arXiv subjects

Etele Molnár

Publications and source records attributed to Etele Molnár.

12 recordsLinked to original sources

arXiv2025

Exact solutions for the moments of the binary collision integral and its relation to the relaxation-time approximation in leading-order anisotropic fluid dynamics

We compute the moments of the nonlinear binary collision integral in the ultrarelativistic hard-sphere approximation for an arbitrary anisotropic distribution function in the local rest frame. This anisotropic distribution function has an angular asymmetry controlled by the parameter of anisotropy $ξ$, such that in the limit of a vanishing anisotropy $\lim_{ξ\rightarrow 0} \hat{f}_{0 \mathbf{k}} = f_{0 \mathbf{k}}$, approaches the spherically symmetric local equilibrium distribution function. The corresponding moments of the binary collision integral are obtained in terms of quadratic products of different moments of the anisotropic distribution function and couple to a well defined set of lower-order moments. To illustrate these results we compare the moments of the binary collision integral to the moments of the widely used relaxation-time approximation of Anderson and Witting in case of a spheroidal distribution function. We found that in an expanding system the nonlinear Boltzmann collision term leads to twice slower equilibration than the relaxation-time approximation. Furthermore we also show that including two dynamical moments helps to resolve the ambiguity which additional moment of the Boltzmann equation to choose to close the conservation laws.

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arXiv2025

Higher-order dissipative anisotropic magnetohydrodynamics from the Boltzmann-Vlasov equation

We apply the method of moments to the relativistic Boltzmann-Vlasov equation and derive the equations of motion for the irreducible moments of arbitrary tensor-rank of the invariant single-particle distribution function. We study two cases, in the first of which the moments are taken to be irreducible with respect to the little group associated with the time-like fluid four-velocity, while in the second case they are assumed to be also irreducible with respect to a space-like four-vector orthogonal to the fluid four-velocity, which breaks the spatial isotropy to a rotational symmetry in the plane transverse to this vector. A systematic truncation and closure of the general moment equations leads, in the first case, to a theory of relativistic higher-order dissipative resistive magnetohydrodynamics. In the second case, we obtain a novel theory of dissipative resistive anisotropic magnetohydrodynamics, where the momentum anisotropy is in principle independent from that introduced by the external magnetic field.

physics.plasm-ph↗

arXiv2024

Shakhov-type extension of the relaxation time approximation in relativistic kinetic theory and second-order fluid dynamics

We present a relativistic Shakhov-type generalization of the Anderson-Witting relaxation time model for the Boltzmann collision integral to modify the ratio of momentum diffusivity to thermal diffusivity. This is achieved by modifying the path on which the single particle distribution function $f_{\mathbf{k}}$ approaches local equilibrium $f_{0\mathbf{k}}$ by constructing an intermediate Shakhov-type distribution $f_{\mathrm{S}\mathbf{k}}$ similar to the 14-moment approximation of Israel and Stewart. We illustrate the effectiveness of this model in case of the Bjorken expansion of an ideal gas of massive particles and the damping of longitudinal waves through an ultrarelativistic ideal gas.

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arXiv2024

Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles

In this paper, we study all transport coefficients of second-order dissipative fluid dynamics derived by V. E. Ambrus et al. [Phys. Rev. D 106, 076005 (2022)] from the relativistic Boltzmann equation in the relaxation-time approximation for the collision integral. These transport coefficients are computed for a classical ideal gas of massive particles, with and without taking into account the conservation of intrinsic quantum numbers. Through rigorous comparison between kinetic theory, second-order dissipative fluid dynamics, and leading-order anisotropic fluid dynamics for a (0+1)--dimensional boost-invariant flow scenario, we show that both fluid-dynamical theories describe the early far-from-equilibrium stage of the expansion reasonably well.

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arXiv2022

Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation

We derive the transport coefficients of second-order fluid dynamics with $14$ dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic Boltzmann equation. Contrary to results previously reported in the literature, we find that the second-order transport coefficients derived using the two methods are in perfect agreement. Furthermore, we show that, unlike in the case of binary hard-sphere interactions, the diffusion-shear coupling coefficients $\ell_{Vπ}$, $λ_{Vπ}$, and $τ_{Vπ}$ actually diverge in some approximations when the expansion order $N_\ell \rightarrow \infty$. Here we show how to circumvent such a problem in multiple ways, recovering the correct transport coefficients of second-order fluid dynamics with $14$ dynamical moments. We also validate our results for the diffusion-shear coupling by comparison to a numerical solution of the Boltzmann equation for the propagation of sound waves in an ultrarelativistic ideal gas.

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arXiv2022

Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon number, and strangeness) using the method of moments. We obtain the continuity equations for multiple conserved charges as well as the conservation equations for the total energy and momentum in the single-fluid approximation. These $4+N_q$ conservation laws are closed by deriving the second-order equations of motion for the dissipative quantities in the $(10+4N_q)$-moment approximation. The resulting fluid-dynamical equations are formally similar to those of a single-component system, but feature different thermodynamic relations and transport coefficients. We derive general relations for all transport coefficients and compute them explicitly in the ultrarelativistic limit.

