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This paper studies the nonlinear Landau damping on the torus T 3 for the Vlasov–Poisson system with radiation damping. We show that even under the influence of the radiation damping effects, the plasma still has the remarkable property of Landau damping. The corresponding density and force field decay exponentially fast as time goes to infinity. [ABSTRACT FROM AUTHOR]

This paper develops and analyses a semi-discrete numerical method for the two-dimensional Vlasov–Stokes system with periodic boundary condition. The method is based on the coupling of the semi-discrete discontinuous Galerkin method for the Vlasov equation with discontinuous Galerkin scheme for the stationary incompressible Stokes equation. The proposed method is both mass and momentum conservative. Since it is difficult to establish non-negativity of the discrete local density, the generalized discrete Stokes operator become non-coercive and indefinite, and under the smallness condition on the discretization parameter, optimal error estimates are established with help of a modified the Stokes projection to deal with the Stokes part and, with the help of a special projection, to tackle the Vlasov part. Finally, numerical experiments based on the dG method combined with a splitting algorithm are performed. [ABSTRACT FROM AUTHOR]

Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. In this work, a variational formulation of the projector splitting is proposed which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach. [ABSTRACT FROM AUTHOR]

The Vlasov–Poisson–Fokker–Planck (VPFP) system is a fundamental model in plasma physics that describes the Brownian motion of a large ensemble of particles within a surrounding bath. Under the high-field scaling, both collision and field are dominant. This paper introduces two Asymptotic-Preserving Neural Network (APNN) methods within a physics-informed neural network (PINN) framework for solving the VPFP system in the high-field regime. These methods aim to overcome the computational challenges posed by high dimensionality and multiple scales of the system. The first APNN method leverages the micro–macro decomposition model of the original VPFP system, while the second is based on the mass conservation law. Both methods ensure that the loss function of the neural networks transitions naturally from the kinetic model to the high-field limit model, thereby preserving the correct asymptotic behavior. Through extensive numerical experiments, these APNN methods demonstrate their effectiveness in solving multiscale and high dimensional uncertain problems, as well as their broader applicability for problems with long time duration and non-equilibrium initial data. [ABSTRACT FROM AUTHOR]

In the upper atmosphere (ionosphere), plasma with two electron populations is very common. The cold electrons ( T e ∼ 1 eV) usually originate in the ionosphere, while the hot electrons ( T e ∼ 100 eV) come from the magnetosphere. In addition to these two electron populations, there may be a beam of electrons streaming along the magnetic field lines. These electrons are responsible for exciting various electrostatic wave modes. In this article, we provide a systematic insight in the evolution of the system, based on the beam energy. With an increase in beam velocity, the beam temporarily recovers a portion of its initial energy as well as a higher saturation energy. The wave energy is lost significantly before saturation and after linear growth at a relatively modest beam velocity. In addition, the low beam velocity generates BGK electron holes in the phase space, which are missing at higher beam velocities. We also present the analysis of the condition of sustained electron holes in the phasespace. [ABSTRACT FROM AUTHOR]

A test problem for the 'particle-in-cell' method is proposed which allows one to check individual errors on each stage of numerical implementation of the method. General testing usually controls only total (final) error. Using the test problem, we analyze errors of a difference method of MacCormack type and the CIC method being the most popular version of the 'particle-in-cell' method. It is shown that the CIC method having also the second formal order of accuracy is seriously inferior to the difference method under the same given error and same grid parameters. In particular, the results of the particle method lose their sense after approximately one calculation period, although the time interval of confidence in simulation data for the difference method is practically unlimited. The testing method proposed here is suitable for an arbitrary one-dimensional version of the 'particle-in-cell' method, and it allows one not only to compare numerical implementations of individual stages with each other, but also to verify available theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigated the two-dimensional, four-field reduced magnetohydrodynamics equations that are used to examine the tearing instability and magnetic reconnection of phenomena in plasmas. The generalized Ohm's law is used in the derivation of the 2D four-field RMHD equations. We established the existence and uniqueness of a strong solution for the 2D four-field RMHD equations under periodic boundary conditions during some time interval in Sobolev-Slobodetskiĭ space with the help of successive approximations and a p r i o r i estimates. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the relativistic Vlasov–Klein–Gordon system in space dimension three. The dynamical model describes a collisionless ensemble of classical particles coupled with a Klein–Gordon field. By combining the Fourier method and smoothing effect of low velocity particles, we prove a higher regularity of the field, which is widely used for the study of Vlasov equation. [ABSTRACT FROM AUTHOR]

