding the production of energetic flat-top distributions and superthermal electrons within the exhausts from magnetic reconnection
,” Phys. Plasmas
22
, 101208
(2015
).15.
C. Z.
Cheng
, S.
Inoue
, Y.
Ono
, and R.
Horiuchi
, “Physical processes of driven magnetic reconnection in collisionless plasmas: Zero guide field case
,” Phys. Plasmas
22
, 101205
(2015
).16.
S.
Zenitani
and T.
Nagai
, “Particle dynamics in the electron current layer in collisionless magnetic reconnection
,” preprint arXiv:1605.07472 (2016
).17.
J.
Büchner
, “Correlation-modulated chaotic scattering in the Earth's magnetosphere
,” Geophys. Res. Lett.
18
, 1595
–1598
, doi: (1991
).18.
T. W.
Speiser
, “Particle trajectories in model current sheets: 1. Analytical solutions
,” J. Geophys. Res.
70
, 4219
, doi: (1965
).19.
J.
Büchner
and L. M.
Zelenyi
, “The separatrix tentacle effect of ion acceleration to the plasma sheet boundary
,” Geophys. Res. Lett.
17
, 127
–130
, doi: (1990
).20.
J.
Büchner
and S.
Teselkin
, “Signatures for remote sensing of reconnection in the distant magnetotail
,” Adv. Space Res.
18
, 45
–50
(1996
).21.
J.
Büchner
and J.-P.
Kuska
, “On the formation of cup-like ion beam distributions in the plasma sheet boundary layer
,” J. Geomagn. Geoelectr.
48
, 781
–797
(1996
).22.
J.
Büchner
and J.-P.
Kuska
, “Consequences of strong ion acceleration in current sheets and due to reconnection
,” Adv. Space Res.
21
, 567
–572
(1998
).23.
K.
Fujimoto
and S.
Machida
, “A generation mechanism of electrostatic waves and subsequent electron heating in the plasma sheet-lobe boundary region during magnetic reconnection
,” J. Geophys. Res.
111
, A09216
, doi: (2006
).24.
J.
Büchner
and L. M.
Zelenyi
, “Regular and chaotic charged particle motion in magnetotaillike field reversals: 1. Basic theory of trapped motion
,” J. Geophys. Res.
94
, 11821
, doi: (1989
).25.
Y.
Asano
, R.
Nakamura
, I.
Shinohara
, M.
Fujimoto
, T.
Takada
, W.
Baumjohann
, C. J.
Owen
, A. N.
Fazakerley
, A.
Runov
, T.
Nagai
, E. A.
Lucek
, and H.
Rème
, “Electron flat-top distributions around the magnetic reconnection region
,” J. Geophys. Res. Space Phys.
113
, A01207
, doi: (2008
).26.
A.
Teste
and G. K.
Parks
, “Counterstreaming beams and flat-top electron distributions observed with Langmuir, Whistler, and compressional Alfvén waves in Earth's magnetic tail
,” Phys. Rev. Lett.
102
, 075003
(2009
).27.
J.
Ng
, J.
Egedal
, A.
Le
, and W.
Daughton
, “Phase space structure of the electron diffusion region in reconnection with weak guide fields
,” Phys. Plasmas
19
, 112108
(2012
).28.
S.
Wang
, L.-J.
Chen
, N.
Bessho
, L. M.
Kistler
, J. R.
Shuster
, and R.
Guo
, “Electron heating in the exhaust of magnetic reconnection with negligible guide field
,” J. Geophys. Res. Space Phys.
121
, 2104
–2130
, doi: (2016
).29.
J.
Büchner
and L. M.
Zelenyi
, “Regular and chaotic particle motion in sheared magnetic field reversals
,” Adv. Space Res.
11
, 177
–182
(1991
).30.
M. V.
Goldman
, G.
Lapenta
, D. L.
Newman
, S.
Markidis
, and H.
Che
, “Jet deflection by very weak guide fields during magnetic reconnection
,” Phys. Rev. Lett.
107
, 135001
(2011
).31.
I.
Silin
and J.
Büchner
, “Three-dimensional Vlasov-code simulations of magnetopause-like current sheets
,” Adv. Space Res.
37
, 1354
–1362
(2006
).32.
P. L.
Pritchett
, “Collisionless magnetic reconnection in an asymmetric current sheet
,” J. Geophys. Res. Space Phys.
113
, A06210
, doi: (2008
).33.
M.
Hesse
, N.
Aunai
, J.
Birn
, P.
Cassak
, R. E.
Denton
, J. F.
Drake
, T.
Gombosi
, M.
Hoshino
, W.
Matthaeus
, D.
Sibeck
, and S.
