An Electron Heating in the Downstream Region of the X-type Neutral LineK. Fujimoto and S. Machida
Department of Geophysics, Graduate School of Science, Kyoto University
Introduction

Lobe

B0In the outflow region outside the electron diffusion region around the X-type neutral line,
electrons are frozen-in to the ambient magnetic field while ions are unmagnetized.
In this region, it is known that the electron motion is basically described by the E × B
motion and electrons can be accelerated up to "the electron Alfven velocity" defined asVAe = BL/(μ0 menps)1/2, beyond the ordinary Alfven velocity (VA = BL/(μ0 minps)1/2).
On the other hand, ions are unmagnetized so that the accelaration is not effective. Thus
it is expected that a large relative velocity between electrons and ions across the ambient
magnetic field (the Hall current) exists inside the ion diffusion region.
In this paper, we investigate possible instabilities and the anomalous electron heating
caused by a cross-field super Alfvenic relative motion between electrons and ions.
(Notice that the following study is conducted in the electoron frame.)

E0SEPARATRIXzE0B0Hall Currents

X-type Neutral LineIn the case of mi/me = 1836

We next study the electron heating due to the unstable waves, making use of2-1/2 dimensional electromagnetic particle simulation.

(b)

0.01

Vd/ve=1.0
0.8
0.6
0.5
0.4

0.003

0.6
0.5
0.4

0.002
40506070
θ°80

Vd/ve=1.0
0.8

0.5

0.8

51.2 λeAngular Frequency

1

Vd/ve=1.0

ωr/ωpeγ/ωpe

B0Growth Rate

0.005

0.6

0.2

Vd/ve=1.0

0.1

0.8

0.05

0.6

ωce
0.50.40.5
0.40.020.0190・Particle-In-Cell method
・Dobly periodic boundaries
・256 × 512 grids
・Δx = Δz = ΔλDe・ωce/ωpe = 0.5, Ti/Te =8.0mi/me = 100, βi = 1.040506070
θ°80

90Vdωlh(a) Vd/ve = 0.8

In the case of mi/me = 100

Vd/ve=2.01.4
1.00.8 0.72030

40506070

0.20.10.05
0.02

Angular Frequency
Vd/ve=2.0ωce
1.4
1.0
Vd/ve=2.0 1.4 0.8 0.7
1.00.8 ωlh0.7120903040506070800tωpe = 0.

Vd < ve

0.590θ°θ°Electrons are easily trapped
along the magnetic field lineby the obliquely propagatingwaves.

‑0.5

0.0180tωpe = 620.

0.5

V‖/c

1.4
1.0
0.8
0.7

0.5

Heating in the parallel
direction due to theKCSI

01

Vd > ve
‑0.5

00.5

V⊥/c

The Kinetic Cross-field Streaming Instability (KCSI) is dominant when Vd < Vcr.
The Electron Cyclotron Drift Instability (ECDI) is dominant when Vd > Vcr.
Vcr ≒ 0.6 ve for the case of mi/me = 1836
Vcr ≒ vefor the case of mi/me = 100‑1‑0.5

0300.51(b) Vd/ve = 2.0‑1‑1

Prospective unstable mode varies according to the electron-ion relative velocity, Vd.

0V⊥/c‑0.5Electron Cyclotron Drift Instability (ECDI)
Kinetic Cross‑Field Streaming Instability (KCSI)‑1tωpe = 140.

Electrons are trapped by theperpendicularly propagatingwaves.

0.5

1

Heating in theperpendicular direction
due to the ECDI

V‖/c

Vd/ve=2.0

ωr/ωpeγ/ωpe1ωlh0.030.01(b)Growth Rate

0.07
0.05

0.020.015

1V‖/c(a)VdElectron Heating

ωce/ωpe = 0.5, Ti/Te = 8.0, βi = 1.00.007

xLobe25.6 λeωlh

k=(k⊥,0,k‖)yIn order to identify the instabilities inside the diffusion region, we solved the kinetic linear
dispersion relation numerically.

0.015

θ

Diffusion Region

Kinetic Linear Theory(a)Target Region

0‑0.5‑10‑1‑0.50V⊥/c30

0.51Saturation Temperature

An electron trapping by electrostatic wave propagating perpendicularly tothe magnetic field is simply described with the use of effective potential.

Wave amplitude saturates when the electron thermalvelocity reaches the drift velocity, which is nearly equal
to the phase velocity of the most unstable wave.

[Chen and Birdsall, 1973]

(b)

(a)

(c)

ΦΦ

Φ

B

ΦB

B

ΦB

ΦB

‑eφ + meωce2x2/2

SummaryReleasemeωce2x2/2meωce2x2/2

Trapping

ΦA

ΦA

ΦA

A linear analysis and 2-1/2 dimensional particle simulations are performed to investigate
mechanisms of electron heating due to the strong Hall current.

meωce2x2/2A
Trapping
xv x00‑eφWave Propagation

Wave Propagationx‑eφxv x0‑eφ

Wave Propagation

・The numerical solution of the kinetic dispersion relation indicates that the prospective
unstable mode varies according to the electron-ion relative velocity.
KCSI for Vd < Vcr,
ECDI for Vd > Vcr.

sat・Our simulation results show that the electron heating mechanism varies according to thedominant instabilities.
Parallel heating by the KCSI,Perpendicular heating by the ECDI.
The theoretical prediction
well agrees with thesimulation results, which
justifies the above model.

・The perpendicular heating by the ECDI is expected to be ineffective when Vd < ve,because unstable waves with the ECDI are likely to be resonant with large number ofelectrons and dumped before they grow to enough amplitude to trap electrons and heatthem effectively.