uu.seUppsala University Publications

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Numerical Vlasov–Maxwell Modelling of Space PlasmaPrimeFaces.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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2002 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Uppsala: Acta Universitatis Upsaliensis , 2002. , p. 28
##### Series

Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 758
##### Keywords [en]

Vlasov equation, Maxwell equation, Fourier method, outflow boundary, domain decomposition
##### National Category

Computational Mathematics
##### Research subject

Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-2929ISBN: 91-554-5427-5 (print)OAI: oai:DiVA.org:uu-2929DiVA, id: diva2:162159
##### Public defence

2002-11-29, Room 2347, Polacksbacken, Uppsala University, Uppsala, 10:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt446",{id:"formSmash:j_idt446",widgetVar:"widget_formSmash_j_idt446",multiple:true}); Available from: 2002-11-06 Created: 2002-11-06 Last updated: 2011-10-26Bibliographically approved
##### List of papers

The Vlasov equation describes the evolution of the distribution function of particles in phase space (**x**,**v**), where the particles interact with long-range forces, but where shortrange "collisional" forces are neglected. A space plasma consists of low-mass electrically charged particles, and therefore the most important long-range forces acting in the plasma are the Lorentz forces created by electromagnetic fields.

What makes the numerical solution of the Vlasov equation a challenging task is that the fully three-dimensional problem leads to a partial differential equation in the six-dimensional phase space, plus time, making it hard even to store a discretised solution in a computer’s memory. Solutions to the Vlasov equation have also a tendency of becoming oscillatory in velocity space, due to free streaming terms (ballistic particles), in which steep gradients are created and problems of calculating the *v *(velocity) derivative of the function accurately increase with time.

In the present thesis, the numerical treatment is limited to one- and two-dimensional systems, leading to solutions in two- and four-dimensional phase space, respectively, plus time. The numerical method developed is based on the technique of Fourier transforming the Vlasov equation in velocity space and then solving the resulting equation, in which the small-scale information in velocity space is removed through outgoing wave boundary conditions in the Fourier transformed velocity space. The Maxwell equations are rewritten in a form which conserves the divergences of the electric and magnetic fields, by means of the Lorentz potentials. The resulting equations are solved numerically by high order methods, reducing the need for numerical over-sampling of the problem.

The algorithm has been implemented in Fortran 90, and the code for solving the one-dimensional Vlasov equation has been parallelised by the method of domain decomposition, and has been implemented using the Message Passing Interface (MPI) method. The code has been used to investigate linear and non-linear interaction between electromagnetic fields, plasma waves, and particles.

1. Outflow boundary conditions for the Fourier transformed one-dimensional Vlasov–Poisson system$(function(){PrimeFaces.cw("OverlayPanel","overlay69633",{id:"formSmash:j_idt495:0:j_idt499",widgetVar:"overlay69633",target:"formSmash:j_idt495:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation$(function(){PrimeFaces.cw("OverlayPanel","overlay107405",{id:"formSmash:j_idt495:1:j_idt499",widgetVar:"overlay107405",target:"formSmash:j_idt495:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Linear wave dispersion laws in unmagnetized relativistic plasma: Analytical and numerical results$(function(){PrimeFaces.cw("OverlayPanel","overlay68493",{id:"formSmash:j_idt495:2:j_idt499",widgetVar:"overlay68493",target:"formSmash:j_idt495:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. Numerical modelling of the two-dimensional Vlasov–Maxwell system$(function(){PrimeFaces.cw("OverlayPanel","overlay108070",{id:"formSmash:j_idt495:3:j_idt499",widgetVar:"overlay108070",target:"formSmash:j_idt495:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

5. Domain decomposition of the Padé scheme and pseudo-spectral method, used in Vlasov simulations$(function(){PrimeFaces.cw("OverlayPanel","overlay108079",{id:"formSmash:j_idt495:4:j_idt499",widgetVar:"overlay108079",target:"formSmash:j_idt495:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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