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Quantum Kinetic Theory for Plasmas: spin, exchange, and particle dispersive effects
Umeå University, Faculty of Science and Technology, Department of Physics.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is about developing and studying quantum mechanical models of plasmas. Quantum effects can be important at high densities, at low temperatures, and in strong electromagnetic fields, in various laboratory and astrophysical systems. The focus is on the electron spin, the intrinsic magnetic moment; exchange interactions, a purely quantum mechanical effect arising from particles being indistinguishable; and particle dispersive effects, essentially the Heisenberg uncertainty principle. The focus is on using phase-space formulations of quantum mechanics, namely Wigner and -functions. These methods allow carrying over techniques from classical plasma physics and identifying quantum as opposed to classical behavior.

Two new kinetic models including the spin are presented, one fully relativistic and to first order in ħ, and one semi-relativistic but to all orders in ħ. Among other example calculations, for the former, conservation laws for energy, momentum, and angular momentum are derived and related to “hidden momentum” and the Abraham-Minkowski dilemma. Both models are discussed in the context of the existing literature.

A kinetic model of exchange interactions, formally similar to a collision operator, is compared to a widely used fluid description based on density functional theory, for the case of electrostatic waves. The models are found to disagree significantly.

A new, non-linear, wave damping mechanism is shown to arise from particle dispersive effects. It can be interpreted as the simultaneous absorption or emission of multiple wave quanta. This multi-plasmon damping is of particular interest for highly degenerate electrons, where it can occur on time scales comparable to or shorter than that of linear Landau damping.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2019. , p. 47
National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:umu:diva-162465ISBN: 978-91-7855-102-6 (print)OAI: oai:DiVA.org:umu-162465DiVA, id: diva2:1344429
Public defence
2019-09-13, N 420, Naturvetarhuset, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2019-08-23 Created: 2019-08-20 Last updated: 2019-08-21Bibliographically approved
List of papers
1. Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation
Open this publication in new window or tab >>Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation
2017 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 2, article id 023207Article in journal (Refereed) Published
Abstract [en]

In this paper, we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long-scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in (h) over bar. Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasidistribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is nontrivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as "hidden momentum" and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

Place, publisher, year, edition, pages
American Physical Society, 2017
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:umu:diva-139142 (URN)10.1103/PhysRevE.96.023207 (DOI)000408118100012 ()
Available from: 2017-10-03 Created: 2017-10-03 Last updated: 2019-08-21Bibliographically approved
2. Relativistic kinetic theory for spin-1/2 particles: Conservation laws, thermodynamics, and linear waves
Open this publication in new window or tab >>Relativistic kinetic theory for spin-1/2 particles: Conservation laws, thermodynamics, and linear waves
2019 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 100, no 2, article id 023201Article in journal (Refereed) Published
Abstract [en]

We study a recently derived fully relativistic kinetic model for spin-1/2 particles. First, the full set of conservation laws for energy, momentum, and angular momentum are given together with an expression for the (nonsymmetric) stress-energy tensor. Next, the thermodynamic equilibrium distribution is given in different limiting cases. Furthermore, we address the analytical complexity that arises when the spin and momentum eigenfunctions are coupled in linear theory by calculating the linear dispersion relation for such a case. Finally, we discuss the model and give some context by comparing with potentially relevant phenomena that are not included, such as radiation reaction and vacuum polarization.

National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-162463 (URN)10.1103/PhysRevE.100.023201 (DOI)000479192700004 ()
Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2019-08-21Bibliographically approved
3. Short-scale quantum kinetic theory including spin-orbit interactions
Open this publication in new window or tab >>Short-scale quantum kinetic theory including spin-orbit interactions
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We present a quantum kinetic theory for spin-1/2 particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in ℏ, based on a gauge-invariant Wigner transformation. Compared to previous works, the spin-orbit interaction leads to a new term in the kinetic equation, containing both the electric and magnetic fields. Like other models with spin-orbit interactions, our model features "hidden momentum". As an example application, we calculate the dispersion relation for linear electrostatic waves in a magnetized plasma, and electromagnetic waves in a unmagnetized plasma. In the former case, we compare the Landau damping due to spin-orbit interactions to that due to the free current. We also discuss our model in relation to previously published works. 

