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: sqq@sdu.edu.cn liuji16@mails.ucas.ac.cn

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.