Zenitani
, “Theory and modeling for the magnetospheric multiscale mission
,” Space Sci. Rev.
199
, 577
–630
(2016
).34.
N.
Bessho
, L.-J.
Chen
, and M.
Hesse
, “Electron distribution functions in the diffusion region of asymmetric magnetic reconnection
,” Geophys. Res. Lett.
43
, 1828
–1836
, doi: (2016
).35.
L.-J.
Chen
, M.
Hesse
, S.
Wang
, N.
Bessho
, and W.
Daughton
, “Electron energization and structure of the diffusion region during asymmetric reconnection
,” Geophys. Res. Lett.
43
, 2405
–2412
, doi: (2016
).36.
M. A.
Shay
, T. D.
Phan
, C. C.
Haggerty
, M.
Fujimoto
, J. F.
Drake
, K.
Malakit
, P. A.
Cassak
, and M.
Swisdak
, “Kinetic signatures of the region surrounding the X line in asymmetric (magnetopause) reconnection
,” Geophys. Res. Lett.
43
, 4145
–4154
, doi: (2016
).37.
M.
Hesse
, Y.-H.
Liu
, L.-J.
Chen
, N.
Bessho
, M.
Kuznetsova
, J.
Birn
, and J. L.
Burch
, “On the electron diffusion region in asymmetric reconnection with a guide magnetic field
,” Geophys. Res. Lett.
43
, 2359
–2364
, doi: (2016
).38.
J.
Egedal
, A.
Le
, W.
Daughton
, B.
Wetherton
, P. A.
Cassak
, L. J.
Chen
, B.
Lavraud
, R. B.
Trobert
, J.
Dorelli
, D. J.
Gershman
, and L. A.
Avanov
, “Spacecraft observations and analytic theory of crescent-shaped electron distributions in asymmetric magnetic reconnection
,” preprint arXiv:1607.05670 (2016
).39.
J. L.
Burch
, R. B.
Torbert
, T. D.
Phan
, L.-J.
Chen
, T. E.
Moore
, R. E.
Ergun
, J. P.
Eastwood
, D. J.
Gershman
, P. A.
Cassak
, M. R.
Argall
, S.
Wang
, M.
Hesse
, C. J.
Pollock
, B. L.
Giles
, R.
Nakamura
, B. H.
Mauk
, S. A.
Fuselier
, C. T.
Russell
, R. J.
Strangeway
, J. F.
Drake
, M. A.
Shay
, Y. V.
Khotyaintsev
, P.-A.
Lindqvist
, G.
Marklund
, F. D.
Wilder
, D. T.
Young
, K.
Torkar
, J.
Goldstein
, J. C.
Dorelli
, L. A.
Avanov
, M.
Oka
, D. N.
Baker
, A. N.
Jaynes
, K. A.
Goodrich
, I. J.
Cohen
, D. L.
Turner
, J. F.
Fennell
, J. B.
Blake
, J.
Clemmons
, M.
Goldman
, D.
Newman
, S. M.
Petrinec
, K. J.
Trattner
, B.
Lavraud
, P. H.
Reiff
, W.
Baumjohann
, W.
Magnes
, M.
Steller
, W.
Lewis
, Y.
Saito
, V.
Coffey
, and M.
Chandler
, “Electron-scale measurements of magnetic reconnection in space
,” Science
352
, aaf2939
(2016
).40.
T. D.
Phan
, J. P.
Eastwood
, P. A.
Cassak
, M.
Øieroset
, J. T.
Gosling
, D. J.
Gershman
, F. S.
Mozer
, M. A.
Shay
, M.
Fujimoto
, W.
Daughton
, J. F.
Drake
, J. L.
Burch
, R. B.
Torbert
, R. E.
Ergun
, L. J.
Chen
, S.
Wang
, C.
Pollock
, J. C.
Dorelli
, B.
Lavraud
, B. L.
Giles
, T. E.
Moore
, Y.
Saito
, L. A.
Avanov
, W.
Paterson
, R. J.
Strangeway
, C. T.
Russell
, Y.
Khotyaintsev
, P. A.
Lindqvist
, M.
Oka
, and F. D.
Wilder
, “MMS observations of electron-scale filamentary currents in the reconnection exhaust and near the X line
,” Geophys. Res. Lett.
43
, 6060
–6069
, doi: (2016
).41.
S. W. H.
Cowley
, “Plasma populations in a simple open model magnetosphere
,” Space Sci. Rev.
26
, 217
–275
(1980
).42.
R. G.
Kleva
, J. F.
Drake
, and F. L.
Waelbroeck
, “Fast reconnection in high temperature plasmas
,” Phys. Plasmas
2
, 23
–34
(1995
).43.
B. N.
Rogers
, R. E.
