supported by NSF grant PHY-0354979
description
Transcript of supported by NSF grant PHY-0354979
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
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.
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.
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
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
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)
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
Penning-Malmberg Trap
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
0
5
10
15
20
25
30
0 0.5 1 1.5
T [eV]
Measured Wave Dispersion
Rp/D < 2
EAW
Trivelpiece Gould
Received Wall Signal
Trivelpiece Gould mode
The plasma response grows smoothly during the drive
10 cycles 21.5 kHz
Received Wall SignalElectron Acoustic Wave
100 cycles 10.7 kHz
During the drive the plasma response is erratic.
Plateau formation
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]
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
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
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
Distribution Function versus Phase
QuickTime™ and aAnimation decompressor
are needed to see this picture.
Distribution Function versus Phase
QuickTime™ and aAnimation decompressor
are needed to see this picture.
Distribution Function versus Phase
QuickTime™ and aAnimation decompressor
are needed to see this picture.
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
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
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
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
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
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
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
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
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:
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.
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
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
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
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
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
Chirped Drive
The frequency is chirped down from
21kHz to10 kHz
Rec
eive
d si
gnal
[ V
olt +
70db
]
Time [ms]
-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
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
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