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arXiv2021

Direct laser-driven electron acceleration and energy gain in helical beams

A detailed study of direct laser-driven electron acceleration in paraxial Laguerre-Gaussian modes corresponding to helical beams $\text{LG}_{0m}$ with azimuthal modes $m=\left\{1,2,3,4,5\right\}$ is presented. Due to the difference between the ponderomotive force of the fundamental Gaussian beam $\text{LG}_{00}$ and helical beams $\text{LG}_{0m}$ we found that the optimal beam waist leading to the most energetic electrons at full width at half maximum is more than twice smaller for the latter and corresponds to a few wavelengths $Δw_0=\left\{6,11,19\right\}λ_0$ for laser powers of $P_0 = \left\{0.1,1,10\right\}$ PW. We also found that for azimuthal modes $m\geq 3$ the optimal waist should be smaller than $Δw_0 < 19 λ_0$. Using these optimal values we have observed that the average kinetic energy gain of electrons is about an order of magnitude larger in helical beams compared to the fundamental Gaussian beam. This average energy gain increases with the azimuthal index $m$ leading to collimated electrons of a few $100$ MeV energy in the direction of the laser propagation.

physics.plasm-ph↗

arXiv2019

Resistive dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation

We derive the equations of motion of relativistic, resistive, second-order dissipative magnetohydrodynamics from the Boltzmann-Vlasov equation using the method of moments. We thus extend our previous work [Phys. Rev. D 98, 076009 (2018)], where we only considered the non-resistive limit, to the case of finite electric conductivity. This requires keeping terms proportional to the electric field $E^μ$ in the equations of motions and leads to new transport coefficients due to the coupling of the electric field to dissipative quantities. We also show that the Navier-Stokes limit of the charge-diffusion current corresponds to Ohm's law, while the coefficients of electrical conductivity and charge diffusion are related by a type of Wiedemann-Franz law.

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arXiv2018

Non-resistive dissipative magnetohydrodynamics from the Boltzmann equation in the 14-moment approximation

We derive the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics from the Boltzmann equation using the method of moments. We assume the fluid to be composed of a single type of point-like particles with vanishing dipole moment or spin, so that the fluid has vanishing magnetization and polarization. In a first approximation, we assume the fluid to be non-resistive, which allows to express the electric field in terms of the magnetic field. We derive equations of motion for the irreducible moments of the deviation of the single-particle distribution function from local thermodynamical equilibrium. We analyze the Navier-Stokes limit of these equations, reproducing previous results for the structure of the first-order transport coefficients. Finally, we truncate the system of equations for the irreducible moments using the 14-moment approximation, deriving the equations of motion of relativistic, non-resistive, second-order dissipative magnetohydrodynamics. We also give expressions for the new transport coefficients appearing due to the coupling of the magnetic field to the dissipative quantities.

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arXiv2016

Closing the equations of motion of anisotropic fluid dynamics by a judicious choice of moment of the Boltzmann equation

In Molnár et al. [Phys. Rev. D 93, 114025 (2016)] the equations of anisotropic dissipative fluid dynamics were obtained from the moments of the Boltzmann equation based on an expansion around an arbitrary anisotropic single-particle distribution function. In this paper we make a particular choice for this distribution function and consider the boost-invariant expansion of a fluid in one dimension. In order to close the conservation equations, we need to choose an additional moment of the Boltzmann equation. We discuss the influence of the choice of this moment on the time evolution of fluid-dynamical variables and identify the moment that provides the best match of anisotropic fluid dynamics to the solution of the Boltzmann equation in the relaxation-time approximation.

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arXiv2010

Relativistic Shock Waves and Mach Cones in Viscous Gluon Matter

To investigate the formation and the propagation of relativistic shock waves in viscous gluon matter we solve the relativistic Riemann problem using a microscopic parton cascade. We demonstrate the transition from ideal to viscous shock waves by varying the shear viscosity to entropy density ratio $η/s$. Furthermore we compare our results with those obtained by solving the relativistic causal dissipative fluid equations of Israel and Stewart (IS), in order to show the validity of the IS hydrodynamics. Employing the parton cascade we also investigate the formation of Mach shocks induced by a high-energy gluon traversing viscous gluon matter. For $η/s = 0.08$ a Mach cone structure is observed, whereas the signal smears out for $η/s \geq 0.32$.

hep-ph↗

arXiv2006

Freeze Out Process with In-Medium Nucleon Mass

We investigate the kinetic freeze out scenario of a nucleon gas through a finite layer. The in-medium mass modification of nucleons and it's impact on the freeze out process is studied. A considerable modification of the thermodynamical parameters temperature, flow-velocity, energy density and particle density has been found in comparison with evaluations which use a constant vacuum nucleon mass.

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