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A model Monte Carlo collision operator for toroidal plasmas
National Centre for Physics, Quaid-i-Azam, University, Pakistan.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.ORCID iD: 0000-0002-7142-7103
2013 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 55, no 10, 105002- p.Article in journal (Refereed) Published
Abstract [en]

In order to simulate radio refquency (RF)-heating in toroidal plasmas in the banana regime a model collision operator has been developed, which relaxes the distribution function towards a prescribed local Maxwellian either determined by experiments or transport codes. The pitch angle scattering by Coulomb collisions gives rise to spatial diffusion in toroidal plasmas because of the coupling between spatial and velocity coordinates. The coupling between the spatial and velocity components results in drift terms in the Monte Carlo formulation of the Fokker-Planck equation due to spatial derivatives of the Jacobian, the fraction of the trapped particles, the density and the temperature profiles. A simple RF operator is used to test the collision operator in conjunction with RF heating. The formation of a high-energy tail on the distribution function during RF heating leads to reduction of the density of the thermal ions as the tail builds up. For central heating this reduction can lead to hollow density profiles of thermal ions. The spatial diffusion caused by the relaxation of the thermal ions towards a prescribed density profile then gives rise to an increase of the density of resonant ions in regions with strong heating where the thermal ions diffuse towards higher energies.

Place, publisher, year, edition, pages
2013. Vol. 55, no 10, 105002- p.
Keyword [en]
Diffusion, Tokamaks, Waves, Equations
National Category
Physical Sciences
URN: urn:nbn:se:kth:diva-120607DOI: 10.1088/0741-3335/55/10/105002ISI: 000324625600003ScopusID: 2-s2.0-84885131727OAI: diva2:616037
Swedish Research Council

QC 20131018. Updated from submitted to published.

Correction in: Plasma Physics and Controlled Fusion, vol. 55, issue 11. article nr. 119601, doi: 10.1088/0741-3335/55/11/119601, wos: 000326242200016, ScopusID: 2-s2.0-84886896267

Available from: 2013-04-15 Created: 2013-04-15 Last updated: 2014-09-16Bibliographically approved
In thesis
1. On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal Plasmas
Open this publication in new window or tab >>On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal Plasmas
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis concerns modelling of Coulomb collisions in toroidal plasma with Monte Carlo operators, which is important for many applications such as heating, current drive and collisional transport in fusion plasmas. Collisions relax the distribution functions towards local isotropic ones and transfer power to the background species when they are perturbed e.g. by wave-particle interactions or injected beams. The evolution of the distribution function in phase space, due to the Coulomb scattering on background ions and electrons and the interaction with RF waves, can be obtained by solving a Fokker-Planck equation.The coupling between spatial and velocity coordinates in toroidal plasmas correlates the spatial diffusion with the pitch angle scattering by Coulomb collisions.

In many applications the diffusion coefficients go to zero at the boundaries or in a part of the domain, which makes the SDE singular. To solve such SDEs or equivalent diffusion equations with Monte Carlo methods, we have proposed a new method, the hybrid method, as well as an adaptive method, which selects locally the faster method from the drift and diffusion coefficients. The proposed methods significantly reduce the computational efforts and improves the convergence.

The radial diffusion changes rapidly when crossing the trapped-passing boundary creating a boundary layer. To solve this problem two methods are proposed. The first one is to use a non-standard drift term in the Monte Carlo equation. The second is to symmetrize the flux across the trapped passing boundary. Because of the coupling between the spatial and velocity coordinates drift terms associated with radial gradients in density, temperature and fraction of the trapped particles appear. In addition an extra drift term has been included to relax the density profile to a prescribed one.

A simplified RF-operator in combination with the collision operator has been used to study the relaxation of a heated distribution function. Due to RF-heating the density of thermal ions is reduced by the formation of a high-energy tail in the distribution function. The Coulomb collisions tries to restore the density profile and thus generates an inward diffusion of thermal ions that results in a peaking of the total density profile of resonant ions.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. xi, 65 p.
Trita-EES, 2013:014
Fusion plasma, thermonuclear fusion, tokamak, Coulomb collisions, stochastic differential equations with singular diffusion coefficients, Monte Carlo schemes, spatial diffusion, modelling, Fokker-Planck equation, RF-heating.
National Category
Fusion, Plasma and Space Physics
urn:nbn:se:kth:diva-120590 (URN)978-91-7501-709-9 (ISBN)
Public defence
2013-05-13, F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)

QC 20130415

Available from: 2013-04-15 Created: 2013-04-12 Last updated: 2013-10-18Bibliographically approved

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