In this paper, we prove the global existence and moment propagation of weak solutions for the repulsive plasma-charge model with a time-varying magnetic field. Multi-point charges are allowed according to an improved mechanism to compensate the asymmetry caused by the point charges, which brings us back to the standard Lions-Perthame’s argument. To deal with two type singularities induced by the point charges and the magnetic field, we combine the ideas from Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015) and Rege (SIAM J Math Anal 53(2):2452–2475, 2021). The density of the plasma is allowed to be constant around the point charges, by applying the moment lemma established in Perthame (Math Methods Appl Sci 13(5):41–452, 1990) and careful compactness argument. The result answers two questions raised in Desvillettes et al. (Ann Inst H Poincaré Anal Non Linéaire 32(2):373–400, 2015). [ABSTRACT FROM AUTHOR]

In this paper, we consider a Vlasov–Poisson system in the presence of radiation damping, which is a two-species Vlasov–Poisson system for electrons and ions with additional terms to describe the effect of accelerated charged particles. We obtain the global-in-time and optimal decay estimates of classical solutions to it for small initial data in the whole space R 3 . Compared to the previous results, no compact support assumptions on initial data is needed in our paper. And we obtain the optimal L x ∞ decay estimates of the charge densities and the electrostatic field, which was not reported in previous literature. For the proofs of our results, we adapt the modified vector field method which was introduced initially by Smulevici for the classical Vlasov–Poisson system for electrons. [ABSTRACT FROM AUTHOR]

In this paper, we provide sufficient conditions for the energy conservation of the DiPerna–Lions solutions given in DiPerna and Lions (Commun Pure Appl Math 42:729–757, 1989), Rein (Commun Math Sci 2:145–158, 2004) to Vlasov–Maxwell systems in R 3 , which requires only macroscopic density ρ ∈ L t 2 L loc 2 for the relativistic case and | ξ | f ∈ L t , x 2 L ξ 1 for the non-relativistic case, improving the results in Sospedra–Alfonso (Commun Math Sci 8:901–908, 2010), Bardos et al. (Q Appl Math 78:193–217, 2020). Next, by mollification in time twice with different parameters and the weak formulations containing t = 0 , we obtain the same results for solutions given in Guo (Commun Math Phys 154:245–263, 1993) with low temporal regularity to the Vlasov–Maxwell systems in bounded domains under some boundary-layer conditions. [ABSTRACT FROM AUTHOR]

In this paper, semi-discrete numerical scheme for the approximation of the periodic Vlasov-viscous Burgers’ system is developed and analyzed. The scheme is based on the coupling of discontinuous Galerkin approximations for the Vlasov equation and local discontinuous Galerkin approximations for the viscous Burgers’ equation. Both these methods use generalized numerical fluxes. The proposed scheme is both mass and momentum conservative. Based on generalized Gauss–Radau projections, optimal rates of convergence in the case of smooth compactly supported initial data are derived. Finally, computational results confirm our theoretical findings. [ABSTRACT FROM AUTHOR]

The kinetic formulation of the model problem of plasma waves excitation by a powerful short laser pulse is numerically studied for the first time. Kinetic and simplest hydrodynamic plasma models are also compared for the problem under consideration. It is shown that the considered hydrodynamic models do not provide good approximations to the solution to the Vlasov kinetic equation, namely, one leads to discontinuous solutions and the other has a significant qualitative distinction. At a low plasma temperature, the effect of non-isothermicity of the process is small, but it can lead to significant distortions of the solution during further heating. The results obtained here imply that the first two moments of the distribution function are not enough to describe the plasma hydrodynamics; higher-order moments should be used. [ABSTRACT FROM AUTHOR]

