Ion Acoustic Wave Excitation and Ion Sheath Evolution

Abstract

A series of computer simulations and experiments has been performed to investigate the time evolution of an ion space-charge sheath from a solid electrode in a plasma. A large negative step potential (eΔV ≫ kTe) is applied to the boundary of a uniform plasma and the response computed. A fluid model is used for cold ions, and hot electrons in thermal equilibrium are assumed as a neutralizing background. Both the computer simulations and the experiments show the formation of an ion space-charge sheath in a few ion plasma periods and a rarefying disturbance propagating into the plasma with the ion acoustic speed. For a plane electrode this disturbance extends to the electrode, resembling a rarefaction wave as found in ordinary fluid dynamics. For cylindrical and spherical electrodes this disturbance breaks away from the sheath and propagates as an ion acoustic wave into the plasma. The addition of substantial ion-neutral collisions is found to prevent separation of the wave from the sheath. The results of the computer simulations and the experiments agree.

Propagation of Solitary Waves in Warm Magnetized Plasma with Two Temperature Electrons

“…(12), integrating with respect to ξ and using boundary condition v z = 0 at n c =1as  and using charge neutrality condition, n i = n e we get (25) Simplification of equation (16) gives rise to an equation of the form (26) Multiplying both sides of equation (26) by the terms inside the parenthesis and after some rather lengthy but straightforward algebra we obtain an equation of the form (27) The boundary condition used in deriving equation (27) is , n c = 1 at Equation (27) can be interpreted as an energy integral of an oscillatory particle of an unit mass with velocity and position n c in a potential well K(n c ). That is the above equation can be considered as a motion of a particle whose pseudoposition is n c at pseudotime ξ with pseudovelocity in a pseudopotential well K(n c ).…”

“…Numerous reports in regard to ion acoustic (ionic sound) waves in plasmas can be found as path finder [24][25][26][27][28][29][30][31]. Quite a number of authors have studied ion acoustic waves/solitons in plasmas consisting of two species of hot and cold electron populations.…”

Modeling of dynamic bipolar plasma sheaths

“…An alternate form of Eq. (14) can be derived by noting that the last two terms form an exact time differential giving the following more compact expression…”

“…If DPb /t in Eq. (14) were set to zero, or if the rate of change of the total sheath electron charge in Eq. (15) were ignored, ks would be incorrectly predicted to be zero.…”

“…(36), the effect of ion inertia, and the importance of including the electron charge density terms in Eq. (14) to model sheath growth.…”