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Electron Acceleration in Kinetic-Size Magnetic Holes
J. Liu1,2,3, S. T. Yao2, Q. Q. Shi2, X. G. Wang4, Q. G. Zong5, Y. Y. Feng1, H. Liu5, R. L.
Guo6, Z. H. Yao7, I. J. Rae8, A. W. Degeling2, A. M. Tian2, C. T. Russell9, Y. T. Zhang1, Y.
X. Wang1,3, L. D. Woodham8, Z. Y. Pu5, C. J. Xiao5, S. Y. Fu5, B. L. Giles10
1National Space Science Center, Chinese Academy of Sciences2ShInstitute of Space Sciences, Shandong University, Weihai
3College of Earth and Planetary Sciences, University of Chinese Academy of Sciences4Department of Physics, Harbin Institute of Technology5School of Earth and space Sciences, Peking University
6Institute of Geology and Geophysics, Chinese Academy of Sciences7Laboratoire de Physique Atmosphérique et Planétaire, STAR Institute, Universitéde Liège
8Mullard Space Science Laboratory, University College London9Department of Earth, Planetary and Space Sciences, University of California, Los Angeles
10NASA Goddard Space Flight Center
E-mail: [email protected] [email protected]
Backgrounds
2
Observation of Kinetic-Size Magnetic Hole
• This structure is typically crossed by a
spacecraft in 0.3s and have a scale of
~10ρe.
• The electron flow vortex is perpendicular
to the background magnetic field.
Magnetic holes (MHs), defined as a structure with significant magnetic field reduction,
were first reported in the solar wind plasmas [Turner et al., 1977].
Yao et al. [2017]
Recently, a type of Kinetic-Size Magnetic Hole
(KSMH) at the electron gyro-scale was
observed at 14:59:34 UT on October 23, 2015
by the Magnetospheric Multi-Scale (MMS)
mission with unprecedented high spatio-
temporal resolution in the terrestrial
magnetosheath [Yao, et al., 2017]:
Backgrounds
3
Observation of Kinetic-Size Magnetic Hole
• Perpendicular direction: H. Liu et al.[2019] showed a rounded
cross-section of this magnetic structure;
• Parallel direction: the fact that enhanced PSD close to 90 degrees
in the pitch angle distributions are in agreement with the
calculated loss cone (dashed lines) between trapped and un-
trapped particle orbits indicates the existence of two mirror points;
Thus, we can know that this magnetic hole is a magnetic bottle-like
structure which can trap electrons.
➢ The structure of the Kinetic-Size Magnetic Hole
[H. Liu et al., 2019. nat. comm]
What is the
cause of the
observed
PADs inside
the KSMH?
Backgrounds
4
Observation of Kinetic-Size Magnetic Hole
In comparison with the ambient plasma outside of the structure, the phase space density (PSD)
for electrons with a pitch-angle ~90°: at the higher energy (> 90 eV) inside the magnetic
depression structure remarkably increases, while at lower energy (< 70 eV) the PSD decreases
significantly.
Dec
reas
e at
90
°In
crea
se a
t 9
0°
equatorial plane
➢ Electron pitch angle distributions in KSMH
MMS1
Backgrounds
5
Evolution of the Structure
✓ Clearly, the MMS1 observations of the magnetic field indicate a shrinking scenario in
the cross-section of the structure by comparing front and rear data of the magnetic field
strength, and a reduced rear Btot near the center. A shrinking rate is then evaluated
approximately ~4 km/s for the outer boundary of the structure.
➢ A shrinking magnetic hole
After determining the center of the structure
via a particle sounding technique, the MMS1
observations of the magnetic field strength
(Btot) are divided into front and rear parts as
the satellite transits the structure. a-b, The
reconstructed 2D configurations based on the
rotational symmetry of the structure using the
front and rear Btot, respectively. c, The front
and the rear Btot plotted as functions of the
radial distance r. Compared with the front
part, the rear part of Btot is weaker near center
and stronger in the outer region. d, The
estimated shrinking rate v=∆d/∆t.
Backgrounds
6
Evolution of the Structure
t= 500 Ω𝑒t= 0 Ω𝑒
Therefore, based on above observations of size distribution and evolution to smaller scales, we
propose a model to reproduce the observation numerically (see details in Appendix A):
➢ Model of shrinking magnetic holes
Backgrounds
7
Evolution of the Structure
It is found that the direction of the electric
field (blue curves with arrows) is
counterclockwise (right-handed) near
center and clockwise (left-handed) in the
outer region. Note that the estimated
maximum electric field is only ~ 14 μV/m(0.014mV/m), too weak to be detected by
the MMS electric field instrument, which
has an accuracy of 0.3 mV/m.
Faraday's law (see details in Appendix B)
rotational symmetry
➢ The induced electric field in the shrinking KSMHs
∆𝐵/∆𝑡
equatorial plane
8
The Electron Energization in KSMHs
Trajectories of two representative
electrons.
• The electron gyration is counterclockwise,
thus in-line with the electric field near the
center but opposite to it in the outer region.
