We investigate the Fermi acceleration of charged particles in 2D MHD anti-parallel plasmoid reconnection, finding a drastic enhancement in energization rate ε ̇ over a standard Fermi model of ε ̇ ∼ ε. The shrinking particle orbit width around a magnetic island due to E → × B → drift produces a ε ̇ ∥ ∼ ε ∥ 1 + 1 / 2 χ power law with χ ∼ 0.75. The increase in the maximum possible energy gain of a particle within a plasmoid due to the enhanced efficiency increases with the plasmoid size and is by multiple factors of 10 in the case of solar flares and much more for larger plasmas. Including the effects of the non-constant E → × B → drift rates leads to further variation in power law indices from ≳ 2 to ≲ 1, decreasing with plasmoid size at the time of injection. The implications for energetic particle spectra are discussed alongside applications to 3D plasmoid reconnection and the effects of a guide field.
REFERENCES
1.
M.
Yamada
,
R.
Kulsrud
, and
H.
Ji
, “
Magnetic reconnection
,” Rev. Mod. Phys.
82
, 603
(2010
).2.
H.
Ji
and
W.
Daughton
, “
Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas
,” Phys. Plasmas
18
, 111207
(2011
).3.
H.
Ji
,
W.
Daughton
,
J.
Jara-Almonte
,
A.
Le
,
A.
Stanier
, and
J.
Yoo
, “
Magnetic reconnection in the era of exascale computing and multiscale experiments
,” Nat. Rev. Phys.
4
, 263
–282
(2022
).4.
A. G.
Emslie
,
B. R.
Dennis
,
G. D.
Holman
, and
H. S.
Hudson
, “
Refinements to flare energy estimates: A followup to ‘energy partition in two solar flare/cme events’ by A. G. Emslie et al
,” J. Geophys. Res.
110
, A11103
, https://doi.org/10.1029/2005JA011305 (2005
).5.
S.
Krucker
,
H. S.
Hudson
,
L.
Glesener
,
S. M.
White
,
S.
Masuda
,
J.-P.
Wuelser
, and
R. P.
Lin
, “
Measurements of the coronal acceleration region of a solar flare
,” Astrophys. J.
714
, 1108
–1119
(2010
).6.
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
).7.
L.-J.
Chen
,
N.
Bessho
,
B.
Lefebvre
,
H.
Vaith
,
A.
Asnes
,
O.
Santolik
,
A.
Fazakerley
,
P. A.
Puhl-Quinn
,
A.
Bhattacharjee
,
Y.
Khotyaintsev
,
P.
Daly
, and
R.
Torbert
, “
Multi-spacecraft observations of the electron current sheet, neighboring magnetic islands, and electron acceleration during magnetotail reconnection
,” Phys. Plasmas
16
, 056501
(2009
).8.
O. V.
Khabarova
,
G. P.
Zank
,
G.
Li
,
O. E.
Malandraki
,
J. A.
le Roux
, and
G. M.
Webb
, “
Small-scale magnetic islands in the solar wind and their role in particle acceleration. II. Particle energization inside magnetically confined cavities
,” Astrophys. J.
827
, 122
(2016
).9.
L.-L.
Zhao
,
G. P.
Zank
,
O.
Khabarova
,
S.
Du
,
Y.
Chen
,
L.
Adhikari
, and
Q.
Hu
, “
An unusual energetic particle flux enhancement associated with solar wind magnetic island dynamics
,” Astrophys. J.
864
, L34
(2018
).10.
L.-L.
Zhao
,
G. P.
Zank
,
Y.
Chen
,
Q.
Hu
,
J. A.
Le Roux
,
S.
Du
, and
L.
Adhikari
, “
Particle acceleration at 5 au associated with turbulence and small-scale magnetic flux ropes
,” Astrophys. J.
872
, 4
(2019
).11.
S.
Zenitani
and
M.
Hoshino
, “
The generation of nonthermal particles in the relativistic magnetic reconnection of pair plasmas
,” Astrophys. J. Lett.
562
, L63
–L66
(2001
).12.
D. A.
Uzdensky
, “
Magnetic reconnection in extreme astrophysical environments
,” Space Sci. Rev.
160
, 45
(2011
).13.
A.
Chien
,
L.
Gao
,
S.
Zhang
,
H.
Ji
,
E. G.
Blackman
,
W.
Daughton
,
A.
Stanier
,
A.
Le
,
F.
Guo
,
R.
Follett
,
H.
Chen
,
G.
Fiksel
,
G.
Bleotu
,
R. C.
Cauble
,
S. N.
Chen
,
A.
Fazzini
,
K.
Flippo
,
O.
French
,
D. H.
Froula
,
J.
Fuchs
,
S.
Fujioka
,
K.
Hill
,
S.
Klein
,
C.
Kuranz
,
P.
Nilson
,
A.
Rasmus
, and
R.
Takizawa
, “
Non-thermal electron acceleration from magnetically driven reconnection in a laboratory plasma
,” Nat. Phys.
19
, 254
(2023
).14.
