Collisionless and collisional effects on plasma waves from a partition squeeze

Abstract

A simple 1D model is presented for the heating caused by cylindrically-symmetric plasma waves in a non-neutral plasma column due to the addition of a symmetric squeeze potential applied to the center of the column. We study this model by using analytical techniques and by using a numerical grids method solution, and we compare the results of this model to previous work (Ashourvan and Dubin (2014)). squeeze divides the plasma into passing and trapped particles; the latter cannot pass over the squeeze potential. In collisionless theory, enhanced heating is caused by additional bounce harmonics induced by the squeeze in the particle distribution, leading to Landau resonances at energies E n for which the bounce frequency ω b (E) and wave frequency ω m satisfy ω m = nω b (E n ). As a result, heating is substantially higher than the case with no squeeze, even when ω m is much greater than the thermal bounce frequency ω b (T ). Adding collisions to the theory creates a boundary layer at the separatrix between trapped and passing particles that further enhances the heating at small ω m /k m v s , where k m is the axial wavenumber and v s is the velocity at the separatrix. However, at large ω m /v s , the heating from the separatrix boundary layer is only a small correction to the heating from collisionless resonances in the trapped particle distribution function. IntroductionTrivelpiece-Gould (TG) modes are electrostatic normal modes of a cylindrical plasma column [Trivelpiece and Gould (1959)]. In this paper, we study the plasma heating (and associated wave damping) caused by cylindrically-symmetric TrivelpieceGould modes with frequency ω m and axial wave number k m , after applying a cylindrically-symmetric 'squeeze' potential to the plasma equilibrium. Without the squeeze, the heating is caused by Landau damping of the wave energy, due to resonant particles with axial velocity v equal to the wave phase velocity ω m /k m . With the squeeze, the heating is enhanced because new resonances appear in the velocity distribution. The new resonances occur because the squeeze potential changes the particle orbits, creating a non-sinusoidal time-dependence for the wave as seen in the particle frame, which induces new resonances at harmonics of the particle bounce frequency ω b , i.e. where ω m = nω b (E) for integer n (where E is the particle kinetic energy).This effect was studied in a previous paper (Ashourvan and Dubin 2014), where it was shown that the enhanced heating scales as the square of the applied squeeze potential ϕ s for small squeeze, provided that the wave phase velocity is large

Superbanana transport in the collisional heating of a plasma column forced across a squeeze potential

“…For this case, we found that the end potentials satisfy d/ ¼ ÀdLðtÞ@/=@z; see the discussion preceding Eq. (21). Using this in Eqs.…”

“…This has been done previously for a special case, as in Ref. 21. Here, we note that the largest collisional effect is the smoothing of the discontinuity in the energy of the bounce-averaged (adiabatic) distribution function, and so we consider only the bounce averaged portion of this equation, which dominates the plasma response in the regime of interest, ( x ( x b .…”

“…Note that the Taylor expansion of /ðz À dL 1 Þ used to derive Eq. (21) requires that dL 1 be small compared with the minimum scale length of variation of /ðzÞ, which we define as k. (In experiments, 12 k is of order the Debye length.) For a rapidly varying "reflecting wall" potential with k ( L 1 , the condition dL 1 ( k is a stringent requirement on dL 1 .…”