Numerical integration methods of the Vlasov equation

Abstract

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Plasma simulation as eigenvalue problem

“…The mathematical origin of the difficulty is the simulation of a continuous eigenvalue problem [2] with .. a finite computer. Any kind of truncation due to the finiteness of the computer changes the problem into an eigenvalue problem with a set of finite discrete eigenvalues which are purely imaginary [3 ].…”

Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition

“…The truncation ranks are also noted in Fig. 17 for the k x , k y , z, v || , µ, t coordinates, respectively (for reference, the full rank values are (64, 16,16,32,8,240)). Nearly all of the truncation is in the velocity space coordinates.…”

“…The inverse compression ratio is, δ (r kx r ky rzrv || rµrt) HOSV D = r kx n kx + r ky n ky + r z n z + r v || n v || + r µ n µ + r t n t + r kx r ky r z r v || r µ r t n kx n ky n z n v || n µ n t , Figure 17: Plot of the truncation error versus inverse compression ratio for a series of truncated HOSVDs. The truncation ranks are noted for the (k x , k y , z, v || , µ, t) coordinates respectively (out of a total of (64, 16,16,32,8,240)). …”

Numerical integration of the Vlasov equation

“…The use of transform methods for the numerical solution of the nonlinear Vlasov equation has been discussed and reviewed in several publications [1,2]. One has to deal with the one-dimensional Vlasov equation…”

“…(1) and (2) are the inverse plasma frequency 0 1 = (4·rr n e2/m)-1/2, the thermal velocity vT = (KT/m)1/2, and the Debye length Ap = (KT/4·rr n e2)1/2.…”