International Topical Meeting on Nuclear Research Applications and Utilization of Accelerators
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AT/RD-05
Charged Particle Collisions for Particle Simulation Methods D. D’Andrea, D. Schneider, and R. Maschek Karlsruhe Institute of Technology, Institute for Nuclear and Energy Technologies, Karlsruhe, Germany Corresponding Author: danilo.dandrea@iket.fzk.de Macroparticle simulation plays a invaluable role in the design and optimization of advanced light sources,electric propulsion systems and modern accelerators. In devices like nuclear fusion systems or highly rarefied plasma flows, collisions between charged particle strongly influence their behaviour, for example in the target part. To describe elastic charged Coulomb collisions it is convenient to start form the Boltzmann collision integral with the classical Rutherford differential cross section. Taylor series expansion up to second order in velocity of the postcollision distribution functions and cutoff value for the impact parameter permits the final integration of the Boltzmann integral to obtain the Fokker–Planck equation. The keys to compute the friction and diffusion coefficients in the Fokker–Planck equation are the Rosenbluth potentials which are complicate integrals of the field particle distribution function and the relative velocity between test and field particles. Since the Rosenbluth potentials are convolution integrals, the use of fast Fourier transform techniques to calculate these quantities and their derivatives rapidly frees from any additional assumptions. Such a determination the Rosenbluth potentials is the basis to model collisional relaxation in a complete selfconsistent manner. In order to fit the 3D Fokker–Planck equation of the scattered distribution function into a particle based framework,the equivalence with the stochastic differential equation (SDE) is exploited. The stochastic variable Cptqis later identified with the charged particle velocity. The friction force vector and a diffusion matrix play the central role. By means of Ito–Taylor expansion and Ito calculus the stochastic differential equation is discretised and numerical schemes are derived. Weak Ito–Taylor schemes together with the Fourier transform method and particlemesh interface techniques represent a remarkable simulation tool to study collisional relaxation processes from first principles. By means of which, a more realistic evaluation of the time scales can be provided since the classical testparticle approach is not necessary anymore. The introduced intraspecies charged particle modelling can be adapted for interspecies electron-ion collisions. Finally, the structure of the developed PICbased method to solve the Fokker–Planck equation also allows to perform coupled simulations.
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