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Modelling of spin and other quantum effects in plasmas
Umeå University, Faculty of Science and Technology, Department of Physics.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The development of quantum mechanics during the 20th century gave rise to a completely new way of describing physics. The interpretation of quantum theory is inherently difficult: for example, many-body systems are described by a so called density matrix which has no straightforward analogue in classical theory. However, in the 30’s Wigner proposed an alternative way of describing many-body systems, using a quasi-probability distribution function. This made the connection between classical and quantum kinetic theory clearer.

This thesis is concerned with modelling of quantum effects in plasmas. The focus lies on describing plasmas containing spin-1/2 particles. For this purpose, new models, based on quantum kinetic theory, are derived. This is achieved by starting from the evolution equation for the density matrix and applying a combination of the Wigner transformation for the position degree of freedom and the Q-transformation for the spin. The properties of the resulting kinetic theory are then investigated and it is shown to satisfy basic necessary criteria such as energy conservation. The kinetic equation is then used to derive a fluid theory for spin-1/2 particles.

In this thesis the kinetic and fluid models are applied to different problems in quantum plasma physics. For example it will be shown that the quantum electrodynamic correction to the electron g-factor can give rise to a wave mode which lacks classical analogue, and that spin may affect the damping rate of Alfvén waves. The models will also be applied to nonlinear problems and it will be shown that they give rise to modifications of the so called spin ponderomotive force.

Place, publisher, year, edition, pages
Umeå: Umeå Universitet , 2012. , 33 p.
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:umu:diva-53320ISBN: 978-91-7459-385-3 (print)OAI: oai:DiVA.org:umu-53320DiVA: diva2:511354
Public defence
2012-04-13, Naturvetarhuset, N430, Umeå Universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2012-03-23 Created: 2012-03-20 Last updated: 2012-03-22Bibliographically approved
List of papers
1. Effects of the g factor in semiclassical kinetic plasma theory
Open this publication in new window or tab >>Effects of the g factor in semiclassical kinetic plasma theory
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2008 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 101, no 24, 245002-245006 p.Article in journal (Refereed) Published
Abstract [en]

A kinetic theory for spin plasmas is put forward, generalizing those of previous authors. In the model, the ordinary phase space is extended to include the spin degrees of freedom. Together with Maxwell's equations, the system is shown to be energy conserving. Analyzing the linear properties, it is found that new types of wave-particle resonances are possible that depend directly on the anomalous magnetic moment of the electron. As a result, new wave modes, not present in the absence of spin, appear. The implications of our results are discussed.

Place, publisher, year, edition, pages
American Physical Society, 2008
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-18708 (URN)10.1103/PhysRevLett.101.245002 (DOI)
Available from: 2009-02-24 Created: 2009-02-24 Last updated: 2012-03-22Bibliographically approved
2. Scalar quantum kinetic theory for spin-1/2 particles: mean field theory
Open this publication in new window or tab >>Scalar quantum kinetic theory for spin-1/2 particles: mean field theory
2010 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 12, 043019- p.Article in journal (Refereed) Published
Abstract [en]

Starting from the Pauli Hamiltonian operator, we derive scalar quantum kinetic equations for spin-1/2 systems. Here, the regular Wigner two-state matrix is replaced by a scalar distribution function in extended phase space. Apart from being a formulation of significant interest, such a scalar quantum kinetic equation makes the comparison with classical kinetic theory straightforward and lends itself naturally to currently available numerical Vlasov and Boltzmann schemes. Moreover, while the quasi-distribution is a Wigner function in regular phase space, it is given by a Q-function in spin space. As such, nonlinear and dynamical quantum plasma problems are readily handled. Moreover, the issue of gauge invariance is treated.

Place, publisher, year, edition, pages
IOP Publishing, 2010
Keyword
Plasma kinetic equations
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-33895 (URN)10.1088/1367-2630/12/4/043019 (DOI)000276741700005 ()
Available from: 2010-05-10 Created: 2010-05-10 Last updated: 2017-12-12Bibliographically approved
3. Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory
Open this publication in new window or tab >>Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory
2010 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 12, 073027-073039 p.Article in journal (Refereed) Published
Abstract [en]

The gauge invariant electromagnetic Wigner equation is taken as the basis of a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge-dependent Wigner function is shown to produce inconsistencies if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and it is shown to be in agreement with the kinetic theory in the long-wavelength approximation, provided that an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.