Denton
, and J. F.
Drake
, “Signatures of collisionless magnetic reconnection
,” J. Geophys. Res.
108
, 1111
, doi: (2003
).44.
J. F.
Drake
, M.
Swisdak
, C.
Cattell
, M. A.
Shay
, B. N.
Rogers
, and A.
Zeiler
, “Formation of electron holes and particle energization during magnetic reconnection
,” Science
299
, 873
–877
(2003
).45.
P. L.
Pritchett
and F. V.
Coroniti
, “Three-dimensional collisionless magnetic reconnection in the presence of a guide field
,” J. Geophys. Res.
109
, A01220
, doi: (2004
).46.
G.
Lapenta
, S.
Markidis
, A.
Divin
, M.
Goldman
, and D.
Newman
, “Scales of guide field reconnection at the hydrogen mass ratio
,” Phys. Plasmas
17
, 082106
(2010
).47.
S.
Markidis
, G.
Lapenta
, A.
Divin
, M.
Goldman
, D.
Newman
, and L.
Andersson
, “Three dimensional density cavities in guide field collisionless magnetic reconnection
,” Phys. Plasmas
19
, 032119
(2012
).48.
G.
Lapenta
, S.
Markidis
, A.
Divin
, M. V.
Goldman
, and D. L.
Newman
, “Bipolar electric field signatures of reconnection separatrices for a hydrogen plasma at realistic guide fields
,” Geophys. Res. Lett.
38
, L17104
, doi: (2011
).49.
G.
Lapenta
, S.
Markidis
, A.
Divin
, D.
Newman
, and M.
Goldman
, “Separatrices: The crux of reconnection
,” J. Plasma Phys.
81
, 325810109
(2014
).50.
W.
Daughton
and H.
Karimabadi
, “Kinetic theory of collisionless tearing at the magnetopause
,” J. Geophys. Res.
110
, A03217
, doi: (2005
).51.
A.
Le
, J.
Egedal
, O.
Ohia
, W.
Daughton
, H.
Karimabadi
, and V. S.
Lukin
, “Regimes of the electron diffusion region in magnetic reconnection
,” Phys. Rev. Lett.
110
, 135004
(2013
).52.
J.
Büchner
, M.
Kuznetsova
, and L. M.
Zelenyi
, “Sheared field tearing mode instability and creation of flux ropes in the Earth magnetotail
,” Geophys. Res. Lett.
18
, 385
–388
, doi: (1991
).53.
J.
Egedal
, W.
Fox
, N.
Katz
, M.
Porkolab
, M.
Øieroset
, R. P.
Lin
, W.
Daughton
, and J. F.
Drake
, “Evidence and theory for trapped electrons in guide field magnetotail reconnection
,” J. Geophys. Res.
113
, A12207
, doi: (2008
).54.
J.
Egedal
, W.
Daughton
, J. F.
Drake
, N.
Katz
, and A.
Le
, “Formation of a localized acceleration potential during magnetic reconnection with a guide field
,” Phys. Plasmas
16
, 050701
(2009
).55.
A.
Le
, J.
Egedal
, W.
Daughton
, W.
Fox
, and N.
Katz
, “Equations of state for collisionless guide-field reconnection
,” Phys. Rev. Lett.
102
, 085001
(2009
).56.
A.
Le
, J.
Egedal
, W.
Fox
, N.
Katz
, A.
Vrublevskis
, W.
Daughton
, and J. F.
Drake
, “Equations of state in collisionless magnetic reconnection
,” Phys. Plasmas
17
, 055703
(2010
).57.
J.
Egedal
, A.
Le
, and W.
Daughton
, “A review of pressure anisotropy caused by electron trapping in collisionless plasma, and its implications for magnetic reconnection
,” Phys. Plasmas
20
, 061201
(2013
).58.
M.
Øieroset
, R. P.
Lin
, T. D.
Phan
, D. E.
Larson
, and S. D.
Bale
, “Evidence for electron acceleration up to 300 keV in the magnetic reconnection diffusion region of Earth' s magnetotail
,” Phys. Rev. Lett.
89
, 195001
(2002
).59.
J.
Egedal
, M.
Øieroset
, W.
Fox
, and R. P.
Lin
, “In situ discovery of an electrostatic potential, trapping electrons and mediating fast reconnection in the Earth's magnetotail
,” Phys. Rev. Lett.
94
, 025006
(2005
).60.
L.-J.
Chen
, N.
Bessho
, B.
Lefebvre
, H.
Vaith
, A.
Fazakerley
, A.
Bhattacharjee
, P. A.
Puhl-Quinn
, A.
Runov
, Y.
Khotyaintsev
, A.
Vaivads
, E.
Georgescu
, and R.
