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 U niversity of C alifornia S an D iego 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 (v z , z = center) coherently with the wave • A non-resonant drive modifies the particle distribution f (v z ) so as to make the mode resonant with the drive.

E lectron A coustic W ave: 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

Other Work on E lectron A coustics W aves • 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 E lectron A coustic W aves are plasma waves with a slow phase velocity ω ≈ 1.3 k v 1 EAW f ( vz ) TG 0.5 0 -4 -3 -2 -1 0 1 2 3 4 v z / v This wave is nonlinear so as to flatten the particle distribution to avoid strong Landau damping.

Dispersion relation • Infinite homogenous plasma (Dorning et al.) k � f 0 2 � 0 = � ( k , � ) = 1 � � p � v d v k 2 k v � � Landau Landau damping 2 2 d v k � f � � i � � p 0 � 1 � � p � f 0 0 k 2 P � v k 2 k v � � � v � / k Trapping “flattens” the distribution in the resonant region (BGK) 2 d v k � f � 0 � 1 � � p 0 k 2 P � v “Thumb diagram” k v � �

Dispersion Relation Infinite size plasma Trapped NNP (long column finite radial size) (homogenous) Langmuir wave Fixed λ D / r p p p ω ω / / ω ω W A E k ⊥ = 0.25 k z λ D k z λ D 30 TG wave 25 20 f [kHz] Experiment: 15 10 fixed k z W A Fixed k z E 5 vary T and measure f 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 T [eV]

Penning-Malmberg Trap

Density and Temperature Profile 20 1.5 1940 -198 1940 -198 15 n i [10 6 cm -3 ] T [eV] 1 10 0.5 5 0 0 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 x(cm) x(cm) r p ~ 0.5 cm Mg + 0.05eV < T < 5 eV n ≈ 1.5 x 107 cm -3 L p ~ 10cm B = 3T

Measured Wave Dispersion 30 Trivelpiece Gould 25 f [kHz] 20 15 EAW 10 5 0 0 0.5 1 1.5 T [eV] R p / λ D < 2

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 During the drive the plasma response is erratic. Plateau formation 100 cycles 10.7 kHz

Fit Multiple Sin-waves to Wall Signal Electron Acoustic Wave Wall signal [volt +70db] The fit consist of data fit two harmonics and the fundamental sin-wave, resulting in a precise description of the wall signal Time [ms]

Wave-coherent distribution function Record the Time of Arrival of the Photons Wall signal [volt +70db] photons Photons are accumulated in 8 separate phase-bin 35.5 36.0 time [ms]

Distribution Function 0 o versus Wave Phase 45 o 90 o Trivelpiece Gould mode f = 21.5 kHz 135 o f ( v z , z=0) T = 0.77 eV 180 o 225 o The coherent distribution function 270 o shows oscillations δ v of the entire distribution 315 o -6000 -4000 -2000 0 2000 4000 6000 These measurements are done in only one ion velocity [m/s] position (plasma center, z~0)

Distribution Function before wave T=0.3 versus Wave Phase T=0.4 after wave 0 o Electron Acoustic Wave f = 10.7 kHz 45 o T = 0.3 eV 90 o f ( v z , z=0) The coherent distribution function 135 o shows: 180 o - oscillating Δ v plateau at v phase 225 o - δ v 0 wiggle at v=0 270 o Δ v 315 o δ v 0 These measurements are done in only one position (plasma center, z=0) -4000 -2000 0 2000 4000 ion velocity [m/s]

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase Shows wiggle 4000 Velocity [m/s] of the entire distribution -4000 Small amplitude 0 90 180 270 360 Phase [degree] Trivelpiece Gould mode This measurement is done in only one position (plasma center)

Distribution Function versus Phase 18055_18305;23 Δ v Shows: Velocity [m/s] - trapped particle island of half- δ v 0 width Δ v - δ v 0 wiggle at v=0 -2000 0 90 180 270 360 Electron Acoustic Wave Phase [degree] This measurement is done in only one position (plasma center)

Model 18055_18305;23 2000 •Two independent Velocity [m/s] waves •Collisions remove discontinuities -2000 0 90 180 270 360 Phase [degree] Electron Acoustic Wave

Island Width Δ v vs Particle Sloshing δ v 0 � v_island ( v ph @10.7 kHz / v ph ) [m/s] (half-width) � v = ( 2 � v 0 v ph ) 1/2 Trapping in each traveling wave gives Δ v The sum of the two waves 1000 gives sloshing δ v 0 Linear theory gives: 100 1/2 10 100 1000 ( ) � v = 2 � v 0 v phase 0 � v 0 at v=0 [m/s] (half-width)

Frequency Variability 10mV drive 60mV drive 400 400 100 cycles TG 100 cycles TG V wall [ µ V] V wall [ µ V] 200 200 EAW 0 0 10 15 20 25 30 10 15 20 25 30 f response [kHz] f response [kHz] 100mV drive 300mV drive 400 400 100 cycles 100 cycles TG V wall [ µ V] V wall [ µ V] EAW 200 200 0 0 10 15 20 25 30 10 15 20 25 30 f response [kHz] f response [kHz] Large amplitude drives are resonant over a wide range of frequencies

Frequency “jump” 60mV drive 400 100 cycles TG V wall [ µ V] 200 EAW 0 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

f (v) evolves to become resonant with drive! 15 15 Below TG mode, 19kHz drive Resonant with TG mode, 21.8kHz drive before wave before wave f (v) phase averaged f (v) phase averaged 10 10 with wave 5 5 with wave wf3_PhoSum_37717_37916___.txt;3 wf3_PhoSum_37456_37655___.txt;2 0 0 -6000 -3000 0 3000 6000 -6000 -3000 0 3000 6000 relative velocity [ m/s ] relative velocity [ m/s ] Non-resonant drive modifies the particle distribution f (v z ) to make the plasma mode resonant with the drive.

Particle Response Coherent with Wave 8 T = 1.75 eV WF19371-19571 v th = 2646. m/s 6 Fixed frequency drive Coherent response [A.U.] 4 100 cycles at f =18kHz 2 0 -2 -4 -6 v phase v phase -8 -3 -2 -1 0 1 2 3 4 v / v th The coherent response give a precise measure of the phase velocity

When the Frequency Changes k z does not change 6000 T = 1.65 eV T ≈ 1.65 eV 2 r p / � D ~ 2 5000 v phase / v th V phase [m/s] 4000 1.5 3000 L p 1 / π 2000 = k z 0.5 1000 Plasma mode excited over a wide range of 0 0 0 5 10 15 20 25 phase velocity: mode frequency [kHz] 1.4 v th < v phase < 2.1 v th

Range of Mode Frequencies 30 Trivelpiece Gould 25 f [kHz] 20 15 EAW 10 5 0 0 0.5 1 1.5 T [eV] When the particle distribution is modified, plasma modes can be excited over a continuum range, and also past the theoretical thumb.

Chirped Drive before wave T = 1.3 eV The frequency is 80 v � 1 chirped down from 40 21kHz to10 kHz 0 with wave The chirped drive 80 v � 2 produce extreme modification of f(v) 40 0 -8000 -4000 0 4000 8000 Damping rate ion velocity [m/s] γ / ω ~ 1 x 10 -5

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