Electron Acoustic Waves in Pure Ion Plasmas F. Anderegg C.F. Driscoll, D.H.E. Dubin, T.M. O

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Electron Acoustic Wavesin Pure Ion Plasmas F.
Anderegg C.F. Driscoll, D.H.E. Dubin, T.M.
ONeil University of California San Diego
supported by NSF grant PHY-0354979
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Overview

• We measure the particle distribution function
  f(vz , z center) coherently with the wave

• A non-resonant drive modifies the particle
• distribution f(vz) so as to make the mode
  resonant
• with the drive.

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Electron Acoustic Wave the mis-named wave

• EAWs are a low frequency branch of standard
  electrostatic plasma waves.

• EAWs are non-linear plasma waves that exist at
  moderately small amplitude.

• Observed in Laser plasmas Pure electron
  plasmas Pure ion plasmas

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Other Work on Electron Acoustics Waves

• Theory neutralized plasmas Holloway and Dorning
  1991
• Theory and numerical non-neutral
  plasmasValentini, ONeil, and Dubin 2006

• Experiments laser plasmas Montgomery et al
  2001Sircombe, Arber, and Dendy 2006
• Experiments pure electron plasmas Kabantsev,
  Driscoll 2006
• Experiments pure electron plasma mode driven by
  frequency chirp Fajans group 2003

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Theory
Electron Acoustic Waves are plasma waves with a
slow phase velocity
This wave is nonlinear so as to flatten the
particle distribution to avoid strong Landau
damping.
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Dispersion relation

• Infinite homogenous plasma (Dorning et
  al.)

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Dispersion Relation
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Penning-Malmberg Trap
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Density and Temperature Profile
rp 0.5 cm
0.05eV lt T lt 5 eV
Mg B 3T
n 1.5 x 107 cm-3
Lp 10cm
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Measured Wave Dispersion
Trivelpiece Gould
EAW
Rp/lD lt 2
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Received Wall Signal
Trivelpiece Gould mode
The plasma response grows smoothly during the
drive
10 cycles 21.5 kHz
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Received Wall Signal
Electron Acoustic Wave
During the drive the plasma response is
erratic. Plateau formation
100 cycles 10.7 kHz
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Fit Multiple Sin-waves to Wall Signal
Electron Acoustic Wave
The fit consist of two harmonics and the
fundamental sin-wave, resulting in a precise
description of the wall signal
fit
data
Wall signal volt 70db
Time ms
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Wave-coherent distribution function
Record the Time of Arrival of the Photons
photons
Photons are accumulated in 8 separate phase-bin
Wall signal volt 70db
35.5
36.0
time ms
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Distribution Function versus Wave Phase
Trivelpiece Gould mode
f 21.5 kHzT 0.77 eV
f(vz, z0)
The coherent distribution function shows
oscillations dv of the entire distribution
These measurements are done in only one position
(plasma center, z0)
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Distribution Function versus Wave Phase
T0.3
T0.4
Electron Acoustic Wave
f 10.7 kHz T 0.3 eV
f(vz, z0)
The coherent distribution function shows -
oscillating Dv plateau at vphase - dv0 wiggle
at v0
Dv
These measurements are done in only one position
(plasma center, z0)
dv0
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Distribution Function versus Phase
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Distribution Function versus Phase
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Distribution Function versus Phase
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Distribution Function versus Phase
Shows wiggle of the entire distribution
4000
Velocity m/s
-4000
Small amplitude
0
90
180
270
360
Phase degree
Trivelpiece Gould mode
This measurement is done in only one position
(plasma center)
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Distribution Function versus Phase
18055_1830523
Dv

• Shows
• trapped particle island of half- width ?v
• dv0 wiggle at v0

Velocity m/s
dv0
-2000
0
90
180
270
360
Electron Acoustic Wave
Phase degree
This measurement is done in only one position
(plasma center)
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Model
18055_1830523

• Two independent waves
• Collisions remove discontinuities

2000
Velocity m/s
-2000
0
90
180
270
360
Phase degree
Electron Acoustic Wave
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Island Width Dv vs Particle Sloshing dv0
Trapping in each traveling wave gives Dv The sum
of the two waves gives sloshing dv0
Linear theory gives
0
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Frequency Variability
Large amplitude drives are resonant over a wide
range of frequencies
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Frequency jump
100 cycles
TG
EAW
f response
f drive
The plasma responds to a non-resonant drive by
re-arranging f(v) such as to make the mode
resonant
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f(v) evolves to become resonant with drive!
Non-resonant drive modifies the particle
distribution f(vz) to make the plasma mode
resonant with the drive.
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Particle Response Coherent with Wave
Fixed frequency drive 100 cycles at f 18kHz
The coherent response give a precise measure of
the phase velocity
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When the Frequency Changes kz does not change
T 1.65 eV
kz p / Lp
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Range of Mode Frequencies
Trivelpiece Gould
EAW
When the particle distribution is modified,
plasma modes can be excited over a continuum
range, and also past the theoretical thumb.
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Chirped Drive
The frequency is chirped down from 21kHz to10 kHz
The chirped drive produce extreme modification of
f(v)
Damping rate g/w 1 x 10-5
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Summary

• Standing Electron Acoustic Waves (EAWs) and
  Trivelpiece Gould waves are excited in pure ion
  plasma.
• Measured dispersion relation agrees with
  Dornings theory

• We observe - Particle sloshing in the trough
  of the wave - Non-linear wave trapping. -
  Close agreement with 2 independent waves
  collisions model

• Surprisingly Non-resonant wave drive modifies
  the particles distribution f(v) to make the
  drive resonant.Effectively excites plasma mode
  at any frequency over a continuous range

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Distribution Function versus Phase
Shows wiggle of the entire distribution
Velocity
Large amplitude
0
90
180
270
360
Phase degree
Trivelpiece Gould mode
This measurement is done in only one position
(plasma center)
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Typical Parameters
rp 0.5 cm
0.05eV lt T lt 5 eV
Mg B 3T
n 1.5 x 107 cm-3
Lp 10cm
Standing wave phase velocity
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Stability
f (v)
Penrose criteria predicts instability if
satisfied
k lt 96 m-1
and k satisfies
Our
230 m-1 is larger than the maximum
gt This plasma is stable
allowed by Penrose criteria
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Chirped Drive
Received signal Volt 70db
Time ms
The frequency is chirped down from 21kHz to10 kHz
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Particles Coherent Response
Trivelpiece Gould mode
vph
vph
The coherent response changes sign at v 0
(almost no particle are present at the phase
velocity)
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Particles Coherent Response
Electron Acoustic Wave
vph
vph
The coherent response changes sign at v 0
at the wave phase velocity
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Distribution Function versus Phase
Dv

• Shows
• trapped particle island of half- width ?v
• dv0 wiggle at v0

Velocity m/s
dv0
-2000
0
90
180
270
360
Electron Acoustic Wave
Phase degree
This measurement is done in only one position
(plasma center)