By edited by H. Usui and Y. Omura.

This can be a number of prolonged lecture notes of the tutorials given on the foreign tuition for house Simulations (ISSS)-7, March 2005, by way of the invited academics who've been actively considering computing device simulation thoughts in house plasma physics.

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9, 75–98, 1972. , Numerical modelling the Fourier transformed two-dimensional Vlasov-Maxwell system, J. Comput. , 190, 501–522, 2003. Elkina, N. and J. B¨uchner, A new conservative unsplit method for the solution of the Vlasov equation, J. Comput. , 213(2), 862–875, 2006. , Numerical solution of the Vlasov-equation: the 1D code, Comput. Phys. , 116, 329– 335, 1999. 46 J. , E. Sonnendr¨ucker, and N. Bertrand, Conservative numerical schemes for the Vlasov equation, J. Comput. , 172, 166–187, 2001.

4 Conservation Relations and Statistical Properties The δ f -PIC simulation model has several important conserved quantities which can be used to monitor the accuracy of the calculations. A fluctuation-dissipation theory for thermal equilibrium can be developed to obtain the electrostatic energy partition per mode with discrete marker particles as the source of excitations (Hu and Krommes, 1994). An inherent feature of the δ f -PIC model is the diffusion of the particle weights in phase space which can lead to a buildup of noise in the moments over time.

For both charge density and force interpolations, the second order quadratic method is used (Birdsall and Langdon, 1985). 4 Conservation Relations and Statistical Properties The δ f -PIC simulation model has several important conserved quantities which can be used to monitor the accuracy of the calculations. A fluctuation-dissipation theory for thermal equilibrium can be developed to obtain the electrostatic energy partition per mode with discrete marker particles as the source of excitations (Hu and Krommes, 1994).