National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-162462 (URN)
Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2019-08-21
4. Nonlinear wave damping due to multi-plasmon resonances
Open this publication in new window or tab >>Nonlinear wave damping due to multi-plasmon resonances
2018 (English)In: Plasma Physics and Controlled Fusion, ISSN 0741-3335, E-ISSN 1361-6587, Vol. 60, no 2, article id 025009Article in journal (Refereed) Published
Abstract [en]

For short wavelengths, it is well known that the linearized Wigner-Moyal equation predicts wave damping due to wave-particle interaction, where the resonant velocity shifted from the phase velocity by a velocity v(q) = hk/2m. Here h is the reduced Planck constant, k is the wavenumber and m is the electron mass. Going beyond linear theory, we find additional resonances with velocity shifts nv(q), n= 2,3, ..., giving rise to a new wave-damping mechanism that we term multi-plasmon damping, as it can be seen as the simultaneous absorption (or emission) of multiple plasmon quanta. Naturally this wave damping is not present in classical plasmas. For a temperature well below the Fermi temperature, if the linear (n = 1) resonant velocity is outside the Fermi sphere, the number of linearly resonant particles is exponentially small, while the multi-plasmon resonances can be located in the bulk of the distribution. We derive sets of evolution equations for the case of two-plasmon and three-plasmon resonances for Langmuir waves in the simplest case of a fully degenerate plasma. By solving these equations numerically for a range of wave-numbers we find the corresponding damping rates, and we compare them to results from linear theory to estimate the applicability. Finally, we discuss the effects due to a finite temperature.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018
Keywords
wave-particle interaction, Wigner equation, Langmuir waves, nonlinear wave damping
National Category
Fusion, Plasma and Space Physics
Identifiers
urn:nbn:se:umu:diva-143622 (URN)10.1088/1361-6587/aa979d (DOI)000418145500002 ()
Funder
Swedish Research Council, 2012-3320
Available from: 2018-01-30 Created: 2018-01-30 Last updated: 2019-08-21Bibliographically approved
5. Exchange corrections in a low-temperature plasma
Open this publication in new window or tab >>Exchange corrections in a low-temperature plasma
2015 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 92, no 1, article id 013104Article in journal (Refereed) Published
Abstract [en]

We have studied the exchange corrections to linear electrostatic wave propagation in a plasma using a quantum kinetic formalism. Specifically, we have considered the zero-temperature limit. In order to simplify the calculations we have focused on the long-wavelength limit, i.e., wavelengths much longer than the de Broglie wavelength. For the case of ion-acoustic waves we have calculated the exchange correction both to the damping rate and the real part of the frequency. For Langmuir waves the frequency shift due to exchange effects is found. Our results are compared with the frequency shifts deduced from commonly used exchange potentials which are computed from density-functional theory.

Place, publisher, year, edition, pages
American Physical Society, 2015
National Category
Physical Sciences
Identifiers
urn:nbn:se:umu:diva-106781 (URN)10.1103/PhysRevE.92.013104 (DOI)000357863500006 ()
Available from: 2015-08-14 Created: 2015-08-07 Last updated: 2019-08-21Bibliographically approved
6. Do hydrodynamic models misestimate exchange effects? Comparison with kinetic theory for electrostatic waves
Open this publication in new window or tab >>Do hydrodynamic models misestimate exchange effects? Comparison with kinetic theory for electrostatic waves
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We have extended previous kinetic results to compute the exchange correction to the electrostatic electron susceptibility for arbitrary frequencies and wavenumbers in the low temperature limit. This has allowed us to make a general comparison with a much used hydrodynamic expression for exchange effects. It is found that the hydrodynamic expression gives a useful approximation when the phase velocity is roughly a factor 2.5 larger than the Fermi velocity. For low phase velocities, as for ion-acoustic waves, wave-particle interaction leads to a strong enhancement of the exchange correction and the hydrodynamic results is smaller by an order of magnitude. 

National Category
Fusion, Plasma and Space Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:umu:diva-162460 (URN)
Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2019-08-21

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