By edited by H. Usui and Y. Omura.

It is a number of prolonged lecture notes of the tutorials given on the overseas university for area Simulations (ISSS)-7, March 2005, through the invited academics who've been actively taken with laptop simulation strategies in area plasma physics.

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**Additional info for Advanced methods for space simulations**

**Example text**

In our example this is the ion-acoustic wave velocity, the ion-sound speed cia = Te /Mi . Consequently we applied a stretching function Vistr = v max sinh ((vi − vres )Str/v max ) sinh(Str) (36) where Str is the stretching factor, Vistr is the velocity value on the non-uniform grid and vi the velocity value on the original, equally spaced grid, vres = cia and v max is the maximum velocity considered. 1). Figure 3 depicts the electron distribution function at an instant of time on the nonuniformly stretched grid near the resonance velocity space grid surface.

Now one has to solve Eq. g. as derived in Section 3. In order to investigate the stability of a plasma system by a practically noiseless Vlasov-code one has to start the system with appropriate initial conditions. First of all, one needs initial electron and ion distribution functions. To introduce free energy into the system, let us assume that the electrons drift against a background of a resting ion distribution. Also, in order to overcome the lack of a low-level background electric field in a noiseless system, let us modulate the electron distribution in space to trigger a spectrum of waves: f e = (1 + a e (x)) 1 (ve − vde )2 exp − 2 2 π · vte 2vte fi = (39) v2 1 exp − i 2 2 π · vti 2vti √ where vtα = Tα /m α (Tα is the temperature) are the electron and ion thermal velocities, respectively, and vde is the drift speed of the electrons as suggested by Arber and Vann (2002).

Klimas, A. J. and W. M. Farrel, A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Physics, 110, 150–163, 1994. , F. Califano, C. Cavazzoni, and P. Travnicek, A numerical scheme for the integration of the Vlasov–Maxwell system of equations, J. Comput. , 179, 495–538, 2002. , R. M. Thorne, and D. Summers, Ion-acoustic instability driven by drifting electrons in a generalized Lorentzian distribution, J. , 47, 445–464, 1992. , W. J. Heikkila, T. Umeda, K. Ninomiya, and H.