References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt145",{id:"formSmash:upper:j_idt145",widgetVar:"widget_formSmash_upper_j_idt145",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt146_j_idt148",{id:"formSmash:upper:j_idt146:j_idt148",widgetVar:"widget_formSmash_upper_j_idt146_j_idt148",target:"formSmash:upper:j_idt146:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Variance reduction methods for numerical solution of plasma kinetic diffusionPrimeFaces.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}); 2012 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Stockholm: KTH Royal Institute of Technology, 2012. , viii, 42 p.
##### Series

Trita-EE, ISSN 1653-5146 ; 2012:007
##### Keyword [en]

variance reduction, Monte Carlo, quasi-Monte Carlo, kinetic diffusion, stochastic differential equation
##### National Category

Fusion, Plasma and Space Physics
##### Identifiers

URN: urn:nbn:se:kth:diva-91332ISBN: 978-91-7501-278-0OAI: oai:DiVA.org:kth-91332DiVA: diva2:509600
##### Presentation

2012-03-30, Seminarierummet, Teknikringen 31, KTH, Stockholm, 12:24 (English)
##### Opponent

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#####

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##### Note

QC 20120314Available from: 2012-03-14 Created: 2012-03-13 Last updated: 2012-03-14Bibliographically approved
##### List of papers

Performing detailed simulations of plasma kinetic diffusion is a challenging task and currently requires the largest computational facilities in the world. The reason for this is that, the physics in a confined heated plasma occur on a broad range of temporal and spatial scales. It is therefore of interest to improve the computational algorithms together with the development of more powerful computational resources. Kinetic diffusion processes in plasmas are commonly simulated with the Monte Carlo method, where a discrete set of particles are sampled from a distribution function and advanced in a Lagrangian frame according to a set of stochastic differential equations. The Monte Carlo method introduces computational error in the form of statistical random noise produced by a finite number of particles (or markers)* N* and the error scales as α*N*^{−β} where *β* = 1/2 for the standard Monte Carlo method. This requires a large number of simulated particles in order to obtain a sufficiently low numerical noise level. Therefore it is essential to use techniques that reduce the numerical noise. Such methods are commonly called variance reduction methods. In this thesis, we have developed new variance reduction methods with application to plasma kinetic diffusion. The methods are suitable for simulation of RF-heating and transport, but are not limited to these types of problems. We have derived a novel variance reduction method that minimizes the number of required particles from an optimization model. This implicitly reduces the variance when calculating the expected value of the distribution, since for a fixed error the optimization model ensures that a minimal number of particles are needed. Techniques that reduce the noise by improving the order of convergence, have also been considered. Two different methods have been tested on a neutral beam injection scenario. The methods are the scrambled Brownian bridge method and a method here called the sorting and mixing method of L´ecot and Khettabi[1999]. Both methods converge faster than the standard Monte Carlo method for modest number of time steps, but fail to converge correctly for large number of time steps, a range required for detailed plasma kinetic simulations. Different techniques are discussed that have the potential of improving the convergence to this range of time steps.

1. Adaptive delta* f* Monte Carlo Method for Simulation of RF-heating and Transport in Fusion Plasmas$(function(){PrimeFaces.cw("OverlayPanel","overlay370967",{id:"formSmash:j_idt423:0:j_idt427",widgetVar:"overlay370967",target:"formSmash:j_idt423:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. An Adaptive delta* f* Monte Carlo Method$(function(){PrimeFaces.cw("OverlayPanel","overlay380409",{id:"formSmash:j_idt423:1:j_idt427",widgetVar:"overlay380409",target:"formSmash:j_idt423:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Randomized quasi-Monte Carlo simulation of fast-ion thermalization$(function(){PrimeFaces.cw("OverlayPanel","overlay508790",{id:"formSmash:j_idt423:2:j_idt427",widgetVar:"overlay508790",target:"formSmash:j_idt423:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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