Place, publisher, year, edition, pages
IOP - Institute of Physics, 2010
Keyword
plasma kinetic equations, electromagnetic waves
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-37365 (URN)10.1088/1367-2630/12/7/073027 (DOI)000281232700006 ()
Available from: 2010-10-28 Created: 2010-10-28 Last updated: 2017-12-12Bibliographically approved
4. From extended phase space dynamics to fluid theory
Open this publication in new window or tab >>From extended phase space dynamics to fluid theory
2010 (English)In: Physics of Plasmas, ISSN 1070-664X, E-ISSN 1089-7674, Vol. 17, no 10, 102109-102112 p.Article in journal (Refereed) Published
Abstract [en]

We derive a fluid theory for spin-1/2 particles starting from an extended kinetic model based on a spin-projected density matrix formalism. The evolution equation for the spin density is found to contain a pressurelike term. We give an example where this term is important by looking at a linear mode previously found in a spin kinetic model.

Place, publisher, year, edition, pages
American Institute of Physics, 2010
Keyword
basic plasma phenomena, waves, instabilities
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-37382 (URN)10.1063/1.3496053 (DOI)000283772200010 ()
Available from: 2010-11-01 Created: 2010-11-01 Last updated: 2017-12-12Bibliographically approved
5. Ponderomotive force due to the intrinsic spin in extended fluid and kinetic models
Open this publication in new window or tab >>Ponderomotive force due to the intrinsic spin in extended fluid and kinetic models
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2011 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 83, no 3, 036410-036416 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we calculate the contribution to the ponderomotive force in a plasma from the electron spin using a recently developed model. The spin-fluid model used in the present paper contains spin-velocity correlations, in contrast to previous models used for the same purpose. Is its then found that previous terms for the spin-ponderomotive force are recovered, but also that additional terms appear. Furthermore, the results due to the spin-velocity correlations are confirmed using the spin-kinetic theory. The significance of our results is discussed.

Place, publisher, year, edition, pages
American Physical Society, 2011
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-50783 (URN)10.1103/PhysRevE.83.036410 (DOI)
Available from: 2011-12-21 Created: 2011-12-21 Last updated: 2017-12-08Bibliographically approved
6. Dynamics of a dusty plasma with intrinsic magnetization
Open this publication in new window or tab >>Dynamics of a dusty plasma with intrinsic magnetization
2009 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 11, no July, 073017- p.Article in journal (Refereed) Published
Abstract [en]

We consider a dusty plasma where dust particles have a magnetic dipole moment. A Hall-MHD type of model, generalized to account for the intrinsic magnetization, is derived. The model is shown to be energy conserving, and the energy density and flux are derived. The general dispersion relation is then derived, and we show that kinetic dust-Alfvén waves exhibit instability for a low dust and ion temperature and high dust density. We discuss the implication of our results.

Place, publisher, year, edition, pages
Institute of Physics, 2009
Keyword
Plasma physics, multicomponent plasma, dusty plasma, magnetized plasma
National Category
Fusion, Plasma and Space Physics
Research subject
Physics
Identifiers
urn:nbn:se:umu:diva-27022 (URN)10.1088/1367-2630/11/7/073017 (DOI)
Available from: 2009-11-06 Created: 2009-11-06 Last updated: 2017-12-12Bibliographically approved
7. Nonlinear wave interaction and spin models in the magnetohydrodynamic regime
Open this publication in new window or tab >>Nonlinear wave interaction and spin models in the magnetohydrodynamic regime
2011 (English)In: New Journal of Physics, ISSN 1367-2630, E-ISSN 1367-2630, Vol. 13, no August, 083017-08331 p.Article in journal (Refereed) Published
Abstract [en]

Here we consider the influence on the electron spin in the magnetohydrodynamic (MHD) regime. Recently developed models that include spin-velocity correlations are taken as the starting point. A theoretical argument is presented, suggesting that in the MHD regime a single-fluid electron model with spin correlations is equivalent to a model with spin-up and spin-down electrons constituting different fluids, but where the spin-velocity correlations are omitted. Three-wave interaction of two shear Alfven waves and a compressional Alfven wave is then taken as a model problem to evaluate the asserted equivalence. The theoretical argument turns out to be supported, because the predictions of the two models agree completely. Furthermore, the three-wave coupling coefficients obey the Manley-Rowe relations, which further support the soundness of the models and the validity of the assumptions made in the derivation. Finally, we point out that the proposed two-fluid model can be incorporated in standard particle-in-cell schemes with only minor modifications.

Place, publisher, year, edition, pages
Bristol, UK: Institute of Physics Pub., 2011
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-47668 (URN)10.1088/1367-2630/13/8/083017 (DOI)000294672100008 ()
Available from: 2011-10-03 Created: 2011-09-27 Last updated: 2017-12-08Bibliographically approved

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