Transcript Non-extensive entropy, turbulent quasi equilibrium, and

Electron acceleration by
Langmuir turbulence
Peter H. Yoon
U. Maryland, College Park
Outline
• Laboratory Beam-Plasma Experiments
• Beam-plasma instability & Langmuir
turbulence
• Solar wind electrons
• Conclusions
Part 1.
LABORATORY BEAM-PLASMA
EXPERIMENTS
• Alexeff et al., Hot-electron plasma by beamplasma 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
Part 2.
BEAM-PLASMA INSTABILITY AND
LANGMUIR TURBULENCE
Bump-in-tail instability
Langmuir Turbulence generated by
beam-plasma interaction
E(x,t)  Ecos(k  x  t),
   pe (1 3k 2 2D ) 

4ne2 
2 3Te
,
1 k
2 
me 
4ne 
Te
  kcS  k
.
mi

Langmuir oscillation
Ion-sound wave
or
Ion-sound wave
t
E(x,t)
x
Langmuir wave
t
E(x,t)
x
E(x,t)  Ecos(k  x  t),
   pe (1 3k  ) 
2 2
D
  kcS  k

4ne2 
2 3Te
,
1 k
2 
me 
4ne 
or
Te
.
mi

   pe (1 3k 22D )

  kc S

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.
Backgroun
d (thermal)
electrons
Beam
electrons
T Umeda, private communications
Bump-in-tail
instability
Beam-plasma or bump-in-tail instability
Bump-on-tail instability
fe(v)
t=0
v
t>0
W. E. Drummond and D.
Pines, Nucl. Fusion Suppl.
3, 1049 (1962).
IL(k)
t>0
k
t=0
A. A. Vedenov, E. P.
Velikhov, R. Z. Sagdeev,
Nucl. Fusion 1, 82
(1961).
 02
E k2
 k   2  k F'kv k 
,
k
4N
df0
e2 
k i ke f 0
2
 2
dk | E k |
 ( k  k v),

3 2
dt
m v i
(2 ) k v e
.
Bump-in-tail
instability
Weak turbulence theory
L. 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
f e  
f e 
Ai f e  Dij


,
t v i 

v

j 
e2
Ai 
4me
Dij 
e 2
me2
Discrete-particle (collisional) effect
k
 dk k 2i   kL ( kL  k v),
 1
 dk
~ g = 1/(nD3)
ki k j
L
L

(


k
v)I

k
k .
2
k  1
2
IkL  pe
 2
t
k
2
ne2
f e 
L L
 dv (  k v)  f e   k Ik k v 
L
k
   dk'V
L
k
 ( kL   ' k'L   '' kS k' )
L
k,k'
 ', '' 1


S
S L
 kL Ik'' L Ik ''k'
  ' k'L Ik ''k'
Ik   '' kL k' Ik'' L IkL 
e 2
 2 2  kL 
me  pe
 ' 1
(k k') 2
 dk'  dv k 2k'2 [ kL  ' k'L  (k  k') v]
 ne2
me  ' L L
f i 
L L
L 'L

 2 (' k' Ik   k Ik' ) f i  m Ik' Ik (k  k') v 

 pe
i

Weak turbulence theory
Long-time behavior of bump-on-tail Langmuir instability
P. H. Yoon, T. Rhee, and C.-M. Ryu, Self-consistent generation of superthermal
electrons by beam-plasma interaction, PRL 95, 215003 (2005).
Outline
• Laboratory Beam-Plasma Experiments
• Beam-plasma instability & Langmuir
turbulence
• Solar wind electrons
• Conclusions
Part 3.
SOLAR WIND ELECTRONS
FAST WIND
e–
SUN
L
SLOW WIND
EARTH
STEREO spacecraft
WIND spacecraft
2007 January 9
Linghua Wang,
Robert P. Lin,
Chadi Salem
fe(v)
Electron
Velocity
Distribution
By Linghua Wang, Davin Larsen, Robert Lin
Outline
• Laboratory Beam-Plasma Experiments
• Beam-plasma instability & Langmuir
turbulence
• Solar wind electrons
• Conclusions
Part 4.
CONCLUSIONS
• 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.