J.
Egedal
,
W.
Daughton
, and
A.
Le
, “
Large-scale electron acceleration by parallel electric fields during magnetic reconnection
,” Nat. Phys.
8
, 321
–324
(2012
).15.
M.
Hoshino
,
T.
Mukai
,
T.
Terasawa
, and
I.
Shinohara
, “
Suprathermal electron acceleration in magnetic reconnection
,” J. Geophys. Res.
106
, 25979
–25997
, https://doi.org/10.1029/2001JA900052 (2001
).16.
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
).17.
H.
Hakobyan
,
M.
Petropoulou
,
A.
Spitkovsky
, and
L.
Sironi
, “
Secondary energization in compressing plasmoids during magnetic reconnection
,” Astrophys. J.
912
, 48
(2021
).18.
J. F.
Drake
,
M.
Swisdak
,
H.
Che
, and
M. A.
Shay
, “
Electron acceleration from contracting magnetic islands during reconnection
,” Nature
443
, 553
–556
(2006
).19.
J. T.
Dahlin
,
J. F.
Drake
, and
M.
Swisdak
, “
The mechanisms of electron heating and acceleration during magnetic reconnection
,” Phys. Plasmas
21
, 092304
(2014
).20.
F.
Guo
,
H.
Li
,
W.
Daughton
, and
Y.-H.
Liu
, “
Formation of hard power laws in the energetic particle spectra resulting from relativistic magnetic reconnection
,” Phys. Rev. Lett.
113
, 155005
(2014
).21.
P.
Montag
,
J.
Egedal
,
E.
Lichko
, and
B.
Wetherton
, “
Impact of compressibility and a guide field on fermi acceleration during magnetic island coalescence
,” Phys. Plasmas
24
, 062906
(2017
).22.
E. G.
Zweibel
and
M.
Yamada
, “
Magnetic reconnection in astrophysical and laboratory plasmas
,” Annu. Rev. Astron. Astrophys.
47
, 291
–332
(2009
).23.
L.
Sironi
and
A.
Spitkovsky
, “
Relativistic reconnection: An efficient source of non-thermal particles
,” Astrophys. J.
783
, L21
(2014
).24.
B.
Ripperda
,
O.
Porth
,
C.
Xia
, and
R.
Keppens
, “
Reconnection and particle acceleration in interacting flux ropes. I. Magnetohydrodynamics and test particles in 2.5d
,” Mon. Not. Roy. Astronom. Soc.
467
, 3279
(2017
).25.
A.
Philippov
,
D. A.
Uzdensky
,
A.
Spitkovsky
, and
B.
Cerutti
, “
Pulsar radio emission mechanism: Radio nanoshots as a low-frequency afterglow of relativistic magnetic reconnection
,” Astrophys. J.
876
, L6
(2019
).26.
F.
Guo
,
Y.-H.
Liu
,
W.
Daughton
, and
H.
Li
, “
Particle acceleration and plasma dynamics during magnetic reconnection in the magnetically dominated regime
,” Astrophys. J.
806
, 167
(2015
).27.
F.
Guo
,
X.
Li
,
W.
Daughton
,
P.
Kilian
,
H.
Li
,
Y.-H.
Liu
,
W.
Yan
, and
D.
Ma
, “
Determining the dominant acceleration mechanism during relativistic magnetic reconnection in large-scale systems
,” Astrophys. J.
879
, L23
(2019
).28.
D.
Ball
,
L.
Sironi
, and
F.
Özel
, “
The mechanism of electron injection and acceleration in transrelativistic reconnection
,” Astrophys. J.
884
, 57
(2019
).29.
H.
Arnold
,
J. F.
Drake
,
M.
Swisdak
, and
J.
Dahlin
, “
Large-scale parallel electric fields and return currents in a global simulation model
,” Phys. Plasmas
26
, 102903
(2019
).30.
F.
Guo
,
Y.-H.
Liu
,
X.
Li
,
H.
Li
,
W.
Daughton
, and
P.
Kilian
, “
Recent progress on particle acceleration and reconnection physics during magnetic reconnection in the magnetically-dominated relativistic regime
,” Phys. Plasmas
27
, 080501
(2020
).31.
X.
Li
,
F.
Guo
,
H.
Li
,
A.
Stanier
, and
P.
Kilian
, “
Formation of power-law electron energy spectra in three-dimensional low-β magnetic reconnection
,” Astrophys. J.
884
, 118
(2019
).32.
J. T.
Dahlin
,
J. F.
Drake
, and
M.
Swisdak
, “
Electron acceleration in three-dimensional magnetic reconnection with a guide field
,” Phys. Plasmas
22
, 100704
(2015
).33.
E. N.
Parker
, “
Sweet's mechanism for merging magnetic fields in conducting fluids
,” J. Geophys. Res.
62
, 509
–520
, https://doi.org/10.1029/JZ062i004p00509 (1957
).34.
T.
Northrop
, “
The guiding center approximation of charged particle motion
,” Ann. Phys.