Torbert
, “Evidence of an extended electron current sheet and its neighboring magnetic island during magnetotail reconnection
,” J. Geophys. Res. Space Phys.
113
, A12213
, doi: (2008
).61.
J. D.
Scudder
, R. D.
Holdaway
, W. S.
Daughton
, H.
Karimabadi
, V.
Roytershteyn
, C. T.
Russell
, and J. Y.
Lopez
, “First resolved observations of the demagnetized electron-diffusion region of an astrophysical magnetic-reconnection site
,” Phys. Rev. Lett.
108
, 225005
(2012
).62.
J.
Egedal
, A.
Le
, N.
Katz
, L.-J.
Chen
, B.
Lefebvre
, W.
Daughton
, and A.
Fazakerley
, “Cluster observations of bidirectional beams caused by electron trapping during antiparallel reconnection
,” J. Geophys. Res. Space Phys.
115
, A03214
, doi: (2010
).63.
O.
Ohia
, J.
Egedal
, V. S.
Lukin
, W.
Daughton
, and A.
Le
, “Demonstration of anisotropic fluid closure capturing the kinetic structure of magnetic reconnection
,” Phys. Rev. Lett.
109
, 115004
(2012
).64.
A.
Le
, W.
Daughton
, H.
Karimabadi
, and J.
Egedal
, “Hybrid simulations of magnetic reconnection with kinetic ions and fluid electron pressure anisotropy
,” Phys. Plasmas
23
, 032114
(2016
).65.
G. F.
Chew
, M. L.
Goldberger
, and F. E.
Low
, “The Boltzmann equation and the one-fluid hydromagnetic equations in the absence of particle collisions
,” Proc. R. Soc. A: Math. Phys. Eng. Sci.
236
, 112
–118
(1956
).66.
M.
Swisdak
, J. F.
Drake
, and M. A.
Shay
, “Transition from antiparallel to component magnetic reconnection
,” J. Geophys. Res.
110
, A05210
, doi: (2005
).67.
C.
Cattell
, J.
Dombeck
, J.
Wygant
, J. F.
Drake
, M.
Swisdak
, M. L.
Goldstein
, W.
Keith
, A.
Fazakerley
, M.
André
, E.
Lucek
, and A.
Balogh
, “Cluster observations of electron holes in association with magnetotail reconnection and comparison to simulations
,” J. Geophys. Res. Space Phys.
110
, A01211
, doi: (2005
).68.
P. L.
Pritchett
, “Onset and saturation of guide-field magnetic reconnection
,” Phys. Plasmas
12
, 062301
(2005
).69.
J. F.
Drake
, M. A.
Shay
, W.
Thongthai
, and M.
Swisdak
, “Production of energetic electrons during magnetic reconnection
,” Phys. Rev. Lett.
94
, 095001
(2005
).70.
P. L.
Pritchett
, “Relativistic electron production during guide field magnetic reconnection
,” J. Geophys. Res.
111
, A10212
, doi: (2006
).71.
M.
Ashour-Abdalla
, J. P.
Berchem
, J.
Büchner
, and L. M.
Zelenyi
, “Shaping of the magnetotail from the mantle: Global and local structuring
,” J. Geophys. Res.
98
, 5651
, doi: (1993
).72.
J.
Birn
, M.
Hesse
, A.
Runov
, and X.-Z.
Zhou
, “Ion beams in the plasma sheet boundary layer
,” J. Geophys. Res. Space Phys.
120
, 7522
–7535
, doi: (2015
).73.
J. P.
McFadden
, C. W.
Carlson
, R. E.
Ergun
, C. C.
Chaston
, F. S.
Mozer
, M.
Temerin
, D. M.
Klumpar
, E. G.
Shelley
, W. K.
Peterson
, E.
Moebius
, L.
Kistler
, R.
Elphic
, R.
Strangeway
, C.
Cattell
, and R.
Pfaff
, “Electron modulation and ion cyclotron waves observed by FAST
,” Geophys. Res. Lett.
25
, 2045
–2048
, doi: (1998
).74.
G.
Parks
, L.
Chen
, M.
Fillingim
, and M.
McCarthy
, “Kinetic characterization of plasma sheet dynamics
,” Space Sci. Rev.
95
, 237
–255
(2001
).75.
S.
Li
, S.
Zhang
, H.
Cai
, and H.
Yang
, “Electron beam-associated symmetric electrostatic solitary waves on the separatrix of magnetic reconnection: Multi-spacecraft analysis
,” Earth Planets Space
67
, 84
(2015
).76.
R.
Nakamura
, V. A.
Sergeev
, W.
Baumjohann
, F.
Plaschke
, W.
Magnes
, D.
Fischer
, A.
Varsani
, D.
