Electron Acoustic Waves in Pure Ion Plasmas F. Anderegg C.F. - - PowerPoint PPT Presentation

Electron Acoustic Waves in 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 plasmas Pure 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 plasmas

Valentini, O’Neil, and Dubin 2006

• Experiments: laser plasmas

Montgomery et al 2001 Sircombe, 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.

0.5 1

• 4
• 3
• 2
• 1

1 2 3 4

f (vz)

vz / v EAW TG

ω ≈ 1.3 k v

Dispersion relation

• Infinite homogenous plasma (Dorning et al.)

0 = (k,) = 1 p

2

k2 dv

Landau

• k f0

v

kv

0 1 p

2

k2 P dv k f

v

kv

• i p

2

k2 f0 v /k

Landau damping

0 1 p

2

k2 P dv k f

v

kv

• “Thumb diagram”

Trapping “flattens” the distribution in the resonant region (BGK)

Dispersion Relation

Infinite size plasma (homogenous)

Langmuir wave E A W

kz λD ω / ω

p

Fixed λD / rp

k⊥ = 0.25

Trapped NNP (long column finite radial size)

kz λD ω / ω

p

Experiment: fixed kz vary T and measure f Fixed kz

5 10 15 20 25 30 0.2 0.4 0.6 0.8 1 1.2 1.4

f [kHz] T [eV]

TG wave E A W

Penning-Malmberg Trap

Density and Temperature Profile

5 10 15 20

• 1.5
• 1
• 0.5

0.5 1 1.5

x(cm)

ni [106 cm-3]

1940 -198

0.5 1 1.5

• 1.5
• 1
• 0.5

0.5 1 1.5

x(cm)

T [eV]

1940 -198

Mg+ B = 3T 0.05eV < T < 5 eV rp ~ 0.5 cm Lp ~ 10cm

n ≈ 1.5 x 107 cm-3

5 10 15 20 25 30 0.5 1 1.5

f [kHz] T [eV]

Measured Wave Dispersion

Rp/λD < 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 Signal

Electron 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

• f the wall signal

Electron Acoustic Wave fit data Time [ms] Wall signal [volt +70db]

Wave-coherent distribution function

Record the Time of Arrival of the Photons

Photons are accumulated in 8 separate phase-bin time [ms] Wall signal [volt +70db] photons 35.5 36.0

Distribution Function versus Wave Phase

The coherent distribution function shows oscillations δv of the entire distribution

These measurements are done in only one position (plasma center, z~0)

f(vz, z=0)

f = 21.5 kHz T = 0.77 eV

0o 45o 90o 135o 180o 225o

• 6000
• 4000
• 2000

2000 4000 6000

315o

ion velocity [m/s]

270o

Trivelpiece Gould mode

0o 45o 90o 135o 180o 225o

• 4000
• 2000

2000 4000

ion velocity [m/s] 315o 270o before wave after wave

Distribution Function versus Wave Phase

The coherent distribution function shows:

• oscillating Δv plateau at vphase
• δv0 wiggle at v=0

These measurements are done in only one position (plasma center, z=0)

f(vz, z=0)

f = 10.7 kHz T = 0.3 eV Electron Acoustic Wave

Δv δv0

T=0.3 T=0.4

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase

This measurement is done in only one position (plasma center)

Trivelpiece Gould mode Small amplitude Velocity [m/s]

• 4000

Shows wiggle

• f the entire

distribution

4000

Phase [degree] 90 180 270 360

Distribution Function versus Phase

Shows:

• trapped particle

island of half- width Δv

• δv0 wiggle at v=0

This measurement is done in only one position (plasma center)

Electron Acoustic Wave Phase [degree] 90 180 270 Δv δv0 Velocity [m/s]

• 2000

360

18055_18305;23

Model

• Two independent

waves

• Collisions remove

discontinuities Electron Acoustic Wave Phase [degree] 90 180 270 Velocity [m/s]

• 2000

360

18055_18305;23

2000

Island Width Δv vs Particle Sloshing δv0

Trapping in each traveling wave gives Δv The sum of the two waves gives sloshing δv0 Linear theory gives:

100 1000 10 100 1000

v_island (vph @10.7 kHz / vph ) [m/s] (half-width) v0 at v=0 [m/s] (half-width) v = ( 2 v0 vph )1/2

v = 2 v0 v phase

( )

1/2

Frequency Variability

Large amplitude drives are resonant over a wide range of frequencies

200 400 10 15 20 25 30

Vwall [µV] fresponse [kHz]

10mV drive

TG

100 cycles 200 400 10 15 20 25 30

Vwall [µV] fresponse [kHz]

60mV drive

TG EAW

100 cycles 200 400 10 15 20 25 30 100mV drive

Vwall [µV] fresponse [kHz]

TG EAW

100 cycles 10 15 20 25 30 200 400 300mV drive

fresponse [kHz] Vwall [µV]

100 cycles

Frequency “jump”

200 400

Vwall [µV]

60mV drive TG EAW

f response f drive

10 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.

5 10 15

• 6000
• 3000

3000 6000 before wave with wave

Below TG mode, 19kHz drive

relative velocity [ m/s ] f (v) phase averaged

5 10 15

• 6000
• 3000

3000 6000

relative velocity [ m/s ] f (v) phase averaged

Resonant with TG mode, 21.8kHz drive before wave with wave

Particle Response Coherent with Wave

Fixed frequency drive 100 cycles at f =18kHz

• 8
• 6
• 4
• 2

2 4 6 8

• 3
• 2
• 1

1 2 3 4 Coherent response [A.U.]

v / vth

T = 1.75 eV vth= 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

1000 2000 3000 4000 5000 6000 5 10 15 20 25

0.5 1 1.5 2

Vphase [m/s] mode frequency [kHz] rp / D ~ 2 T = 1.65 eV

vphase / vth

T ≈ 1.65 eV

1.4 vth < vphase< 2.1 vth Plasma mode excited

• ver a wide range of

phase velocity:

5 10 15 20 25 30 0.5 1 1.5

f [kHz] 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 γ/ω ~ 1 x 10-5

• 8000
• 4000

4000 8000 40 80

ion velocity [m/s] with wave

v 2 40 80

before wave

v1

T = 1.3 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