Hallatschek, K.

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MPG.PuRe

High accuracy Landau collision operator and transport coefficients forgyrokinetic and fluid turbulence simulationsK. HallatschekMax-Planck-Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, GermanyA code for the gyro-transformed (pulled-back) matrix elements of the linearized but other-wise complete Landau operator required by gyrokinetic (GK) [1] edge turbulence simulationswas developed, inspired by the advantageous use of half-sided Hermite (or related) polynomialsPi as velocity space basis functions in [1, 2].This approach turned out to be amazingly successful. It takes only seconds to calculate theLandau matrix elements for hundreds of polynomials for all normally required perpendicularwavenumbers of a turbulence simulation up to machine precision, automatically fulfilling allapplicable conservation laws and the H-theorem. In the case that extremely high wavenumbersare to be computed kρi & 100 (e.g. for ETG turbulence) nevertheless a cut-off was required. Forthese a novel fast asymptotic approximation procedure is presented.With the code it is also possible to calculate Braginskii-style transport coefficients, muchmore precise than so far published [3, 4] and study alternative definitions of fluid transportcoefficients – those are usually based on the particular ordering scheme used, and cannot providemore than the first order in the expansion parameters. 0 0.2 0.4 0.6 0.8 1 1.2 1x10-10  1x10-9  1x10-8  1x10-7  1x10-6  1x10-5  0.0001  0.001  0.01me/miαeiThis way, certain analyti-cally overlooked, transport co-efficients can be computed,such as the mass-ratio depen-dent ion electron cross heatflux qi,e =αeinTiτii/mi∂‖Te, thecoefficient of which (αei) isshown on the side.Clearly these effects are sig-nificant and should be taken into account in any fluid turbulence simulation of realistic colli-sional Deuterium plasmas, not the least to arrive at a meaningful comparison between fluid andkinetic simulations.[1] J. Candy, E.A. Belli, R.V. Bravenec, J. Comput. Phys. 324, 73 (2016)[2] M. Landreman, D.R. Ernst, J. Comput. Phys. 243, 130 (2013)[3] P.J. Catto, A. N. Simakov, Phys. Plasmas 11, 90 (2004)[4] A.S. Richardson, NRL plasma formulary, (2019)48th EPS Conference on Plasma Physics P5a.121

High accuracy Landau collision operator and transport coefficients for gyrokinetic and fluid turbulence simulations

http://hdl.handle.net/21.11116/0000-000B-F464-1

High accuracy Landau collision operator and transport coefficients for gyrokinetic and fluid turbulence simulations

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