Schmid
, T. K. M.
Nakamura
, C. T.
Russell
, R. J.
Strangeway
, H. K.
Leinweber
, G.
Le
, K. R.
Bromund
, C. J.
Pollock
, B. L.
Giles
, J. C.
Dorelli
, D. J.
Gershman
, W.
Paterson
, L. A.
Avanov
, S. A.
Fuselier
, K.
Genestreti
, J. L.
Burch
, R. B.
Torbert
, M.
Chutter
, M. R.
Argall
, B. J.
Anderson
, P.-A.
Lindqvist
, G. T.
Marklund
, Y. V.
Khotyaintsev
, B. H.
Mauk
, I. J.
Cohen
, D. N.
Baker
, A. N.
Jaynes
, R. E.
Ergun
, H. J.
Singer
, J. A.
Slavin
, E. L.
Kepko
, T. E.
Moore
, B.
Lavraud
, V.
Coffey
, and Y.
Saito
, “Transient, small-scale field-aligned currents in the plasma sheet boundary layer during storm time substorms
,” Geophys. Res. Lett.
43
, 4841
–4849
, doi: (2016
).77.
I.
Shinohara
, T.
Nagai
, M.
Fujimoto
, T.
Terasawa
, T.
Mukai
, K.
Tsuruda
, and T.
Yamamoto
, “Low-frequency electromagnetic turbulence observed near the substorm onset site
,” J. Geophys. Res. Space Phys.
103
, 20365
–20388
, doi: (1998
).78.
M.
Zhou
, Y.
Pang
, X. H.
Deng
, Z. G.
Yuan
, and S. Y.
Huang
, “Density cavity in magnetic reconnection diffusion region in the presence of guide field
,” J. Geophys. Res. Space Phys.
116
, A06222
, doi: (2011
).79.
M.
Zhou
, H.
Li
, X.
Deng
, S.
Huang
, Y.
Pang
, Z.
Yuan
, X.
Xu
, and R.
Tang
, “Characteristic distribution and possible roles of waves around the lower hybrid frequency in the magnetotail reconnection region
,” J. Geophys. Res. Space Phys.
119
, 8228
–8242
, doi: (2014
).80.
N.
Elkina
and J.
Büchner
, “A new conservative unsplit method for the solution of the Vlasov equation
,” J. Comput. Phys.
213
, 862
–875
(2006
).81.
K.-W.
Lee
, J.
Büchner
, and N.
Elkina
, “Collisionless transport of energetic electrons in the solar corona at current-free double layers
,” Astron. Astrophys.
478
, 889
(2008
).82.
M. V.
Goldman
, D. L.
Newman
, and P.
Pritchett
, “Vlasov simulations of electron holes driven by particle distributions from PIC reconnection simulations with a guide field
,” Geophys. Res. Lett.
35
, L22109
, doi: (2008
).83.
K.-W.
Lee
and J.
Büchner
, “Collisionless turbulent transport and anisotropic electron heating in coronal flare loops
,” Astron. Astrophys.
535
, 61
(2011
).84.
W.
Fox
, M.
Porkolab
, J.
Egedal
, N.
Katz
, and A.
Le
, “Laboratory observation of electron phase-space holes during magnetic reconnection
,” Phys. Rev. Lett.
101
, 255003
(2008
).85.
Y. V.
Khotyaintsev
, A.
Vaivads
, M.
André
, M.
Fujimoto
, A.
Retinò
, and C. J.
Owen
, “Observations of slow electron holes at a magnetic reconnection site
,” Phys. Rev. Lett.
105
, 165002
(2010
).86.
A.
Retinò
, A.
Vaivads
, M.
André
, F.
Sahraoui
, Y.
Khotyaintsev
, J. S.
Pickett
, M. B.
Bavassano Cattaneo
, M. F.
Marcucci
, M.
Morooka
, C. J.
Owen
, S. C.
Buchert
, and N.
Cornilleau-Wehrlin
, “Structure of the separatrix region close to a magnetic reconnection X-line: Cluster observations
,” Geophys. Res. Lett.
33
, L06101
, doi: (2006
).87.
P.
Kilian
, T.
Burkart
, and F.
Spanier
, “The influence of the mass ratio on particle acceleration by the filamentation instability
,” in High Performance Computing in Science and Engineering'11
, edited by W. E.
Nagel
, D. B.
Kröner
, and M. M.
Resch
(Springer
, Berlin, Heidelberg
, 2012
), pp. 5
–13
.88.
E. G.
Harris
, “On a plasma sheath separating regions of oppositely directed magnetic field
,” Nuovo Cimento.
23
, 115
–121
(1962
).89.
M.
Melzani
, C.
Winisdoerffer
, R.
