References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt147",{id:"formSmash:upper:j_idt147",widgetVar:"widget_formSmash_upper_j_idt147",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt148_j_idt150",{id:"formSmash:upper:j_idt148:j_idt150",widgetVar:"widget_formSmash_upper_j_idt148_j_idt150",target:"formSmash:upper:j_idt148:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal PlasmasPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH Royal Institute of Technology, 2013. , xi, 65 p.
##### Series

Trita-EES, 2013:014
##### Keyword [en]

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
##### Identifiers

URN: urn:nbn:se:kth:diva-120590ISBN: 978-91-7501-709-9OAI: oai:DiVA.org:kth-120590DiVA: diva2:615851
##### Public defence

2013-05-13, F3, Lindstedtsvägen 26, KTH, Stockholm, 14:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

##### List of papers

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.

QC 20130415

Available from: 2013-04-15 Created: 2013-04-12 Last updated: 2013-10-18Bibliographically approved1. On Solving Singular Diffusion Equations With Monte Carlo Methods$(function(){PrimeFaces.cw("OverlayPanel","overlay380424",{id:"formSmash:j_idt432:0:j_idt436",widgetVar:"overlay380424",target:"formSmash:j_idt432:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. On Monte Carlo operators describing Coulomb collisions in toroidal plasmas$(function(){PrimeFaces.cw("OverlayPanel","overlay497326",{id:"formSmash:j_idt432:1:j_idt436",widgetVar:"overlay497326",target:"formSmash:j_idt432:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. On modelling Coulomb collisions in toroidal plasmas with orbit averaged Monte Carlo operators$(function(){PrimeFaces.cw("OverlayPanel","overlay616034",{id:"formSmash:j_idt432:2:j_idt436",widgetVar:"overlay616034",target:"formSmash:j_idt432:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. A model Monte Carlo collision operator for toroidal plasmas$(function(){PrimeFaces.cw("OverlayPanel","overlay616037",{id:"formSmash:j_idt432:3:j_idt436",widgetVar:"overlay616037",target:"formSmash:j_idt432:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1090",{id:"formSmash:lower:j_idt1090",widgetVar:"widget_formSmash_lower_j_idt1090",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1091_j_idt1093",{id:"formSmash:lower:j_idt1091:j_idt1093",widgetVar:"widget_formSmash_lower_j_idt1091_j_idt1093",target:"formSmash:lower:j_idt1091:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});