In this article, we study microscopic properties of a two-dimensional Coulomb gas ensemble near a conical singularity arising from insertion of a point charge in the bulk of the droplet. In the determinantal case, we characterize all rotationally symmetric scaling limits ("Mittag-Leffler fields") and obtain universality of them when the underlying potential is algebraic. Applications include a central limit theorem for log | p n (ζ) | where pn is the characteristic polynomial of an n:th order random normal matrix. [ABSTRACT FROM AUTHOR]

We consider a two-dimensional determinantal Coulomb gas confined by a class of radial external potentials. In the limit of large number of particles, the Coulomb particles tend to accumulate on a compact set S, the support of the equilibrium measure associated with a given external potential. If the particles are forced to be completely confined in a disk D due to a hard-wall constraint on ∂ D ⊂ Int S , then the equilibrium configuration changes and the equilibrium measure acquires a singular component at the hard wall. We study the local statistics of Coulomb particles in the vicinity of the hard wall and prove that their local correlations are expressed in terms of "Laplace-type" integrals, which appear in the context of truncated unitary matrices in the regime of weak non-unitarity. [ABSTRACT FROM AUTHOR]

We are concerned with the properties of weak solutions for the relativistic Vlasov–Klein–Gordon system. Under some suitable regularity hypotheses on the density of particles and field, we show the renormalization property and global (local) entropy conservation laws. In addition, by virtue of the additional integrability condition ∫ R 3 1 + | v | 2 f d v ∈ L ∞ ((0 , T) ; L 2 (R x 3)) , we prove that global (local) energy for the weak solutions are conserved. [ABSTRACT FROM AUTHOR]

We introduce and study certain variants of Gamow's liquid drop model in which an anisotropic surface energy replaces the perimeter. After existence and nonexistence results are established, the shape of minimizers is analyzed. Under suitable regularity and ellipticity assumptions on the surface tension, Wulff shapes are minimizers in this problem if and only if the surface energy is isotropic. In sharp contrast, Wulff shapes are the unique minimizers for certain crystalline surface tensions. We also introduce and study several related liquid drop models with anisotropic repulsion for which the Wulff shape is the minimizer in the small mass regime. [ABSTRACT FROM AUTHOR]

The future of the industry development depends greatly on the permanently ensured energy needs and can be achieved only through the use of a variety of sustainable energy sources where the solar energy, which gains its optimal exploitation directly by linking it to the properties of solar cells and in particular to the crystallographic quality of the used semiconductor substrates, is one of them. Many growth processes are used to obtain a high quality of semiconductor formation and deposition, among them the DC sputtering. In this work, based on the Monte-Carlo method, a 3D DC sputtering simulation of the CZTS {\mathrm{CZTS}} , Si {\mathrm{Si}} and CIGS {\mathrm{CIGS}} semiconductors thin film formation is proposed by considering Argon as vacuum chamber bombardment gas. We extrapolate firstly the best sputtering yield possible of the semiconductors CZTS {\mathrm{CZTS}} and Silicon represented by their chemical formulas Cu 2 ⁢ ZnSnS 4 {\mathrm{Cu}_{2}\mathrm{Zn}\mathrm{Sn}\mathrm{S}_{4}} and Si {\mathrm{Si}} , respectively, by the application of different energies and incidence angles. From the obtained results, firstly we deduce that the best sputtering angle is 85 ∘ {85^{\circ}} ; in the same time, CZTS {\mathrm{CZTS}} is more efficient comparing to the Si {\mathrm{Si}}. Secondly, with the application of this angle ( 85 ∘ {85^{\circ}}) in the sputtering process for the CZTS {\mathrm{CZTS}} ( Cu 2 ⁢ ZnSnS 4 {\mathrm{Cu}_{2}\mathrm{Zn}\mathrm{Sn}\mathrm{S}_{4}}) and CIGS {\mathrm{CIGS}} represented by its chemical formula CuIn x ⁢ Ga (1 - x) ⁢ Se 2 {\mathrm{Cu}\mathrm{In}_{x}\mathrm{Ga}_{(1-x)}\mathrm{Se}_{2}} , and the variation of the bombardment energy in order to find the total ejected atoms from each element of these two materials, we deduce that the sulfide ( S 4 {\mathrm{S}_{4}}) and selenide ( Se 2 {\mathrm{Se}_{2}}) elements give the majority of the sputtering yield amount obtained. [ABSTRACT FROM AUTHOR]

