Electron Acoustic Waves in Pure Ion Plasmas F. Anderegg C. F 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. 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 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 w ≈ 1.3 k 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.) Trapping “flattens” the distribution in the resonant region (BGK) Landau damping “Thumb diagram”

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

Penning-Malmberg Trap

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

Measured Wave Dispersion Trivelpiece Gould EAW Rp/lD < 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 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]

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 time [ms] 36.0

Distribution Function versus Wave Phase Trivelpiece Gould mode f = 21.5 kHz T = 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)

Distribution Function versus Wave Phase 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 dv0 These measurements are done in only one position (plasma center, z=0)

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase

Distribution Function versus Phase Shows wiggle of the entire distribution 4000 Velocity [m/s] -4000 Small amplitude 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 Dv Shows: trapped particle island of half- width v dv0 wiggle at v=0 Velocity [m/s] dv0 -2000 90 180 270 360 Phase [degree] Electron Acoustic Wave This measurement is done in only one position (plasma center)

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

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:

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

Frequency “jump” f response f drive 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

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.

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

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

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.

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

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 Shows wiggle of the entire distribution Velocity 90 180 270 360 Large amplitude Phase [degree] Trivelpiece Gould mode This measurement is done in only one position (plasma center)

Typical Parameters n ≈ 1.5 x 107 cm-3 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

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

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

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)

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

Distribution Function versus Phase Dv Shows: trapped particle island of half- width v dv0 wiggle at v=0 Velocity [m/s] dv0 -2000 90 180 270 360 Phase [degree] Electron Acoustic Wave This measurement is done in only one position (plasma center)