A new unconditionally stable algorithm for steady state fluid simulation of high density plasma discharge is suggested. The physical origin of restriction on simulation time step is discussed and a new method to overcome it is explained. To compare the new method with previous other methods, a one dimensional fluid simulation of inductively coupled plasma (ICP) discharge is performed.
The validity of the frequently used drift-diffusion representation of the momentum equation in fluid simulations of high density plasma discharges is investigated. The drift-diffusion expressions are good approximations for both the electron and ion at high pressure. However, for low pressure, the inertial term cannot be neglected in the ion momentum equation, although the drift-diffusion representation of electrons is still valid. The available criterion for the valid pressure regime is $v_B$/($\nu_{i/e,N}L$)≪1; where $v_B$ is the Bohm velocity, $v_{i/e,N}$ is the ion/electron-neutral collision freuquency and L is the dimension of the system. In addition, a new method to treat the inertial terms by introducing an effective ambipolar electric field, $E^{eff}$, is proposed, and the results are compared to the full ion momentum equation case.
