arXiv subjects

Jens Zamanian

Publications and source records attributed to Jens Zamanian.

17 recordsLinked to original sources

arXiv2022

Plasma dynamics at the Schwinger limit and beyond

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 for ultra-strong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined.

physics.plasm-ph↗

arXiv2021

Quantum Kinetic Theory of Plasmas

As is well-known, for plasmas of high density and modest temperature, the classical kinetic theory needs to be extended. Such extensions can be based on the Schrödinger Hamiltonian, applying a Wigner transform of the density matrix, in which case the Vlasov equation is replaced by the celebrated Wigner-Moyal equation. Extending the treatment to more complicated models, we investigate aspects such as spin dynamics (based on the Pauli Hamiltonian), exchange effects (using the Hartree-Fock approximation), Landau quantization, and quantum relativistic theory. In the relativistic theory we first study cases where the field strength is well beyond Schwingers critical field. Both weakly relativistic theory (gamma factors close to unity) and strongly relativistic theory are investigated, using assumptions that allow for a separation of electron and positron states. Finally, we study the Dirac-Heisenberg-Wigner (DHW) formalism, which is a fully quantum relativistic theory, allowing for field strengths of the order of the Schwinger critical field or even larger. As a result, the quantum kinetic theory is extended to cover phenomena such as Zitterbewegung and electron-positron pair creation. While the focus of this review is on the quantum kinetic models, we illustrate the theories with various applications throughout the manuscript.

physics.plasm-ph↗

arXiv2021

Spacetime-dependent electric field effects in vacuum and plasma using the Wigner-formalism

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 3+1-system of four coupled partial differential equations, which are completed by Ampere's law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in 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.

physics.plasm-ph↗

arXiv2020

Kinetic theory for spin-1/2 particles in ultra-strong magnetic fields

When the Zeeman 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 ultra-strong 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.

physics.plasm-ph↗

arXiv2019

Short-scale quantum kinetic theory including spin-orbit interactions

We present a quantum kinetic theory for spin-$1/2$ particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in $\hbar$, 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.

physics.plasm-ph↗

arXiv2019

Do hydrodynamic models misestimate exchange effects? Comparison with kinetic theory for electrostatic waves

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.

physics.plasm-ph↗

arXiv2017

Quantum kinetic theories in degenerate plasmas

In this review we give an overview of recent work on quantum kinetic theories of plasmas. We focus, in particular, on the case where the electrons are fully degenerate. For such systems, perturbation methods using the distribution function can be problematic. Instead we present a model that considers the dynamics of the Fermi surface. The advantage of this model is that, even though the value of the distribution function can be greatly perturbed outside the equilibrium Fermi surface, deformation of Fermi surface is small up very large amplitudes. Next, we investigate the short-scale dynamics for which the Wigner-Moyal equation replaces the Vlasov equation. In particular, we study wave-particle interaction, and deduce that new types of wave damping can occur due to the simultaneous absorption (or emission) of multiple wave quanta. Finally, we consider exchange effects within a quantum kinetic formalism to find a model more accurate than ones using exchange potentials from density functional theory. We deduce the exchange corrections to the dispersion relations for Langmuir and ion-acoustic waves. Comparing with results based on exchange potentials deduced from density functional theory we find that the latter models are reasonably accurate for Langmuir waves, but rather inaccurate for ion acoustic waves.

physics.plasm-ph↗

arXiv2017

Nonlinear wave damping due to multi-plasmon resonances

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 $v_q = \hbar k/2m$. Here $\hbar$ 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 $n v_q$, $n = 2, 3, \ldots$, giving rise to a new wave-damping mechanism that we term \emph{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.

physics.plasm-ph↗

arXiv2017

Fully relativistic kinetic equation for spin-1/2 particles in the long scale-length approximation

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 $\hbar$. 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 quasi-distribution 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 non-trivially 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.

physics.plasm-ph↗

arXiv2015

Exchange effects in a cold plasma

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.

physics.plasm-ph↗

arXiv2014

Lagrangian approach to the semi-relativistic electron dynamics in the mean-field approximation

We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in $1/c$. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semi-relativistic approximation to the full Dirac-Maxwell equations.

quant-ph↗

arXiv2013

Three-wave interaction and Manley-Rowe relations in quantum hydrodynamics

The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for a generalized Bohm de Broglie term. It is found that the Manley-Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.

physics.plasm-ph↗

arXiv2011

Strong field effects in laser pulses: the Wigner formalism

We investigate strong field vacuum effects using a phase space approach based on the Wigner formalism. We calculate the Wigner function in a strong null-field background exactly, using lightfront field theory. The Wigner function exhibits the distinct features of strong field QED: in particular we identify the effective mass in a laser pulse, compare it to the well-known mass shift in a periodic plane wave and identify signals of multi-photon absorption and emission. Finally, we show how to extend our results to describe vacuum pair production in colliding laser pulses.

hep-ph↗

arXiv2010

From extended phase space dynamics to fluid theory

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 pressure-like term. We give an example where this term is important by looking at a linear mode previously found in a spin kinetic model.

physics.plasm-ph↗

arXiv2009

Scalar quantum kinetic theory for spin-1/2 particles: mean field theory

Starting from the Pauli Hamiltonian operator, we derive a 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 principal interest, such scalar quantum kinetic equation makes the comparison to 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. Applications (e.g. ultra-dense laser compressed targets and their diagnostics), possible extensions, and future improvements of the presented quantum statistical model are discussed.

cond-mat.quant-gas↗

arXiv2009

Ferroplasmas: Magnetic Dust Dynamics in a Conducting Fluid

We consider a dusty plasma, in which the 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 is derived. The general dispersion relation is then derived, and we show that kinetic Alfvén waves exhibit an instability for a low temperature and high density plasma. We discuss the implication of our results.

physics.plasm-ph↗

arXiv2008

Effects of the $g$-factor in semi-classical kinetic plasma theory

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. Analysing 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.

physics.plasm-ph↗