Post on 01-Jan-2016
description
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.