arXiv subjects

Gert Brodin

Publications and source records attributed to Gert Brodin.

At least 19 recordsLinked to original sources

arXiv2025

Modified vacuum polarization in the presence of a plasma

We study vacuum polarization due to strong fields, in the presence of an electron-positron plasma. For this purpose, we expand quantum kinetic equations using weak fields and slow temporal scales as expansion parameters. It is demonstrated that the evolution of the Dirac field can be described by classical-like distribution functions for electrons and positrons, which are weakly coupled through quantum interactions. Furthermore, we deduce that these coupling terms give rise to well-known expressions for vacuum polarization, in addition to quantum modifications proportional to the content of real particles. Depending on the initial plasma density, the dominant quantum corrections to classical evolution may arise from real particle couplings or from the vacuum polarization associated with virtual particles. The implications of our results are discussed.

physics.plasm-ph↗

arXiv2025

Probing the transition from classical to quantum radiation reaction in relativistic plasma

We study the transition from classical radiation reaction, described by the Landau-Lifshitz model, to the quantum mechanical regime. The plasma is subject to a circularly polarized field where the self-consistent plasma current is the source of the electromagnetic field through Ampere's law. The radiation reaction implies wave energy loss, frequency up-conversion, and a modified distribution function. Increasing the value of the quantum $\chi$-parameter, the quantum results gradually differ from the classical ones. Moreover, the deviation between models also depends on the plasma parameters, including density and temperature. We discuss the implications of our findings.

physics.plasm-ph↗

arXiv2024

Applicability of semi-classical theories in the strong field plasma regime

For many purposes, classical plasma dynamics models can work surprisingly well even for strong electromagnetic fields, approaching the Schwinger critical fields, and high frequencies, approaching the Compton frequency. However, the applicability of classical models tends to depend rather sensitively on the details of the problem. In the present paper, we study the specific case of plasma oscillations to draw a line between the classical and quantum relativistic regimes. Due to the field geometry of study, mechanisms like radiation reaction and Breit-Wheeler pair production, which tend to be important for electromagnetic fields, are rather effectively suppressed. Moreover, we find that the polarization current due to the electron spin is generally negligible for frequencies below the Compton frequency, compared to the free current, whose magnitude is well-approximated by the classical Vlasov theory. However, we show that pair creation due to the Schwinger mechanism can sometimes be important for surprisingly modest field strengths, of the order of 10 % of the critical field or even smaller. A rough guideline for when the classical Vlasov theory can be applied is given

physics.plasm-ph↗

arXiv2024

Anomalous conductivity due to relativistic Landau quantization

We use a recently developed kinetic model derived from the Dirac equation, in order to study electromagnetic wave propagation in superstrong magnetic fields, such as in magnetars, where relativistic Landau quantization is prominent. The leading contribution to the conductivity tensor in such a plasma is calculated. It is found that the electron Hall current has an anomalous contribution, in the quantum relativistic regime, where the effective particle energy has a significant contribution from the diamagnetic and Zeeman energy. As a result, a new quantum resonance frequency appears, and the dispersion relation for the left- and right-hand polarized modes are strongly modified for long and moderate wavelengths. The implications for magnetar physics are discussed.

physics.plasm-ph↗

arXiv2023

Applicability of the Klein-Gordon equation for pair production in vacuum and plasma

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.

physics.plasm-ph↗

arXiv2023

Ponderomotive force due to the intrinsic spin for electrostatic waves in a magnetized plasma

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, dependent 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. Naturally, this does not prevent the opposite case from being the more common one.

physics.plasm-ph↗

arXiv2022

Radiation reaction effects in relativistic plasmas -- the electrostatic limit

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 wavenumber, 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.

physics.plasm-ph↗

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↗

arXiv2022

Wave-particle interactions in quantum plasmas

Wave-particle interaction (WPI) is one of the most fundamental processes in plasma physics in which one most prominent example is the Landau damping. Owing to its excellent energy-exchange mechanism, the WPI has gained increasing interest not only from theoretical points of view but also its many important applications including plasma heating and plasma acceleration. In this review work, we present theoretical backgrounds of linear and nonlinear wave-particle interactions in quantum plasmas. Specifically, we focus on the wave-particle interactions for homogeneous plasma waves (i.e., waves with infinite extent rather than a localized pulse) as well as for propagating electrostatic waves in the weak and strong quantum regimes to demonstrate the modifications of several classical features including those associated with resonant and trapped particles. Finally, the future perspectives of WPI in quantum plasmas are presented.

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

Landau damping of electron-acoustic waves due to multi-plasmon resonances

The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the Fermi-Dirac distribution at finite temperature. By employing the multi-scale asymptotic expansion technique to the one-dimensional Wigner-Moyal and Poisson equations, it is shown that the effects of multi-plasmon resonances lead to a modified complex Korteweg-de Vries (KdV) equation with a new nonlocal nonlinearity. Besides giving rise to a nonlocal nonlinear term, the wave-particle resonance also modifies the local nonlinear coupling coefficient of the KdV equation. The latter is shown to conserve the number of particles, however, the wave energy decays with time. A careful analysis shows that the two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of EAWs. An approximate soliton solution of the KdV equation is also obtained, and it is shown that the nonlinear Landau damping causes the wave amplitude to decay slowly with time compared to the classical theory.

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

Transition from wakefield generation to soliton formation

It is well known that when a short laser pulse propagates in an underdense plasma, it induces longitudinal plasma oscillations at the plasma frequency after the pulse, typically referred to as the 'wakefield'. However, for plasma densities approaching the critical density wakefield generation is suppressed, and instead the EM-pulse undergoes nonlinear self-modulation. In this article we have studied the transition from the wakefield generation to formation of quasi-solitons as the plasma density is increased. For this purpose we have applied a one dimensional (1D) relativistic cold fluid model, which has also been compared with particle-in-cell simulations. A key result is that the energy loss of the EM-pulse due to wakefield generation has its maximum for a plasma density of the order 10 percent of the critical density, but that wakefield generation is sharply suppressed when the density is increased further.

physics.plasm-ph↗

arXiv2017

Effects of group velocity and multi-plasmon resonances on the modulation of Langmuir waves in a degenerate plasma

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schr{ö}dinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multi-plasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multi-plasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where $ \hbar k\sim mv_{F}$ with $\hbar$ denoting the reduced Planck's constant, $m$ the electron mass and $v_F$ the Fermi velocity, however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multi-plasmon effects are forbidden.

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↗