Measurement of Landau damping of electron plasma waves in the linear and trapping regimes

Experiments are presented on collisionless damping of standing plasma waves in pure-electron plasma columns. Specifically, the first quantitative measurements of “linear Landau damping” and “nonlinear wave-particle trapping oscillations” of m_&thetas; = 0 Trivelpiece-Gould (T-G) modes in a pure electron plasma are discussed in detail.; Linearly excited T-G standing waves are observed and the dispersion for long wavelength modes is measured. Prior experiments on T-G modes commonly showed exponential damping independent of amplitude, but no agreement with linear damping theory. In the present experiments, we characterize the damping from ultra-low amplitude thermal excitations to large amplitudes where particle trapping dominates.; At low wave amplitudes (δn/n ₀ < 10−3), the measured linear damping rate (10−3 < γ_L/ω < 10 −1) agrees quantitatively with Landau damping theory for moderate plasma temperatures (1 < T_e < 3 eV, 3 < v_&phis;/v¯ < 5). This damping is shown to be due to resonant particles; a dramatic decrease in the damping rate is observed when the resonant particles are eliminated by truncating the nominally Maxwellian velocity distribution. Surprisingly, no correspondence is found with the somewhat more subtle theory predictions of “bounce resonant damping,” nor with damping due to “dephasing” in the plasma end sheaths.; At larger wave amplitudes (10−3 < δ n/n₀ < 10−2), the excited T-G wave initially damps at the Landau rate, but the wave-resonant particles become trapped in the wave potential, sloshing with frequency $wT\equiv eEzkz/m$, as first analyzed by O'Neil in 1965. This causes the wave amplitude to re-grow and oscillate in amplitude, approaching a BGK state. The measured times characterizing the first bounce oscillation are found to agree quantitatively (to about 20%) with predictions based on a self-consistent numerical calculation. Small discrepancies between the theory and the measured amplitude oscillation times are shown to be due to additional damping processes which are not dependent on the resonant particles.; At late times, a weak exponential damping of the wave is observed. Measurement of the average (nonlinear) decay rate for large amplitude waves is shown to be consistent with the collisional repopulation of the distribution function as described by Zakharov and Karpman in 1963. Measurements of the early-time wave amplitude peaks and valleys are consistent with the naively predicted plateau amplitude for a BGK state. Small discrepancies between the measured effective plateau amplitude and the expected BGK equilibrium amplitude is likely the result of extra damping from either resistive damping in the detection electronics or collisional repopulation, or both.