Finite Element Method for Charged-Particle Calculations

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Abstract
A new method for solving the Boltzmann-Fokker-Planck equation is presented. Following the finite element technique, the solution is projected onto a space defined by linear discontinuous basis functions. Three approaches for the angular flux are derived and compared: the first two for a coupled energy-position discretization and the third one for the coupled energy-position-angle discretization. The last was specifically developed for highly anisotropic problems, such as ion beams impinging on an inertial confinement fusion target. Numerical results show clearly that the finite element approaches are higher order approximations. The convergence rate, stability, and performance compared with other methods are examined.