The Kinetic Module in CFD-ACE+ solves a 4-dimensional Fokker Planck equation for a Probability Distribution Function in the form

Here c(u) is density of states, D_y and V_y are diffusion and drift coefficients in physical space, D_u and V_u are diffusion and drift coefficients along u-axis, and S is a source term. The variable has different meanings for different problems.

The Kinetic Module has been used in three major options:

• Plasma
  The Plasma option is used to calculate the Electron Energy Probability Function (EEPF) in gas discharge plasma. In this case, u means energy, c(u)=u^1/2, and denotes the EEPF. The transport coefficients of the FP equation are calculated by selecting the Plasma, Chemistry, and Electromagnetic Modules.
• Semiconductor
  This option is used to calculate the EEPF in semiconductor devices. In this case, dependence is determined by the band structure of the material. The Semi Device Module should be activated for this option.
• Constant
  In this option, coefficients of the FP equation are defined by user in the GUI. The variable u can have a different meaning depending on the problem type. This option has been used, for instance, to include molecular level phenomena known to affect the continuum level solution and to desctibe the action of molecular motors and ligand binding in the presence of shear flow.

The figures display the usage of the FP solver for gas discharge plasmas. Current R&D is focused on the development of Direct Numerical Solvers for the Boltzmann equation for multi-disciplinary applications. For more information, please contact us.