kth.sePublications
Change search
Refine search result
1 - 6 of 6
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Rows per page
  • 5
  • 10
  • 20
  • 50
  • 100
  • 250
Sort
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
  • Standard (Relevance)
  • Author A-Ö
  • Author Ö-A
  • Title A-Ö
  • Title Ö-A
  • Publication type A-Ö
  • Publication type Ö-A
  • Issued (Oldest first)
  • Issued (Newest first)
  • Created (Oldest first)
  • Created (Newest first)
  • Last updated (Oldest first)
  • Last updated (Newest first)
  • Disputation date (earliest first)
  • Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
  • 1.
    Mukhtar, Qaisar
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On Monte Carlo Operators for Studying Collisional Relaxation in Toroidal Plasmas2013Doctoral 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.

    Download full text (pdf)
    Qaisar_Thesis
  • 2.
    Mukhtar, Qaisar
    et al.
    National Centre for Physics, Quaid-i-Azam, University, Pakistan.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    A model Monte Carlo collision operator for toroidal plasmas2013In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 55, no 10, p. 105002-Article in journal (Refereed)
    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.

  • 3.
    Mukhtar, Qaisar
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On modelling Coulomb collisions in toroidal plasmas with orbit averaged Monte Carlo operatorsArticle in journal (Other academic)
  • 4.
    Mukhtar, Qaisar
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On modelling Coulomb collisions in toroidal plasmas with relevance for orbit averaged Monte Carlo operators2013In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 55, no 9, p. 095011-Article in journal (Refereed)
    Abstract [en]

    2D Monte Carlo operators describing the Coulomb collisions in pitch angle and radius are studied, which are applicable to axisymmetric toroidal plasmas. The coupling between the spatial and velocity coordinates in toroidal plasmas requires the spatial Jacobian to be included in the collision operator, which is essential to solve the Fokker-Planck equation correctly. The sharp variation of diffusion at the trapped-passing boundary for a tokamak gives rise to differences in the de-trapping probability of the particles into co- and counter-passing orbits, which also produces asymmetry in the distribution function. This problem is solved by using standard and non-standard drift terms, and by symmetrizing the transport across the trapped-passing boundary. Collision operators that relax the distribution function to a prescribed density profile have been developed for simplified models. To obtain converged results, different models are developed and tested that are applicable to diffusion problems with discontinuous diffusion coefficients.

  • 5.
    Mukhtar, Qaisar
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On Monte Carlo operators describing Coulomb collisions in toroidal plasmas2011Conference paper (Other academic)
  • 6.
    Mukhtar, Qaisar
    et al.
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Hellsten, Torbjörn
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    Johnson, Thomas
    KTH, School of Electrical Engineering (EES), Fusion Plasma Physics.
    On Solving Singular Diffusion Equations With Monte Carlo Methods2010In: IEEE Transactions on Plasma Science, ISSN 0093-3813, E-ISSN 1939-9375, Vol. 38, no 9, p. 2185-2189Article in journal (Refereed)
    Abstract [en]

    Diffusion equations in one, two, or three dimensions with inhomogeneous diffusion coefficients are usually solved with finite-difference or finite-element methods. For higher dimensional problems, Monte Carlo solutions to the corresponding stochastic differential equations can be more effective. The inhomogeneities of the diffusion constants restrict the time steps. When the coefficient in front of the highest derivative of the corresponding differential equation goes to zero, the equation is said to be singular. For a 1-D stochastic differential equation, this corresponds to the diffusion coefficient that goes to zero, making the coefficient strongly inhomogeneous, which, however, is a natural condition when the process is limited to a region in phase space. The standard methods to solve stochastic differential equations near the boundaries are to reduce the time step and to use reflection. The strong inhomogeneity at the boundary will strongly limit the time steps. To allow for longer time steps for Monte Carlo codes, higher order methods have been developed with better convergence in phase space. The aim of our investigation is to find operators producing converged results for large time steps for higher dimensional problems. Here, we compare new and standard algorithms with known steady-state solutions.

1 - 6 of 6
CiteExportLink to result list
Permanent link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf