Kinetic Trajectory Simulation Model for Magnetized Plasma Sheath

Abstract

Plasma wall interaction is an important phenomenon in all applications, where plasma comes into contact with a material wall. The understanding of plasma sheath, a thin layer that is formed between the core plasma and the wall, is crucial in understanding as well as controlling the particle and energy fluxes reaching the surface. Because of sharp gradients in the sheath region the fluid approach, which is usually used to explain the core plasma and presheath region, does not yield accurate results in the sheath region. In order to understand the characteristics of the sheath formed in a magnetized plasma the method of kinetic trajectory simulation (KTS) has been used and also the coupling of presheath-sheath has been extended. Assuming that, at the sheath entrance distribution functions of ion and electron to be cut-off Maxwellian the final self consistent states are obtained by solving the governing kinetic equations, iteratively. In order to satisfy the Bohm-Chodura condition, initial velocity of ions entering the sheath region is taken equal to the ion acoustic velocity. As the plasma sheath region is small compared to the collision mean free path and also the particle densities are less compared to the presheath region, the sheath region is assumed to be collisionsless. It has been observed that the presheath electron temperature affects the Child-sheath thickness and the space charge density reaching the wall. Furthermore, improved distribution of electrons, i.e., consideration of cut-off by the negative wall yields our simulation result to deviate from earlier works without cut-off by about 3%. The coupling scheme, developed, provides a basis for smooth transition of plasma parameters in presheath-sheath interface. Ion velocity at presheathsheath boundary is also affected by obliqueness of the field. Velocity of ion increases towards the wall as the obliqueness of the field increases. In the presence of oblique magnetic field in the plasma sheath, the damping of ion velocity with time has been observed. It is shown that the velocity waves are damped in plasma without collisions in the time scale of the order of seconds. As the obliqueness of the field changes the separation of the mean values as well as the maximum amplitude of all the three components of the velocity also change. Mean value of Gcomponent of velocity is nearly equal to zero for all angles at magnetic field 2.5 mT, but the mean value of H and Icomponents of velocity varies with nearly equal amplitudes. When the field is greater than zero, the mean value of Gcomponent is almost equal to zero, but the mean values of H and Icomponents of velocities are both nearly equal to 10 m/s at zero field. But for the greater value of magnetic field, the two components of velocities are split with different mean values. The frequency of oscillations of three component of velocity of ions changes as the magnetic field changes. The maximum amplitude of Gcomponent of velocity is almost independent of the magnetic field but the maximum amplitudes of H and Icomponents of velocity change and show oscillating nature as the magnetic field changes also. As the obliqueness of the field changes the mean values, beat frequency as well as the maximum amplitude of the three components of the velocity also change but frequency of oscillation almost remains same at magnetic field 2 mT. Modulation frequency of ions in a magnetized plasma sheath has been observed for different angles at constant magnetic field 6 mT. Also, by varying angle average values, maximum amplitude, damping factor as well as frequency of oscillation of the velocities are studied. For H and Icomponents of velocity maximum amplitudes change but for Gcomponent the maximum amplitude remains constant. However, there is a quite change observed in the values of damping factor and modulation frequency for all component of velocity. Frequency of oscillation of all velocity components of ions remains same. At 30 and 60

, shoulder is not seen but at 75 , shoulder in the velocity profile is obtained around 0.05 second for each component of velocity. The amplitude of the oscillating velocity decreases with time and the mean values of different component of velocity changes as well. The computed and fitted values of the vector sum of oscillatory part of all three components of velocities match. At angle 30

, damping rate of vector sum of oscillatory part of total velocity increases with the magnetic field increases from 1 mT to 5 mT. On the other hand vector sum of oscillating part of initial velocity is almost equal for magnetic field 1 mT, 3 mT and 5 mT at the same angle 30

. But for different obliqueness of the magnetic field, the initial velocity of the vector sum of oscillating part at 90

is greater than that at 30

and 60 . The input physical parameters taken are consistent with earlier previous works and

comparison reveal that our results agree well. The present magnetized plasma wall transition study provides a basis for proper understanding of the plasma sheath, which has useful applications in fusion devices as well as in many industrial applications of plasma.