15
, 79
–101
(1961
).35.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
, Numerical Recipes in C
, 2nd ed.
(
Cambridge University Press
,
Cambridge
, 1992
).36.
Y.-M.
Huang
and
A.
Bhattacharjee
, “
Distribution of plasmoids in high-Lundquist-number magnetic reconnection
,” Phys. Rev. Lett.
109
, 265002
(2012
).37.
Y.-M.
Huang
and
A.
Bhattacharjee
, “
Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime
,” Phys. Plasmas
17
, 062104
(2010
).38.
P. N.
Guzdar
,
J. F.
Drake
,
D.
McCarthy
,
A. B.
Hassam
, and
C. S.
Liu
, “
Three-dimensional fluid simulations of the nonlinear drift-resistive ballooning modes in tokamak edge plasmas
,” Phys. Fluids B: Plasma Phys.
5
, 3712
–3727
(1993
).39.
P.
Kilian
,
X.
Li
,
F.
Guo
, and
H.
Li
, “
Exploring the acceleration mechanisms for particle injection and power-law formation during transrelativistic magnetic reconnection
,” Astrophys. J.
899
, 151
(2020
).40.
O.
French
,
F.
Guo
,
Q.
Zhang
, and
D.
Uzdensky
, “
Particle injection and nonthermal particle acceleration in relativistic magnetic reconnection
,” arXiv:2210.08358 (2022
).41.
L.
Sironi
, “
Nonideal fields solve the injection problem in relativistic reconnection
,” Phys. Rev. Lett.
128
, 145102
(2022
).42.
M.
Lemoine
, “
First-principles Fermi acceleration in magnetized turbulence
,” Phys. Rev. Lett.
129
, 215101
(2022
).43.
D. H.
Brooks
,
H. P.
Warren
, and
E.
Landi
, “
Measurements of coronal magnetic field strengths in solar active region loops
,” Astrophys. J. Lett.
915
, L24
(2021
).44.
B.
Chen
,
C.
Shen
,
D. E.
Gary
,
K. K.
Reeves
,
G. D.
Fleishman
,
S.
Yu
,
F.
Guo
,
S.
Krucker
,
J.
Lin
,
G. M.
Nita
et al, “
Measurement of magnetic field and relativistic electrons along a solar flare current sheet
,” Nat. Astron.
4
, 1140
–1147
(2020
).45.
N. F.
Loureiro
,
R.
Samtaney
,
A. A.
Schekochihin
, and
D. A.
Uzdensky
, “
Magnetic reconnection and stochastic plasmoid chains in high-Lundquist-number plasmas
,” Phys. Plasmas
19
, 042303
(2012
).46.
H.
Arnold
,
J.
Drake
,
M.
Swisdak
,
F.
Guo
,
J.
Dahlin
,
B.
Chen
,
G.
Fleishman
,
L.
Glesener
,
E.
Kontar
,
T.
Phan
et al, “
Electron acceleration during macroscale magnetic reconnection
,” Phys. Rev. Lett.
126
, 135101
(2021
).47.
J. T.
Dahlin
,
J. F.
Drake
, and
M.
Swisdak
, “
Parallel electric fields are inefficient drivers of energetic electrons in magnetic reconnection
,” Phys. Plasmas
23
, 120704
(2016
).48.
L.
Sironi
,
D.
Giannios
, and
M.
Petropoulou
, “
Plasmoids in relativistic reconnection, from birth to adulthood: First they grow, then they go
,” Mon. Not. Roy. Astronom. Soc.
462
, 48
–74
(2016
).49.
S.
Majeski
,
H.
Ji
,
J.
Jara-Almonte
, and
J.
Yoo
, “
Guide field effects on the distribution of plasmoids in multiple scale reconnection
,” Phys. Plasmas
28
, 092106
(2021
).50.
J. T.
Dahlin
, “
Prospectus on electron acceleration via magnetic reconnection
,” Phys. Plasmas
27
, 100601
(2020
).51.
M.
Zhou
,
N. F.
Loureiro
, and
D. A.
Uzdensky
, “
Multi-scale dynamics of magnetic flux tubes and inverse magnetic energy transfer
,” J. Plasma Phys.
86
, 535860401
(2020
).52.
S.
Zenitani
and
T.
Miyoshi
, “
Plasmoid-dominated turbulent reconnection in a low-β plasma
,” Astrophys. J.
894
, L7
(2020
).53.
G. G.
Howes
,
S. C.
Cowley
,
W.
Dorland
,
G. W.
Hammett
,
E.
Quataert
, and
A. A.
Schekochihin
, “
Astrophysical gyrokinetics: Basic equations and linear theory
,” Astrophys. J.
651
, 590
–614
(2006
).54.
J. F.
Drake
,
M. A.
Shay
, and
M.
Swisdak
, “
The Hall fields and fast magnetic reconnection
,” Phys. Plasmas
15
, 042306
(2008
).55.
L.
Malyshkin
, “
Model of Hall reconnection
,” Phys. Rev. Lett.
101
, 225001
(2008
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
