supported by nsf grant phy-0354979
DESCRIPTION
Electron Acoustic Waves in Pure Ion Plasmas F. Anderegg C.F. Driscoll, D.H.E. Dubin, T.M. O’Neil U niversity of C alifornia S an D iego. supported by NSF grant PHY-0354979. We observe “ Electron” Acoustic Waves (EAW) in magnesium ion plasmas. Measure wave dispersion relation. Overview. - PowerPoint PPT PresentationTRANSCRIPT
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Electron Acoustic Wavesin Pure Ion Plasmas
F. Anderegg C.F. Driscoll, D.H.E. Dubin, T.M. O’Neil
University of California San Diego
supported by NSF grant PHY-0354979
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Overview
• We observe “Electron” Acoustic Waves (EAW) in magnesium ion plasmas.
Measure wave dispersion relation.
• 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.
• Observed in: Laser plasmasPure electron plasmas Pure ion plasmas
• EAWs are non-linear plasma waves that exist at moderately small amplitude.
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Other Work on Electron Acoustics Waves
• Theory: neutralized plasmas Holloway and Dorning 1991
• Theory and numerical: non-neutral plasmasValentini, O’Neil, 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 Fajan’s 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.
0
0.5
1
-4 -3 -2 -1 0 1 2 3 4
vz / v
EAW
TG
≈ 1.3 k v
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Dispersion relation• Infinite homogenous plasma (Dorning et al.)
0=ε(k,)=1−p2
k2 dvLandau∫k∂f0∂vkv−
0≈1−p2
k2 P dvk∂f0∂vkv−∫ −iπp2
k2∂f0∂v/k
Landau damping
0≈1−p2
k2 P dvk∂f0∂vkv−∫ “Thumb diagram”
Trapping “flattens” the distribution in the resonant region (BGK)
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Dispersion RelationInfinite size plasma(homogenous)
Langmuir wave
EAW
kz D
/
p
Fixed D / rp
k = 0.25
Trapped NNP(long column finite radial size)
kz D
/
p
Experiment: fixed kz vary T and measure f
Fixed kz
0
5
10
15
20
25
30
0 0.2 0.4 0.6 0.8 1 1.2 1.4
T [eV]
TG wave
EAW
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Penning-Malmberg Trap
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Density and Temperature Profile
0
5
10
15
20
-1.5 -1 -0.5 0 0.5 1 1.5x(cm)
1940 -198
0
0.5
1
1.5
-1.5 -1 -0.5 0 0.5 1 1.5x(cm)
1940 -198
Mg+
B = 3T
0.05eV < T < 5 eV rp ~ 0.5 cm
Lp ~ 10cmn ≈ 1.5 x 107 cm-3
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0
5
10
15
20
25
30
0 0.5 1 1.5
T [eV]
Measured Wave Dispersion
Rp/D < 2
EAW
Trivelpiece Gould
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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 SignalElectron Acoustic Wave
100 cycles 10.7 kHz
During the drive the plasma response is erratic.
Plateau formation
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Fit Multiple Sin-waves to Wall Signal
The fit consist of two harmonics and the fundamental sin-wave, resulting in a precise description of the wall signal
Electron Acoustic Wave
fitdata
Time [ms]
Wal
l sig
nal [
volt
+70
db]
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Wave-coherent distribution function
Record the Time of Arrival of the Photons
Photons are accumulated in 8 separate phase-bin
time [ms]
Wal
l sig
nal [
volt
+70
db]
photons
35.5 36.0
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Distribution Function versus Wave Phase
The coherent distribution function shows oscillations v of the entire distribution
These measurements are done in only one position (plasma center, z~0)
f(vz,
z=0)
f = 21.5 kHzT = 0.77 eV
0o
45o
90o
135o
180o
225o
-6000 -4000 -2000 0 2000 4000 6000
315o
ion velocity [m/s]
270o
Trivelpiece Gould mode
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0o
45o
90o
135o
180o
225o
-4000 -2000 0 2000 4000ion velocity [m/s]
315o
270o
before wave
after wave
Distribution Function versus Wave Phase
The coherent distribution function shows:
- oscillating v plateau at vphase
- v0 wiggle at v=0
These measurements are done in only one position (plasma center, z=0)
f(vz,
z=0)
f = 10.7 kHzT = 0.3 eV
Electron Acoustic Wave
v
v0
T=0.3
T=0.4
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Distribution Function versus Phase
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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Distribution Function versus Phase
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are needed to see this picture.
