Sunjung Kim

CHEA Journal Club 3 May 2018 (THU)

Quiet-Time Solar Wind Electron Velocity Distribution Function

[Wang et al. (2012)]

Halo

Super-Halo

Core

[Ergun et al. (1998)]

Strahl

2

Bump-on-tail instabilityLangmuir Turbulence generated by

beam-plasma interaction

Beam-Plasma Instability: Linear Theory

Bump-on-tail distribution

Elec

tron

dist

ribut

ion

velocity

Lang

mui

r wav

e gr

owth

rate

wave number

Langmuir wave dispersion relation and Landau damping rate

Beam-Plasma Instability: Quasi-Linear Theory

Particle Kinetic Equation

Velocity friction

Velocity space diffusion

Linear wave-particleresonance Wave Particle

Spontaneous emission(Discrete particle effect)

Induced emission(Quasi-linear growth/damping rate)

Wave Kinetic Equation

Linear wave-particleresonance Wave Particle

velocity wave number

Elec

tron

dist

ribut

ion

Lang

mui

r wav

e in

tens

ity

Beam‐Plasma Instability: Nonlinear Theory

Particle Kinetic Equation

2 ', ''1 k

L dk' Vk,k 'L ( k

L 'k 'L ' ' kk '

S )

kLIk '

'LIkk ' ''S 'k '

L Ikk ' ''S Ik

L ' ' kk 'L Ik '

'LIkL

Wave Kinetic Equation

Linear wave-particle

Wave-wave

Nonlinearwave-particle

2 ', ''1 k

L dk' Vk,k 'L ( k

L 'k 'L ' ' kk '

S )

kLIk '

'LIkk ' ''S 'k '

L Ikk ' ''S Ik

L ' ' kk 'L Ik '

'LIkL

Wave Kinetic Equation

Linear wave-particle

Wave-wave

Nonlinear wave-wave resonance

Wave (kk)

Wave(k–kʼk – kʼ)

Wave(kʼkʼ)

2 ', ''1 k

L dk' Vk,k 'L ( k

L 'k 'L ' ' kk '

S )

kLIk '

'LIkk ' ''S 'k '

L Ikk ' ''S Ik

L ' ' kk 'L Ik '

'LIkL

Wave Kinetic Equation

Nonlinearwave-particle

Nonlinear wave-particle resonance

Particle

Wave(kk)

Wave(kʼkʼ)

𝛿 𝜎𝜔 𝜎 𝜎′′𝜔

e

e

E, pe ee

E, kcSi

Debye cloud

Langmuir oscillation Ion-sound wave

k

pe (1 3k2D

2 )

kcS

Forward L waveBackward L wave

Forward S waveBackward S wave

Three‐wave decay process

e iL

L’

S

e iL

L’

SS

𝛿 𝜎𝜔 𝜎 𝜔 𝜎′′𝜔

Results 𝒈𝟏𝒏𝝀𝑫𝟑

𝟓 𝟏𝟎 𝟑,𝒏𝒃𝒏 𝟏𝟎 𝟐,

𝑽𝟎𝒗𝒆

𝟒,𝑻𝒆𝑻𝒊

𝟕

𝒈 𝟏/𝒏𝝀𝑫𝟑 , 𝝎𝒑𝒆𝒕 𝟐 𝟏𝟎𝟒

Comparison with 1D PIC Simulation

Comparison with 1D PIC Simulation

P.H. Yoon’s Theory

1D PIC Simulation

Jongsoo Woo et al. (2007)

g1nλ

5 10

Comparison with 1D PIC Simulation

P.H. Yoon’s Theory

1D PIC Simulation

Jongsoo Woo et al. (2007)

• Suprathermal electrons are generated by Beam-plasma interaction.

• The collisionality, defined via the ``plasma parameter’’ 𝒈 𝟏/𝒏𝝀𝑫𝟑 , plays an important role in the generation of suprathermal electrons.

• A small but moderately finite value of 𝒈 is necessary for the superthermal tail to be generated, implying that purely collisionless 𝒈 𝟎 Vlasov theory cannot produce a superthermal population.

20

Summary