Walder
, D.
Folini
, J. M.
Favre
, S.
Krastanov
, and P.
Messmer
, “Apar-T: Code, validation, and physical interpretation of particle-in-cell results
,” Astron. Astrophys.
558
, A133
(2013
).90.
R.
Horiuchi
and T.
Sato
, “Particle simulation study of collisionless driven reconnection in a sheared magnetic field
,” Phys. Plasmas
4
, 277
(1997
).91.
P.
Ricci
, J. U.
Brackbill
, W.
Daughton
, and G.
Lapenta
, “Collisionless magnetic reconnection in the presence of a guide field
,” Phys. Plasmas
11
, 4102
(2004
).92.
J. D.
Huba
, “Hall magnetic reconnection: Guide field dependence
,” Phys. Plasmas
12
, 012322
(2005
).93.
D. E.
Wendel
, M.
Hesse
, N.
Bessho
, M. L.
Adrian
, and M.
Kuznetsova
, “Nongyrotropic electrons in guide field reconnection
,” Phys. Plasmas
23
, 022114
(2016
).94.
C.
Norgren
, D. B.
Graham
, Y. V.
Khotyaintsev
, M.
André
, A.
Vaivads
, L.-J.
Chen
, P.-A.
Lindqvist
, G. T.
Marklund
, R. E.
Ergun
, W.
Magnes
, R. J.
Strangeway
, C. T.
Russell
, R. B.
Torbert
, W. R.
Paterson
, D. J.
Gershman
, J. C.
Dorelli
, L. A.
Avanov
, B.
Lavraud
, Y.
Saito
, B. L.
Giles
, C. J.
Pollock
, and J. L.
Burch
, “Finite gyroradius effects in the electron outflow of asymmetric magnetic reconnection
,” Geophys. Res. Lett.
43
, 6724
–6733
, doi: (2016
).95.
S. P.
Gary
, Theory of Space Plasma Microinstabilities
(Cambridge University Press
, 1993
).96.
D. B.
Graham
, A.
Vaivads
, Y. V.
Khotyaintsev
, and M.
André
, “Whistler emission in the separatrix regions of asymmetric magnetic reconnection
,” J. Geophys. Res. Space Phys.
121
, 1934
–1954
, doi: (2016
).97.
A.
Le
, J.
Egedal
, W.
Daughton
, J. F.
Drake
, W.
Fox
, and N.
Katz
, “Magnitude of the Hall fields during magnetic reconnection
,” Geophys. Res. Lett.
37
, L03106
, doi: (2010
).98.
J.
Egedal
, W.
Daughton
, and A.
Le
, “Large-scale electron acceleration by parallel electric fields during magnetic reconnection
,” Nat. Phys.
8
, 321
–324
(2012
).99.
B. F.
McMillan
and I. H.
Cairns
, “Parallel and lower hybrid turbulence in low β plasmas driven by strong parallel currents and the resulting parallel electron and perpendicular ion energization
,” Phys. Plasmas
14
, 012103
(2007
).100.
M.
Fujimoto
, I.
Shinohara
, and H.
Kojima
, “Reconnection and waves: A review with a perspective
,” Space Sci. Rev.
160
, 123
–143
(2011
).101.
K.
Fujimoto
, “Wave activities in separatrix regions of magnetic reconnection
,” Geophys. Res. Lett.
41
, 2721
–2728
, doi: (2014
).102.
P. L.
Pritchett
and F. S.
Mozer
, “Asymmetric magnetic reconnection in the presence of a guide field
,” J. Geophys. Res.
114
, A11210
, doi: (2009
).103.
A.
Divin
, G.
Lapenta
, S.
Markidis
, D. L.
Newman
, and M. V.
Goldman
, “Numerical simulations of separatrix instabilities in collisionless magnetic reconnection
,” Phys. Plasmas
19
, 042110
(2012
).104.
G. K.
Parks
, M.
McCarthy
, R. J.
Fitzenreiter
, J.
Etcheto
, K. A.
Anderson
, R. R.
Anderson
, T. E.
Eastman
, L. A.
Frank
, D. A.
Gurnett
, C.
Huang
, R. P.
Lin
, A. T. Y.
Lui
, K. W.
Ogilvie
, A.
Pedersen
, H.
Reme
, and D. J.
Williams
, “Particle and field characteristics of the high-latitude plasma sheet boundary layer
,” J. Geophys. Res.
89
, 8885
, doi: (1984
).105.
Y.
Omura
, H.
Matsumoto
, T.
Miyake
, and H.
Kojima
, “Electron beam instabilities as generation mechanism of electrostatic solitary waves in the magnetotail
,” J. Geophys. Res. Space Phys.
101
, 2685
–2697
, doi: (1996
).106.