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Distribution Function versus Phase
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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Distribution Function versus Phase
This measurement is done in only one position (plasma center)
Trivelpiece Gould mode
Small amplitude
Vel
ocit
y [m
/s]
-4000
Shows wiggle of the entire distribution
4000
Phase [degree]
0 90 180 270 360
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Distribution Function versus Phase
Shows:- trapped particle
island of half-
width v
- v0 wiggle at v=0
This measurement is done in only one position (plasma center)
Electron Acoustic WavePhase [degree]0 90 180 270
v
v0
Vel
ocit
y [m
/s]
-2000
360
18055_18305;23
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Model
•Two independent waves
•Collisions remove discontinuities
Electron Acoustic WavePhase [degree]0 90 180 270
Vel
ocit
y [m
/s]
-2000
360
18055_18305;23
2000
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Island Width v vs Particle Sloshing v0
Trapping in each traveling wave gives v
The sum of the two waves gives sloshing v0
Linear theory gives:100
1000
10 100 1000
δv0 at v=0 [m/s] (half-width)
Δv = ( 2 δv0 v
ph )1/2
0v = 2 δv0 v phase( )1/2
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Frequency Variability
Large amplitude drives are resonant over a wide range of frequencies
0
200
400
10 15 20 25 30fresponse
[ ]kHz
10 mV drive
TG100 cycles
0
200
400
10 15 20 25 30fresponse
[ ]kHz
60 mV drive
TG
EAW
100 cycles
0
200
400
10 15 20 25 30
100mV drive
fresponse
[ ]kHz
TG
EAW
100 cycles
10 15 20 25 300
200
400300mV drive
fresponse
[kHz]
100 cycles
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Frequency “jump”
0
200
40060mV rivε
TG
EAW
f response
f drive10 15 20 25 30
frequency [kHz]
The plasma responds to a non-resonant drive by re-arranging f(v) such as to make the mode resonant
100 cycles
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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.
0
5
10
15
-6000 -3000 0 3000 6000
before wave
with wave
wf3_PhoSum_37456_37655___.txt;2
Below TG mode, 19kHz drive
relative velocity [ m/s ]
0
5
10
15
-6000 -3000 0 3000 6000
relative velocity [ m/s ]
Resonant with TG mode, 21.8kHz drive
before wave
with wave
wf3_PhoSum_37717_37916___.txt;3
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Particle Response Coherent with Wave
Fixed frequency drive 100 cycles at f =18kHz
-8
-6
-4
-2
0
2
4
6
8
-3 -2 -1 0 1 2 3 4
v / vth
T = 1.75 eVv
th= 2646. m/s
WF19371-19571
vphase
vphase
The coherent response give a precise measure of the phase velocity
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When the Frequency Changes kz does not change
k z = π
/ L p
0
1000
2000
3000
4000
5000
6000
0 5 10 15 20 250
0.5
1
1.5
2
mode frequency [kHz]
rp /
D ~ 2
= 1.65 T eVT ≈ 1.65 eV
1.4 vth < vphase< 2.1 vth
Plasma mode excited over a wide range of phase velocity:
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0
5
10
15
20
25
30
0 0.5 1 1.5
T [eV]
Range of Mode Frequencies
EAW
Trivelpiece Gould
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 chirped drive produce extreme modification of f(v)
The frequency is chirped down from
21kHz to10 kHz
Damping rate ~ 1 x 10-5
-8000 -4000 0 4000 80000
40
80
ion velocity [m/s]
with wave
vφ 2
0
40
80
before wave
vφ1
= 1.3 T eV
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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 Dorning’s 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
This measurement is done in only one position (plasma center)
Shows wiggle of the entire distribution
Trivelpiece Gould mode
Vel
ocit
y
Phase [degree]0 90 180 270 360 Large amplitude
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Typical Parameters
Mg+
B = 3T
0.05eV < T < 5 eV rp ~ 0.5 cm
Lp ~ 10cmn ≈ 1.5 x 107 cm-3
D
=4 π n e
2
⎛
⎝⎜
⎞
⎠⎟
1 / 2
= 0 . 2 4 c mT
e V
1 / 2
n7
1 / 2
k Tf
r= 5
B3 T
n7
[ k H z ]
Standing wave phase velocity
vp h a s e = = 2 f L p [ m s ]
1 0 k H z
⎛
⎝⎜
f ⎞
⎠⎟
k
= 2 0 0 0
vt h
=k T
m= 2 0 0 0 T
eV
1 / 2
[ m s ] ν ii ≅ 1 s −1 n7 T−3
2eV
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Stability
Penrose criteria predicts instability if
-8000 -4000 0 4000 80000
40
80
120
ion velocity [m/s]
v0
f (v)
f (v0) − f (v)
v−v0( )2−∞
∞
∫ dv < 0
k < p2 f (v0)−f (v)
v−v0( )2−∞
∞∫ dvand k satisfies
satisfied
k < 96 m-1
= 230 m-1 is larger than the maximum
=> This plasma is stable
k⊥= 1rp
2
ln(rw rp)Our
allowed by Penrose criteria
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Chirped Drive
The frequency is chirped down from
21kHz to10 kHz
Rec
eive
d si
gnal
[ V
olt +
70db
]
Time [ms]
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-1
0
1
-6000 -3000 0 3000 6000
ion velocity [m/s]
Particles Coherent Response
The coherent response changes sign at v = 0 (almost no particle are present at the phase velocity)
vph vph
Trivelpiece Gould mode
f ~∂ f
0
v−vph
∂v
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Particles Coherent Response
-20
0
20
-4000 -2000 0 2000 4000
ion velocity [m/s]
The coherent response changes sign at: v = 0 at the wave phase velocity
vph vph
Electron Acoustic Wave
f ~∂ f
0
v−vph
∂v
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QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Distribution Function versus Phase
Shows:- trapped particle
island of half-
width v
- v0 wiggle at v=0
This measurement is done in only one position (plasma center)
Electron Acoustic WavePhase [degree]
0 90 180 270 360
v
v0
Vel
ocit
y [m
/s]
-2000