The numerical simulation of hot and low density plasmas using the Vlasov–Poisson model is necessary for many practical applications such as the characterization of laboratory and astrophysical plasmas. The numerical treatment of the Vlasov equation is addressed using Eulerian methods when high precision and low noise are required. Among these methods, we highlight those based on finite-volumes without splitting, which have shown to be a good option for capturing small structures in phase space with low dissipation while preserving positivity. The problem is that kinetic simulations usually require the discretization of 3–6-dimensional phase-spaces which results in a huge number of ordinary differential equations (ODEs). This stands out the importance of using efficient schemes for the time integration. In this article, linear multistep methods are implemented for the time stepping of the resulting equations, and compared against traditional Runge–Kutta ones. Schemes with built-in error estimation are also implemented in an attempt to perform adaptive stepsize control. Their accuracy, stability and computational cost are compared through the simulation of classical benchmark problems for the two-dimensional Vlasov–Poisson system. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the convergence analysis of a class of asymptotic preserving particle schemes (Filbet and Rodrigues in SIAM J. Numer. Anal. 54(2):1120–1146, 2016) for the Vlasov equation with a strong external magnetic field. In this regime, classical Particle-in-Cell methods are subject to quite restrictive stability constraints on the time and space steps, due to the small Larmor radius and plasma frequency. The asymptotic preserving discretization that we are going to study removes such a constraint while capturing the large-scale dynamics, even when the discretization (in time and space) is too coarse to capture fastest scales. Our error bounds are explicit regarding the discretization, stiffness parameter, initial data and time. [ABSTRACT FROM AUTHOR]

This paper is devoted to the linearized Vlasov–Poisson–Fokker–Planck system in presence of an external potential of confinement. We investigate the large time behaviour of the solutions using hypocoercivity methods and a notion of scalar product adapted to the presence of a Poisson coupling. Our framework provides estimates which are uniform in the diffusion limit. As an application in a simple case, we study the one-dimensional case and prove the exponential convergence of the nonlinear Vlasov–Poisson–Fokker–Planck system without any small mass assumption. [ABSTRACT FROM AUTHOR]

By a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels 1 and -γ{-\gamma}, respectively, where 0

We introduce a family of boundary confinements for Coulomb gas ensembles, and study them in the two-dimensional determinantal case of random normal matrices. The family interpolates between the free boundary and hard edge cases, which have been well studied in various random matrix theories. The confinement can also be relaxed beyond the free boundary to produce ensembles with fuzzier boundaries, i.e., where the particles are more and more likely to be found outside of the boundary. The resulting ensembles are investigated with respect to scaling limits and distribution of the maximum modulus. In particular, we prove existence of a new point field—a limit of scaling limits to the ultraweak point when the droplet ceases to be well defined. [ABSTRACT FROM AUTHOR]

We consider the Vlasov–Poisson system that is equipped with an external magnetic field to describe the time evolution of the distribution function of a plasma. An optimal control problem where the external magnetic field is the control itself has already been investigated by Knopf (Calc Var 57:134, 2018). However, in real technical applications it will not be possible to choose the control field in such a general fashion as it will be induced by fixed field coils. In this paper we will use the fundamentals that were established by Knopf (Calc Var 57:134, 2018) to analyze an optimal control problem where the magnetic field is a superposition of the fields that are generated by N fixed magnetic field coils. Thereby, the aim is to control the plasma in such a way that its distribution function matches a desired distribution function at some certain final time T as closely as possible. This problem will be analyzed with respect to the following topics: existence of a globally optimal solution, necessary conditions of first order for local optimality, derivation of an optimality system, sufficient conditions of second order for local optimality and uniqueness of the optimal control under certain conditions. [ABSTRACT FROM AUTHOR]

This paper is devoted to the numerical approximation of a three temperature plasma model: one for the ions, one for the electrons and one for the radiation (photons). A reformulation of the model is proposed that allows to build a convex combination-based scheme that unconditionally satisfies a maximum principle, at each sub-iteration of the non-linear iterative process. This yields a very robust scheme that can handle stiff source terms. In addition, the methodology is extended to include the contribution of a radiative flux (Rosseland diffusion approximation) and electronic and ionic conductivities (Spitzer–Härm diffusion approximation). Several numerical results are carried out to demonstrate the interest of the numerical approach. [ABSTRACT FROM AUTHOR]