J.
Hwang
, K.
Rha
, J.
Seough
, and P. H.
Yoon
, “Electron distributions observed with Langmuir waves in the plasma sheet boundary layer
,” Phys. Plasmas
21
, 092121
(2014
).107.
R. E.
Ergun
, J. C.
Holmes
, K. A.
Goodrich
, F. D.
Wilder
, J. E.
Stawarz
, S.
Eriksson
, D. L.
Newman
, S. J.
Schwartz
, M. V.
Goldman
, A. P.
Sturner
, D. M.
Malaspina
, M. E.
Usanova
, R. B.
Torbert
, M.
Argall
, P.-A.
Lindqvist
, Y.
Khotyaintsev
, J. L.
Burch
, R. J.
Strangeway
, C. T.
Russell
, C. J.
Pollock
, B. L.
Giles
, J. J. C.
Dorelli
, L.
Avanov
, M.
Hesse
, L. J.
Chen
, B.
Lavraud
, O.
Le Contel
, A.
Retino
, T. D.
Phan
, J. P.
Eastwood
, M.
Oieroset
, J.
Drake
, M. A.
Shay
, P. A.
Cassak
, R.
Nakamura
, M.
Zhou
, M.
Ashour-Abdalla
, and M.
André
, “Magnetospheric multiscale observations of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the magnetopause
,” Geophys. Res. Lett.
43
, 5626
–5634
, doi: (2016
).108.
Y.
Omura
, W.
Heikkila
, T.
Umeda
, K.
Ninomiya
, and H.
Matsumoto
, “Particle simulation of plasma response to an applied electric field parallel to magnetic field lines
,” J. Geophys. Res.
108
, 1197
, doi: (2003
).109.
B.
Coppi
, F.
Pegoraro
, R.
Pozzoli
, and G.
Rewoldt
, “Slide-away distributions and relevant collective modes in high-temperature plasmas
,” Nucl. Fusion
16
, 309
–328
(1976
).110.
K.
Papadopoulos
and P. J.
Palmadesso
, “Excitation of lower hybrid waves in a plasma by electron beams
,” Phys. Fluids
19
, 605
(1976
).111.
S.
Migliuolo
, “Lower hybrid waves in finite-β plasmas, destabilized by electron beams
,” J. Geophys. Res. Space Phys.
90
, 377
–385
, doi: (1985
).112.
B. F.
McMillan
and I. H.
Cairns
, “Lower hybrid turbulence driven by parallel currents and associated electron energization
,” Phys. Plasmas
13
, 052104
(2006
).113.
J. B.
McBride
, “Theory and simulation of turbulent heating by the modified two-stream instability
,” Phys. Fluids
15
, 2367
(1972
).114.
C. S.
Wu
, D.
Winske
, K.
Papadopoulos
, Y. M.
Zhou
, S. T.
Tsai
, and S. C.
Guo
, “A kinetic cross-field streaming instability
,” Phys. Fluids
26
, 1259
(1983
).115.
R. A.
Treumann
and W.
Baumjohann
, Advanced Space Plasma Physics
(Imperial College Press/Scientific Publishing Co.
, 2001
).116.
K.
Fujimoto
and S.
Machida
, “An electron heating mechanism in the outflow region from the X-type neutral line
,” J. Geophys. Res.
108
, 1349
, doi: (2003
).117.
M.
Scholer
, I.
Sidorenko
, C. H.
Jaroschek
, R. A.
Treumann
, and A.
Zeiler
, “Onset of collisionless magnetic reconnection in thin current sheets: Three-dimensional particle simulations
,” Phys. Plasmas
10
, 3521
–3527
(2003
).118.
H.
Che
, J. F.
Drake
, M.
Swisdak
, and P. H.
Yoon
, “Nonlinear development of streaming instabilities in strongly magnetized plasma
,” Phys. Rev. Lett.
102
, 145004
(2009
).119.
H.
Che
, J. F.
Drake
, M.
Swisdak
, and P. H.
Yoon
, “Electron holes and heating in the reconnection dissipation region
,” Geophys. Res. Lett.
37
, L11105
, doi: (2010
).120.
K. J.
Reitzel
and G. J.
Morales
, “Dynamics of narrow electron streams in magnetized plasmas
,” Phys. Plasmas
5
, 3806
(1998
).121.
T.
Miyake
, Y.
Omura
, and H.
Matsumoto
, “Electrostatic particle simulations of solitary waves in the auroral region
,” J. Geophys. Res. Space Phys.
105
, 23239
–23249
, doi: (2000
).122.
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
).123.
J. R.
Wygant
, A.
Keiling
, C. A.
Cattell
, R. L.
Lysak
, M.
