Monte Carlo approach vs Fluid model.


We are often asked by potential customers, where the electron Monte Carlo approach implemented in HPEM and accessible via QVT gives an advantage in modelling plasma? Why not just use a fluid model alone?

 Fluid ModelMonte Carlo
Electron TemperatureCalculated by the electron energy balance equation implying Maxwellian EEDFsObtained from the spatially resolved EEDFs. Accounts for non-Maxwellian EEDFs
Electron Impact RatesRates are calculated from EEDFs obtained from a global Boltzmann - Solver. Local rates are assigned according to the local electron temperature. This does somewhat account for non-Maxwellian EEDFs, however, the influence of, for example, high energy electrons in the bulk created by sheath interactions are not covered.Rates are calculated from the spatially resolved EEDFs. This does take non-local effects such as high energy electrons created in the sheath region penetrating into the plasma bulk into account.
Transport Parameters
The diffusion coefficient and mobility are calculated using the local electron temperature and corresponding collision frequency from global EEDFThe diffusion coefficient and mobility are calculated using the electron temperature and collision frequency obtained from the spatially resolved EEDFs
ConclusionThe fluid model has only limited abilities to take non-local effects and non-Maxwellian effects into account. An example is high energy electrons created in the sheath region travelling into the bulk as they are observed in low pressure CCPs.All parameters used in the fluid model are directly derived from the actual, spatially derived EEDFs taking non-local effects and non-Maxwellian EEDFs fully into account.