We study existence and uniqueness of the solution to the Vlasov–Poisson system describing a plasma constituted by different species evolving in R 3 , whose particles interact via the Coulomb potential. The species can have both positive or negative charge. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law, extending a result contained in Caprino et al. (J Stat Phys 169:1066–1097,2017), which was restricted to finite total mass. [ABSTRACT FROM AUTHOR]

We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of nonnegative distribution functions f + and f - representing two species of charged matter with positive and negative charge, respectively. If their initial velocities are small compared to the speed of light, c , then in lowest order, the Newtonian or classical limit, their motion is governed by the Vlasov–Poisson system. We investigate higher-order corrections with an explicit control on the error terms. The Darwin order correction, order | v ¯ / c | 2 , has been proved previously. In this contribution, we obtain the dissipative corrections due to radiation damping, which are of order | v ¯ / c | 3 relative to the Newtonian limit. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order. [ABSTRACT FROM AUTHOR]

We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic field F μ ν that is the sum of a plane travelling wave F t μ ν (c t - z) and a static part F s μ ν (x , y , z) ; it adopts the light-like coordinate ξ = c t - z instead of time t as an independent variable. We illustrate it in a few cases of extreme acceleration, first of an isolated particle, then of electrons in a plasma in plane hydrodynamic conditions: the Lorentz–Maxwell and continuity PDEs can be simplified or sometimes even completely reduced to a family of decoupled systems of ordinary ones; this occurs e.g. with the impact of the travelling wave on a vacuum-plasma interface (what may produce plasma waves or the slingshot effect). [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a new discontinuous finite element idea for the time fractional diffusion-wave equation defined in bounded domain. The time fractional derivatives are described in the Caputo's sense. By applying the sine transform on the time fractional diffusion-wave equation, we make the equation depend on time. Then we use definition of Caputo's derivative and by defining l-degree discontinuous finite element with interpolated coefficients we solve the mentioned equation. Error estimate, existence and uniqueness are proved. Finally, the theoretical results are tested by some numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of an ionization wave propagation in air, described by a coupled set of convection-diffusion-reaction equations and a Poisson equation. The standard three-species and more complex eleven-species models with simple chemistry are formulated. The PDEs are solved by a finite volume method that is theoretically second order in space and time on an unstructured adaptive grid. The upwind scheme and the diamond scheme are used for the discretization of the convective and diffusive fluxes, respectively. The Poisson equation is also discretized by the diamond scheme. The results of both models are compared in details for a test case. The influence of physically pertinent boundary conditions at electrodes is also presented. Finally, we deal with numerical accuracy study of implicit scheme in two variants for simplified standard model. It allows us in the future to compute simultaneously and efficiently a process consisting of short time discharge propagation and long-term after-discharge phase or repetitively pulsed discharge. [ABSTRACT FROM AUTHOR]

We study the linearized Vlasov–Poisson–Ampère equation for non-constant Boltzmannian states with one region of trapped particles in dimension one and construct the eigenstructure in the context of the scattering theory. This is based on the use of semi-discrete variables (moments in velocity), and it leads to a new Lippmann–Schwinger variational equation. The continuity in quadratic norm of the operator is proved, and the well posedness is proved for a small value of the scaling parameter. It gives a proof of Linear Landau damping for inhomogeneous Boltzmannian states. The linear HMF model is an example. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of the Vlasov-Poisson system in the presence of radiation damping. A propagation result for velocity moments of order k > 3 is established in (Kunze and Rendall in Ann. Henri Poincaré 2:857–886, 2001). In this paper, we prove existence of global solutions propagating velocity and velocity-spatial moments of order k > 2 and establish an explicit polynomially growing in time bound on the moments. [ABSTRACT FROM AUTHOR]

