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In this paper, a phase-space description of electron-positron pair-creation will be applied, based on a Wigner transformation of the Klein-Gordon equation. The resulting theory is similar in many respects to the equations from the Dirac-Heisenberg-Wigner formalism. However, in the former case, all physics related to particle spin is neglected. In the present paper we compare the pair-production rate in vacuum and plasmas, with and without spin effects, in order to evaluate the accuracy and applicability of the spinless approximation. It is found that for modest frequencies of the electromagnetic field, the pair production rate of the Klein-Gordon theory is a good approximation to the Dirac theory, provided the matter density is small enough for Pauli blocking to be neglected, and a factor of two related to the difference in the vacuum energy density is compensated for.  

Under the extreme conditions that can be found around dense stars and in the accretion discs of black holes, several strong-field quantum phenomena dominate the dynamics of the plasma. This includes the creation of matter and anti-matter from the vacuum (Schwinger mechanism), radiation reaction and Landau quantization. Some of these strong field phenomena were presented theoretically a century ago but have never been verified in experiments due to the difficulty of creating the required extreme conditions in the lab. However, with the development of laser facilities in the past decades, it will be possible to observe several extreme physical phenomena in the near future. To conduct experiments on these extreme phenomena, theoretical simulations need to be constructed as a guide for optimizing experiments.

This thesis is concerned with developing and analyzing strong field phenomena in kinetic plasma models. The focus is to extend current kinetic models to include several physical phenomena that are relevant to future experiments on laser-plasma interaction. In particular, a kinetic theory based on the Wigner transformation of the Dirac equation has been analyzed in different regimes. This kinetic model is used to study the plasma dynamics at the Schwinger limit, where collective plasma effects and several quantum processes are studied.

Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms in the regime of ultrastrong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined. Finally, comparisons with competing mechanisms such as radiation reaction and Breit-Wheeler pair production are made.

We study the contribution from the electron spin to the ponderomotive force, using a quantum kinetic model, including the spin-orbit correction. Specifically, we derive an analytical expression for the ponderomotive force, applicable for electrostatic waves propagating parallel to an external magnetic field. To evaluate the expression, we focus on the case of Langmuir waves and on the case of the spin resonance wave mode, where the classical and spin contributions to the ponderomotive force are compared. Somewhat surprisingly, depending on the parameter regime, we find that the spin contribution to the ponderomotive force may dominate for the Langmuir wave, whereas the classical contribution can dominate for the spin resonance mode.

We study the evolution of electrostatic plasma waves, using the relativistic Vlasov equation extended by the Landau-Lifshitz radiation reaction, accounting for the back-reaction due to the emission of single particle Larmor radiation. In particular, the Langmuir wave damping is calculated as a function of wave number, initial temperature, and initial electric field amplitude. Moreover, the background distribution function loses energy in the process, and we calculate the cooling rate as a function of initial temperature and initial wave amplitude. Finally, we investigate how the relative magnitude of wave damping and background cooling varies with the initial parameters. In particular, it is found that the relative contribution to the energy loss associated with background cooling decreases slowly with the initial wave amplitude.

We have studied the linear dispersion relation for Langmuir waves in plasmas of very high density, based on the Dirac-Heisenberg-Wigner formalism. The vacuum contribution to the physical observables leads to ultraviolet divergences, which are removed by a charge renormalization. The remaining vacuum contribution is small and is in agreement with previously derived expressions for the time-dependent vacuum polarization. The main new feature of the theory is a damping mechanism similar to Landau damping, but where the plasmon energy gives rise to creation of electron-positron pairs. The dependence of the damping rate (pair-creation rate) on the wavenumber, temperature, and density is analyzed. Finally, the analytical results of linearized theory are compared with numerical solutions.

We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.

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. 

When the Zecman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a kinetic equation for electrons, focusing on the phenomenon of Landau quantization in such ultrastrong but constant magnetic fields, neglecting short-scale quantum phenomena. It turns out that the usual relativistic gamma factor of the Vlasov equation is replaced by an energy operator, depending on the spin state, and also containing momentum derivatives. Furthermore, we show that the energy eigenstates in a magnetic field can be computed as eigenfunctions of this operator. The dispersion relation for electrostatic waves in a plasma is computed, and the significance of our results is discussed.

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.