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Numerical solution of quasilinear kinetic diffusion equations in toroidal plasmas
KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

One of the main challenges for the realization of a working fusion power plant is an increased detailed understanding of kinetic phenomena in toroidal plasmas. The tokamak is a toroidal, magnetically confined plasma device and is currently the main line towards a power plant. The spatial and temporal scales in a tokamak plasma are extreme and the only tractable path for quantitative studies is to rely on computer simulations. Present day simulation codes can resolve only some of these scales. Nevertheless they still require the largest high performance computing (HPC) resources available in the world. In combination with the increase of computational performance, it is therefore necessary to improve the numerical algorithms used in the simulations.

In this thesis we have developed new numerical methods designed for Monte Carlo simulation of plasma kinetic diffusion. Examples are simulation of fast-ion thermalization and radio-frequency heating. The aim has been to reduce the statistical random noise in particle codes, produced by a finite number of particles (or markers). Traditionally the statistical noise is improved by increasing the number of particles (N) or by simulating the perturbation of the distribution (with particles) from a known distribution function. This is the well known δf method. In this thesis we have developed a new type of δf method, which minimizes the number of particles used in a simulation. The computational speedup of the new method is substantial. In this thesis, we have further benchmarked quasi-Monte Carlo techniques that improve the convergence rate from N−1/2 to N−1 for some cases.

In Monte Carlo simulations, error appears also from the time step discretization. Based on the mathematics of operator splitting, a new scheme for the pitch-angle scattering diffusion process has been developed that outperforms the standard methods. Finally this thesis also presents a new code, SELFO-light, for self-consistent simulations of ion cyclotron resonance heating, suitable for routine calculations, which couples a one dimensional Fokker-Planck model with the finite element wave solver LION.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. , xiii, 54 p.
Series
Trita-EE, ISSN 1653-5146 ; 2013:012
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:kth:diva-120345ISBN: 978-91-7501-697-9 (print)OAI: oai:DiVA.org:kth-120345DiVA: diva2:614400
Public defence
2013-04-26, F3, Lindstedtsvägen 26, KTH, Stockholm, 13:15 (English)
Opponent
Supervisors
Note

QC 20130405

Available from: 2013-04-05 Created: 2013-04-04 Last updated: 2013-04-05Bibliographically approved
List of papers
1. An Adaptive delta f Monte Carlo Method
Open this publication in new window or tab >>An Adaptive delta f Monte Carlo Method
2010 (English)In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 38, no 9, 2190-2197 p.Article in journal (Refereed) Published
Abstract [en]

A new adaptive delta f Monte Carlo method is presented with an application to radio frequency heating and transport in fusion plasmas. The method is suitable when an initial zeroth-order approximation of the distribution function is known. The difference between our method and earlier delta f methods is that we model the source term, obtained from the delta f ansatz, by adding particles. The rate of particles is defined by the inhomogeneous term in the Fokker-Planck equation. We develop an adaptive scheme for modifying the unperturbed part G(x) such that the number of particles used in the simulation for a fixed weight is minimized. This implicitly reduces the variance and improves computational efficiency. The method is tested on a one-dimensional Fokker-Planck model for RF-heating and compared against the analytical stationary solution.

Keyword
Control-variate, Monte Carlo (MC), variance reduction, delta f method
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-27685 (URN)10.1109/TPS.2010.2051686 (DOI)000283252500015 ()2-s2.0-77956619121 (Scopus ID)
Note
QC 20101221Available from: 2010-12-21 Created: 2010-12-20 Last updated: 2017-12-11Bibliographically approved
2. Randomized quasi-Monte Carlo simulation of fast-ion thermalization
Open this publication in new window or tab >>Randomized quasi-Monte Carlo simulation of fast-ion thermalization
2012 (English)In: Computational Science & Discovery, ISSN 1749-4680, E-ISSN 1749-4699, Vol. 5, no 1, 014010- p.Article in journal (Refereed) Published
Abstract [en]

This work investigates the applicability of the randomized quasi-Monte Carlo method for simulation of fast-ion thermalization processes in fusion plasmas, e.g. for simulation of neutral beam injection and radio frequency heating. In contrast to the standard Monte Carlo method, the quasi-Monte Carlo method uses deterministic numbers instead of pseudo-random numbers and has a statistical weak convergence close to O(N -1), where N is the number of markers. We have compared different quasi-Monte Carlo methods for a neutral beam injection scenario, which is solved by many realizations of the associated stochastic differential equation, discretized with the Euler-Maruyama scheme. The statistical convergence of the methods is measured for time steps up to 2 14.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2012
Keyword
Monte Carlo, quasi-Monte Carlo, low discrepancy sequence, variance reduction
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-91197 (URN)10.1088/1749-4699/5/1/014010 (DOI)2-s2.0-84866342521 (Scopus ID)
Note

QC 20121114. Updated from submitted to published.

Available from: 2012-03-13 Created: 2012-03-09 Last updated: 2017-12-07Bibliographically approved
3. Composition schemes forthe stochastic differential equation describing collisional pitch-angle diffusion
Open this publication in new window or tab >>Composition schemes forthe stochastic differential equation describing collisional pitch-angle diffusion
(English)Article in journal (Other academic) Submitted
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-120380 (URN)
Note

QS 2013

Available from: 2013-04-05 Created: 2013-04-05 Last updated: 2013-04-05Bibliographically approved
4. Multilevel Monte Carlo and control-variate simulation of Coulomb collisions
Open this publication in new window or tab >>Multilevel Monte Carlo and control-variate simulation of Coulomb collisions
(English)Manuscript (preprint) (Other academic)
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:kth:diva-120381 (URN)
Note

QS 2013

Available from: 2013-04-05 Created: 2013-04-05 Last updated: 2014-01-28Bibliographically approved
5. On Self-Consistent ICRH Modelling
Open this publication in new window or tab >>On Self-Consistent ICRH Modelling
Show others...
(English)Article in journal (Other academic) Submitted
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-119996 (URN)
Note

QS 2013

Available from: 2013-03-26 Created: 2013-03-26 Last updated: 2013-04-05Bibliographically approved

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