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa-Wakatani (HW) equations were proposed in 1983. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Metallic nanoparticles have unique optical properties such as localized surface plasmon resonance (LSPR) effect, which can be used to improve the energy absorption and photocatalytic properties of semiconductor bases. In this paper, we construct a model to study the influence of Ag or Au nanoparticles (cubes or spheres) on the solar energy absorption and photocatalytic properties of nitrogen doped TiO 2 (or N-TiO 2 ). Effects of specific nanoparticle coupling parameters, such as particle shape, size, doping period (metal–metal distance) and separation distance (metal–semiconductor distance), on the properties of N-TiO 2 are studied in detail. We show that the photocurrent improvement can be optimized by setting suitable geometric parameters. In particular, the separation distance between metallic nanoparticles and N-TiO 2 D should be around 6–7 nm, and the period of doping P should be around 360 nm. The silver cubes with edge length L = 120 n m show the best performance. The results can help the design of solar energy materials, in which metallic nanoparticles may play an important role. [ABSTRACT FROM AUTHOR]

A numerical method is developed for the spatially homogeneous Fokker–Planck–Landau (FPL) equation for the case of Coulomb collisions. The equation is put into a form so that finite difference methods for parabolic type PDE’s can be applied. Through a transformation of variables the velocity space computation is reduced to a bounded domain, and finite differencing is done with a well defined, exact, boundary condition corresponding to | v | at infinity. For the discretization in time implicit differencing is used. An analysis is carried out on the discrete approximation as applied to a linear FPL equation, and for the linear equation it is proved that the numerical method is unconditionally stable and convergent. Computational work is then done that demonstrates the unconditional stability and accuracy of the numerical method for the nonlinear FPL equation. [ABSTRACT FROM AUTHOR]

Classification of optimal group-invariant solutions has been carried out for cylindrical Korteweg-de Vries equation. It is a nonlinear evolution equation often found in studies of fluid mechanics and plasmas. An optimal system of subalgebras is obtained for the group of Lie generators associated with the equation, and then, the group-invariant solutions are obtained for each member in the optimal class. The procedure for calculating other group-invariant solutions from the optimal class is also illustrated with an example. [ABSTRACT FROM AUTHOR]

We investigate the Cauchy problem for the Vlasov-Poisson system with radiation damping. By virtue of energy estimate and a refined velocity average lemma, we establish the global existence of nonnegative weak solution and asymptotic behavior under the condition that initial data have finite mass and energy. Furthermore, by building a Gronwall inequality about the distance between the Lagrangian flows associated to the weak solutions, we can prove the uniqueness of weak solution when the initial data have a higher order velocity moment. [ABSTRACT FROM AUTHOR]

In this paper we establish the asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is investigated in the three dimensional case with a non-constant magnetic field. In the long time asymptotic limit, the motion can be split in two parts: one stationary flow along the lines of the magnetic field and the guiding center motion in the orthogonal plane of the magnetic field where classical drift velocities and invariants (magnetic moment) are recovered. [ABSTRACT FROM AUTHOR]

We briefly report on some results regarding the impact of very short and intense laser pulses on a cold, low-density plasma initially at rest, and the consequent acceleration of plasma electrons to relativistic energies. Locally and for short times the pulse can be described by a transverse plane electromagnetic travelling-wave and the motion of the electrons by a purely Magneto-Fluido-Dynamical model with a very simple dependence on the transverse electromagnetic potential, while the ions can be regarded as at rest; the Lorentz-Maxwell and continuity equations are reduced to the Hamilton equations of a Hamiltonian system with 1 degree of freedom, in the case of a plasma with constant initial density, or a collection of such systems otherwise. We can thus describe both the well-known wakefield behind the pulse and the recently predicted slingshot effect, i.e. the backward expulsion of high energy electrons just after the laser pulse has hit the surface of the plasma. [ABSTRACT FROM AUTHOR]

We consider the zero-resistivity limit for Hasegawa–Wakatani equations in a cylindrical domain when the initial data are Stepanov almost-periodic in the axial direction. First, we prove the existence of a solution to Hasegawa–Wakatani equations with zero resistivity; second, we obtain uniform a priori estimates with respect to resistivity. Such estimates can be obtained in the same way as for our previous results; therefore, the most important contribution of this paper is the proof of the existence of a local-in-time solution to Hasegawa–Wakatani equations with zero resistivity. We apply the theory of Bohr–Fourier series of Stepanov almost-periodic functions to such a proof. [ABSTRACT FROM PUBLISHER]