![Page 1: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/1.jpg)
Electron acceleration by Langmuir turbulence
Peter H. YoonU. Maryland, College Park
![Page 2: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/2.jpg)
Outline
• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir
turbulence• Solar wind electrons• Conclusions
![Page 3: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/3.jpg)
LABORATORY BEAM-PLASMA EXPERIMENTS
Part 1.
![Page 4: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/4.jpg)
• 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.
![Page 5: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/5.jpg)
• Tarumov et al., Investigation of a hydrogen plasma with “hot” electrons, Sov. Phys. JETP, 25, 31 (1967).
![Page 6: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/6.jpg)
During the discharge phase the hot electron component was 1/10, which increased to 1/3 in the decay phase.
![Page 7: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/7.jpg)
• Levitskii and Shashurin, Spatial development of plasma-beam instability, Sov. Phys. JETP, 25, 227 (1967).
![Page 8: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/8.jpg)
![Page 9: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/9.jpg)
• Whelan and Stenzel, Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system, Phys. Fluids, 28, 958 (1985).
![Page 10: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/10.jpg)
![Page 11: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/11.jpg)
Outline
• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir
turbulence• Solar wind electrons• Conclusions
![Page 12: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/12.jpg)
BEAM-PLASMA INSTABILITY AND LANGMUIR TURBULENCE
Part 2.
![Page 13: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/13.jpg)
Bump-in-tail instabilityLangmuir Turbulence generated by
beam-plasma interaction
![Page 14: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/14.jpg)
€
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
![Page 15: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/15.jpg)
t
x
E(x,t)
Ion-sound wave
![Page 16: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/16.jpg)
t
x
E(x,t)
Langmuir wave
![Page 17: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/17.jpg)
€
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
![Page 18: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/18.jpg)
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.
![Page 19: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/19.jpg)
Background (thermal) electrons
Beam electrons
![Page 20: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/20.jpg)
![Page 21: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/21.jpg)
![Page 22: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/22.jpg)
T Umeda, private communications
![Page 23: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/23.jpg)
![Page 24: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/24.jpg)
Bump-in-tailinstability
![Page 25: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/25.jpg)
Beam-plasma or bump-in-tail instability
![Page 26: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/26.jpg)
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).
![Page 27: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/27.jpg)
€
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),
![Page 28: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/28.jpg)
Bump-in-tailinstability
![Page 29: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/29.jpg)
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)
![Page 30: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/30.jpg)
Backscattered L wave
![Page 31: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/31.jpg)
![Page 32: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/32.jpg)
![Page 33: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/33.jpg)
€
∂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
![Page 34: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/34.jpg)
Weak turbulence theory
![Page 35: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/35.jpg)
![Page 36: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/36.jpg)
![Page 37: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/37.jpg)
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
![Page 38: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/38.jpg)
Outline
• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir
turbulence• Solar wind electrons• Conclusions
![Page 39: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/39.jpg)
SOLAR WIND ELECTRONSPart 3.
![Page 40: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/40.jpg)
SUNEARTHFAST WINDSLOW WINDe –L
![Page 41: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/41.jpg)
![Page 42: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/42.jpg)
![Page 43: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/43.jpg)
STEREO spacecraft
![Page 44: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/44.jpg)
![Page 45: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/45.jpg)
WIND spacecraft
![Page 46: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/46.jpg)
2007 January 9Linghua Wang, Robert P. Lin, Chadi Salem
![Page 47: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/47.jpg)
By Linghua Wang, Davin Larsen, Robert Lin
fe(v)ElectronVelocityDistribution
![Page 48: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/48.jpg)
Outline
• Laboratory Beam-Plasma Experiments • Beam-plasma instability & Langmuir
turbulence• Solar wind electrons• Conclusions
![Page 49: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/49.jpg)
CONCLUSIONSPart 4.
![Page 50: Electron acceleration by Langmuir turbulence Peter H. Yoon U. Maryland, College Park](https://reader036.vdocuments.net/reader036/viewer/2022062423/56649f435503460f94c633a8/html5/thumbnails/50.jpg)
• 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.