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supported by NSF grant PHY-0354979

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.

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supported by NSF grant PHY-0354979

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  1. Electron Acoustic Wavesin Pure Ion PlasmasF. AndereggC.F. Driscoll, D.H.E. Dubin, T.M. O’NeilUniversity of California San Diego supported by NSF grant PHY-0354979

  2. We observe “Electron” Acoustic Waves (EAW) in magnesium ion plasmas. Measure wave dispersion relation. 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.

  3. 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

  4. 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

  5. w ≈ 1.3 kv 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.

  6. Landau damping Trapping “flattens” the distribution in the resonant region (BGK) “Thumb diagram” Dispersion relation • Infinite homogenous plasma (Dorning et al.)

  7. Trapped NNP (long column finite radial size) Infinite size plasma (homogenous) Fixed lD / rp Langmuir wave w / wp w / wp EAW k = 0.25 kzlD kzlD TG wave Experiment: fixed kz vary T and measure f EAW Fixed kz Dispersion Relation

  8. Penning-Malmberg Trap

  9. Density and Temperature Profile rp ~ 0.5 cm 0.05eV < T < 5 eV Mg+ B = 3T n ≈ 1.5 x 107 cm-3 Lp ~ 10cm

  10. Measured Wave Dispersion Trivelpiece Gould EAW Rp/lD < 2

  11. Received Wall Signal Trivelpiece Gould mode The plasma response grows smoothly during the drive 10 cycles 21.5 kHz

  12. Received Wall Signal Electron Acoustic Wave During the drive the plasma response is erratic. Plateau formation 100 cycles 10.7 kHz

  13. 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 data fit Wall signal [volt +70db] Time [ms]

  14. 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]

  15. Distribution Function versus Wave Phase Trivelpiece Gould mode f = 21.5 kHzT = 0.77 eV f(vz, z=0) The coherent distribution function shows oscillations dv of the entire distribution These measurements are done in only one position (plasma center, z~0)

  16. T=0.3 Distribution Function versus Wave Phase T=0.4 Electron Acoustic Wave f = 10.7 kHz T = 0.3 eV f(vz, z=0) The coherent distribution function shows: - oscillating Dv plateau at vphase - dv0 wiggle at v=0 Dv These measurements are done in only one position (plasma center, z=0) dv0

  17. Distribution Function versus Phase

  18. Distribution Function versus Phase

  19. Distribution Function versus Phase

  20. 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)

  21. Distribution Function versus Phase 18055_18305;23 Dv • Shows: • trapped particle island of half- width v • dv0 wiggle at v=0 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)

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

  23. 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

  24. 100 cycles TG 100 cycles TG EAW 100 cycles 100 cycles TG EAW Frequency Variability Large amplitude drives are resonant over a wide range of frequencies

  25. 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

  26. 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.

  27. Particle Response Coherent with Wave Fixed frequency drive 100 cycles at f =18kHz The coherent response give a precise measure of the phase velocity

  28. Plasma mode excited over a wide range of phase velocity: 1.4 vth < vphase< 2.1 vth When the Frequency Changes kz does not change T ≈ 1.65 eV kz = p / Lp

  29. 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.

  30. 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

  31. 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

  32. 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)

  33. Typical Parameters rp ~ 0.5 cm 0.05eV < T < 5 eV Mg+ B = 3T n ≈ 1.5 x 107 cm-3 Lp ~ 10cm Standing wave phase velocity

  34. Stability f (v) Penrose criteria predicts instability if satisfied k < 96 m-1 and k satisfies Our = 230 m-1 is larger than the maximum => This plasma is stable allowed by Penrose criteria

  35. Chirped Drive Received signal [ Volt +70db ] Time [ms] The frequency is chirped down from 21kHz to10 kHz

  36. 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)

  37. Particles Coherent Response Electron Acoustic Wave vph vph The coherent response changes sign at: v = 0 at the wave phase velocity

  38. Distribution Function versus Phase Dv • Shows: • trapped particle island of half- width v • dv0 wiggle at v=0 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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