Temerin
, F. S.
Mozer
, C. A.
Kletzing
, J. D.
Scudder
, V.
Streltsov
, W.
Lotko
, and C. T.
Russell
, “Evidence for kinetic Alfvén waves and parallel electron energization at 4-6 R E altitudes in the plasma sheet boundary layer
,” J. Geophys. Res. Space Phys.
107
, 1201
, doi: (2002
).124.
J. F.
Drake
, M.
Swisdak
, K. M.
Schoeffler
, B. N.
Rogers
, and S.
Kobayashi
, “Formation of secondary islands during magnetic reconnection
,” Geophys. Res. Lett.
33
, L13105
, doi: (2006
).125.
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
).126.
M.
Bárta
, J.
Büchner
, M.
Karlický
, and P.
Kotrč
, “Spontaneous current-layer fragmentation and cascading reconnection in solar flares. II. Relation to observations
,” Astrophys. J.
730
, 47
(2011
).127.
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
).128.
N. F.
Loureiro
, A. A.
Schekochihin
, and S. C.
Cowley
, “Instability of current sheets and formation of plasmoid chains
,” Phys. Plasmas
14
, 100703
(2007
).129.
A.
Bhattacharjee
, Y.-M.
Huang
, H.
Yang
, and B.
Rogers
, “Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability
,” Phys. Plasmas
16
, 112102
(2009
).130.
N. F.
Loureiro
and D. A.
Uzdensky
, “Magnetic reconnection: From the Sweet-Parker model to stochastic plasmoid chains
,” Plasma Phys. Controlled Fusion
58
, 014021
(2016
).131.
J. L.
Burch
and T. D.
Phan
, “Magnetic reconnection at the dayside magnetopause: Advances with MMS
,” Geophys. Res. Lett.
43
, 8327
, doi: (2016
).132.
M.
Øieroset
, T. D.
Phan
, C.
Haggerty
, M. A.
Shay
, J. P.
Eastwood
, D. J.
Gershman
, J. F.
Drake
, M.
Fujimoto
, R. E.
Ergun
, F. S.
Mozer
, M.
Oka
, R. B.
Torbert
, J. L.
Burch
, S.
Wang
, L. J.
Chen
, M.
Swisdak
, C.
Pollock
, J. C.
Dorelli
, S. A.
Fuselier
, B.
Lavraud
, B. L.
Giles
, T. E.
Moore
, Y.
Saito
, L. A.
Avanov
, W.
Paterson
, R. J.
Strangeway
, C. T.
Russell
, Y.
Khotyaintsev
, P. A.
Lindqvist
, and K.
Malakit
, “MMS observations of large guide field symmetric reconnection between colliding reconnection jets at the center of a magnetic flux rope at the magnetopause
,” Geophys. Res. Lett.
43
, 5536
–5544
, doi: (2016
).133.
S.
Eriksson
, F. D.
Wilder
, R. E.
Ergun
, S. J.
Schwartz
, P. A.
Cassak
, J. L.
Burch
, L.-J.
Chen
, R. B.
Torbert
, T. D.
Phan
, B.
Lavraud
, K. A.
Goodrich
, J. C.
Holmes
, J. E.
Stawarz
, A. P.
Sturner
, D. M.
Malaspina
, M. E.
Usanova
, K. J.
Trattner
, R. J.
Strangeway
, C. T.
Russell
, C. J.
Pollock
, B. L.
Giles
, M.
Hesse
, P.-A.
Lindqvist
, J. F.
Drake
, M. A.
Shay
, R.
Nakamura
, and G. T.
Marklund
, “Magnetospheric multiscale observations of the electron diffusion region of large guide field magnetic reconnection
,” Phys. Rev. Lett.
117
, 015001
(2016
).134.
R.
Nakamura
, W.
Baumjohann
, M.
Fujimoto
, Y.
Asano
, A.
Runov
, C. J.
Owen
, A. N.
Fazakerley
, B.
Klecker
, H.
Rème
, E. A.
Lucek
, M.
Andre
, and Y.
Khotyaintsev
, “Cluster observations of an ion-scale current sheet in the magnetotail under the presence of a guide field
,” J. Geophys. Res. Space Phys.
113
, A07S16
, doi: (2008
).135.
Z. J.
Rong
, W. X.
Wan
, C.
Shen
, X.
Li
, M. W.
Dunlop
, A. A.
Petrukovich
, L.-N.
Hau
, T. L.
Zhang
, H.
Rème
, A. M.
Du
, and E.
Lucek
, “Profile of strong magnetic field B y component in magnetotail current sheets
,” J. Geophys. Res. Space Phys.
117
, A06216
, doi: (2012
).© 2016 Author(s).
2016
Author(s)
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