Electron acceleration by Langmuir turbulence

Peter H. YoonU. Maryland, College Park

Outline

• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir

turbulence• Solar wind electrons• Conclusions

LABORATORY BEAM-PLASMA EXPERIMENTS

Part 1.

• Alexeff et al., Hot-electron plasma by beam-plasma interaction, PRL, 10, 273 (1963).

5 keV DC electron beam interacting with plasma yields 250 keV X ray photons.

• Tarumov et al., Investigation of a hydrogen plasma with “hot” electrons, Sov. Phys. JETP, 25, 31 (1967).

During the discharge phase the hot electron component was 1/10, which increased to 1/3 in the decay phase.

• Levitskii and Shashurin, Spatial development of plasma-beam instability, Sov. Phys. JETP, 25, 227 (1967).

• Whelan and Stenzel, Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system, Phys. Fluids, 28, 958 (1985).

Outline

• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir

turbulence• Solar wind electrons• Conclusions

BEAM-PLASMA INSTABILITY AND LANGMUIR TURBULENCE

Part 2.

Bump-in-tail instabilityLangmuir Turbulence generated by

beam-plasma interaction

€

E(x, t) = Ecos(k • x −ωt),

ω =ω pe (1+ 3k 2λD2 ) =

4πne2

me1+ k 2 3Te

4πne2

⎛

⎝ ⎜

⎞

⎠ ⎟, or

ω = kcS = kTemi

.

Langmuir oscillation Ion-sound wave

t

x

E(x,t)

Ion-sound wave

t

x

E(x,t)

Langmuir wave

€

E(x, t) = Ecos(k • x −ωt),

ω =ω pe (1+ 3k 2λD2 ) =

4πne2

me1+ k 2 3Te

4πne2

⎛

⎝ ⎜

⎞

⎠ ⎟, or

ω = kcS = kTemi

.

€

ω =ω pe (1+ 3k 2λD2 )

€

ω =kcS

1D approxiation

Ions (protons) are taken as a quasi-steady state, and the electrons are made of two components, one background Gaussian distribution, and a tenuous beam component.

Background (thermal) electrons

Beam electrons

T Umeda, private communications

Bump-in-tailinstability

Beam-plasma or bump-in-tail instability

Bump-on-tail instabilityvfe(v)t = 0t > 0kIL(k)t = 0t > 0

A. A. Vedenov, E. P. Velikhov, R. Z. Sagdeev, Nucl. Fusion 1, 82 (1961).

W. E. Drummond and D. Pines, Nucl. Fusion Suppl. 3, 1049 (1962).

€

ε.

k = πω0

2

k 2 ωkF ']kv=ω k⋅E k

2

4πN,

df0dt

= πe2

m2

∂

∂v idk∫ | Ek |2

kike(2π )3k 2

∂f0∂veδ (ωk − k⋅ v),

Bump-in-tailinstability

Weak turbulence theoryL. M. Gorbunov, V. V. Pustovalov, and V. P. Silin, Sov. Phys. JETP 20, 967 (1965)

L. M. Al’tshul’ and V. I. Karpman, Sov Phys. JETP 20, 1043 (1965)

L. M. Kovrizhnykh, Sov. Phys. JETP 21, 744 (1965)

B. B. Kadomtsev, Plasma Turbulence (Academic Press, 1965)

V. N. Tsytovich, Sov. Phys. USPEKHI 9, 805 (1967)

V. N. Tsytovich, Nonlinear Effects in Plasma (Plenum Press, 1970)

V. N. Tsytovich, Theory of Turbulent Plasma (Consultants Bureau, 1977)

A. G. Sitenko, Fluctuations and Non-Linear Wave Interactions in Plasmas (Pergamon, 1982)

Backscattered L wave

€

∂fe∂t

=∂

∂v iAi fe +Dij

∂fe∂v j

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟,

Ai =e2

4πmedk∫ kik 2

σ =±1

∑ σωkLδ (σωk

L − k⋅ v),

Dij =πe2

me2 dk∫

kik jk 2

σ =±1

∑ δ (σωkL − k⋅ v)Ik

σL .

€

∂IkσL

∂t=πω pe

2

k 2 dv∫ δ (σωkL − k⋅ v)

ne2

πfe +σωk

LIkσLk⋅

∂fe∂v

⎛

⎝ ⎜

⎞

⎠ ⎟

€

+2σ ',σ ''=±1

∑ σωkL dk'∫ Vk,k '

L δ (σωkL −σ 'ωk '

L −σ ' 'ωk −k 'S )

× σωkLIk 'σ 'LIk −k '

σ ''S −σ 'ωk 'L Ik −k 'σ ''S Ik

σL −σ ' 'ωk −k 'L Ik '

σ 'LIkσL

( )

€

−πe2

me2ω pe

2 σωkL

σ '=±1

∑ dk'∫ dv∫ (k⋅k')2

k 2k '2δ[σωk

L −σ 'ωk 'L − (k − k')⋅ v]

×ne2

πω pe2 (σ 'ωk '

L IkσL −σωk

LIk 'σ 'L ) f i −

memiIk 'σ 'LIk

σL (k − k')⋅∂f i∂v

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

~ g = 1/(nD3)

Discrete-particle (collisional) effect

Weak turbulence theory

P. H. Yoon, T. Rhee, and C.-M. Ryu, Self-consistent generation of superthermal electrons by beam-plasma interaction, PRL 95, 215003 (2005).

Long-time behavior of bump-on-tail Langmuir instability

Outline

• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir

turbulence• Solar wind electrons• Conclusions

SOLAR WIND ELECTRONSPart 3.

SUNEARTHFAST WINDSLOW WINDe –L

STEREO spacecraft

WIND spacecraft

2007 January 9Linghua Wang, Robert P. Lin, Chadi Salem

By Linghua Wang, Davin Larsen, Robert Lin

fe(v)ElectronVelocityDistribution

Outline

• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir

turbulence• Solar wind electrons• Conclusions

CONCLUSIONSPart 4.

• Beam-plasma interaction is a fundamental problem in plasma physics.

• Laboratory experiment shows electrons accelerated by beam-plasma interaction.

• Electron beam-excited Langmuir turbulence theory adequately explains the laboratory results and predict the formation of energetic tail distribution.

• Solar wind electrons feature energetic tail population confirming Langmuir turbulence acceleration theory.