• The lower energy electron only gyrates in the
inner region while the higher energy electron
crosses the inner region to reach the outer
region.
The higher energy electrons are accelerated
(non-adiabatic) while the lower energy electrons
are decelerated (quasi-adiabatic) inside the
shrinking magnetic depression structures.
➢ Test particle simulations
9
The Electron Energization in KSMHs
( )l S S S
B BW q E dl q E dS q dS q dS
t t
= = = − =
( ) ( )
( )
( ) ( )
( ) ( )
0,
= 0,
0,
r r B r r B
r r B
r r r rB B
r r r rB B
S S
L B
s
B L c
S S
c L
S S
B Bq dS dS
t t
Bq dS d r
t
B Bq dS dS r d r
t t
B Bq dS dS r d
t t
= +
+
+
2
=2
2
=
S
L
L
L
Bq dS
q B r
B
=
0,0
0,
B
B MH
Br r
t
Br r r
t
Adiabatic acceleration. Acceleration inside the shrinking KSMHs.
Τ𝜕 𝜕𝑡 ≪ 𝜔𝐿 and 𝛻𝐵~0
The energy gain ∆𝑊 of a charged particle during one gyroperiod:
21
2L Lq r =
Deceleration
Acceleration
lower energy
higher energy
equatorial plane
➢ Theoretical Analysis
➢ Explanation for the electron PADs
Deceleration
Acceleration
10
The behavior of internal particles
For the electrons whose PSDs decreases with energy, the PSDs at lower energy after
deceleration becomes lower than the background, and the PSDs at higher energy after
acceleration becomes greater than the background.
Backgrounds
11
Numerical simulation
The simulation results are well consistent with the observation.
A simulation containing fifty million electrons distributed over various positions with different
pitch angles and energies is further carried out to study the effect of the energy dependent
acceleration process on the electron distributions.
Backgrounds
12
Summary
In this study, we research a KSMH event from Yao et al.(2017) in detail and propose a
new nonadiabatic acceleration process for electrons inside KSMH:
• When the KSMH shrinks, magnetic intensity inside the KSMHs decreases near the
center and increases in the outer part;
• The electrons may move across different regions and loss energy for electrons with
smaller gyroradius, or gain energy for electrons with larger gyroradius;
• For the electrons whose PSDs decreases with energy, the PSDs at lower energy after
deceleration becomes lower than the background, and the PSDs at higher energy
after acceleration becomes greater than the background.
To validate this, we implement a test particle simulation for electrons in a KSMH and
find that the simulation results are consistent with the observations.
Backgrounds
13
Discussion ➢ The turbulent environment of the structure
Thus, this magnetic cavity should be referred to as a structure embedded in the turbulent plasma
and this work may also provide a possible mechanism to reveal the outstanding question of
energy dissipation of the turbulence.
• The disordered magnetic field
and electron number density
fluctuations, as well as their
power-law spectra are consistent
with the classical features of
plasma turbulence;
• the scale of this structure is in the
dissipation range of turbulence
and the perpendicular electron
temperature in the structure is
clearly higher than that in outside.
Thank you!
Appendix A: The magnetic field model
15
22 1 ( )
2ˆp
r
r
p
p
rj e
r
−
= j
2 2( ) ( )0
0
z zpd d
p p p
p
jr r e j e
r
− −
= = ,
➢ Diamagnetic Current
The observation from Yao et al.,2017 The calculation from our model.
𝛻 × 𝛻 × 𝑨 =4𝜋
𝑐𝒋
0+
1 1
c t c t
=
= −− = −
B A B
A AE
➢ The Comparison of Observations and Model
➢ Electromagnetic Field
ˆ ˆ ˆ
1 1ˆ ˆ ˆ= E=
1
=
1 1
z
z
z z
z
E E EEBz
t z z z
E E E
E E
z z
E EE E
z z
E E
− = − − − +
= − − − −
− −
ˆ ˆ ˆ 0z
z z
B B
B B B B z B
B B
= + + = =
0
1
z
z
EB
zt
EEB
t zB
Et
= = −
−
=
=0
+ =-
z
z
E B
z t
EE
z
E E B
t
−
So we have:
Appendix B: Theoretical derivation about the electric field
16
As the structure shrinks, the magnetic field intensity decreases ( Τ𝜕𝐵 𝜕𝑡 < 0) near the central region of the
structure and increases in the edge region ( Τ𝜕𝐵 𝜕𝑡 > 0), as shown in Fig. 4b. In cylindrical coordinates, we
can get ΤΤ𝐸𝜑 𝑟 + 𝜕𝐸𝜑 𝜕𝑟 = − Τ𝜕𝐵 𝜕𝑡 from Faraday’s Law. Therefore, we integrate numerically using the
boundary condition 𝐸𝜑 = 0 at 𝑟 = 0 with given Τ𝜕𝐵 𝜕𝑡 to obtain 𝐸𝜑 as shown in Fig. 4c. In our simulation,
we solved equation in Appendix A, another form of Faraday's Law, to obtain the same result.