TY - JOUR

T1 - The integration of the vlasov equation in configuration space

AU - Cheng, C. Z.

AU - Knorr, Georg

N1 - Funding Information:
* This work was supported in part by ERDA (formerly AEC), Grant AT(1 l-1)-2059. + This work was submitted in partial fulfillment of the requirements for a Ph.D. degree, Department of Physics and Astronomy, University of Iowa, Iowa City. *Present address: Princeton Plasma Physics Laboratory, Princeton University, Princeton, N.J. 08540.

PY - 1976/11

Y1 - 1976/11

N2 - A convenient, fast, and accurate method of solving the one-dimensional Vlasov equation numerically in configuration space is described. It treats the convective terms in the x and v directions separately and produces a scheme of second order in Δt. The resulting free-streaming and accelerating equations are computed with Fourier interpolation and spline interpolation methods respectively. The numerical method is tested witth linear and nonlinear problems. The method is very accurate and efficient. A new method of smoothing the distribution function is given. It reduces the computational effort by artificially increasing the entropy of the system. As a result, the distribution function is smooth enough to be well represented on a given mesh. The methods can be generalized in a straightforward way to deal with more complicated cases such as problems with nonperiodic spatial boundary conditions, two- and three-dimensional problems with and without external magnetic and/or electric fields.

AB - A convenient, fast, and accurate method of solving the one-dimensional Vlasov equation numerically in configuration space is described. It treats the convective terms in the x and v directions separately and produces a scheme of second order in Δt. The resulting free-streaming and accelerating equations are computed with Fourier interpolation and spline interpolation methods respectively. The numerical method is tested witth linear and nonlinear problems. The method is very accurate and efficient. A new method of smoothing the distribution function is given. It reduces the computational effort by artificially increasing the entropy of the system. As a result, the distribution function is smooth enough to be well represented on a given mesh. The methods can be generalized in a straightforward way to deal with more complicated cases such as problems with nonperiodic spatial boundary conditions, two- and three-dimensional problems with and without external magnetic and/or electric fields.

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U2 - 10.1016/0021-9991(76)90053-X

DO - 10.1016/0021-9991(76)90053-X

M3 - Article

AN - SCOPUS:0001370361

VL - 22

SP - 330

EP - 351

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 3

ER -