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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]

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 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]

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]

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]

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]

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 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]

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]

Electric propulsion is now a successful method for primary and secondary propulsion of deep space long-duration missions and for geosynchronous satellite attitude control. The Plasma Physics Laboratory of UnB has been developing a permanent magnet Hall thruster (PHALL) for the UNIESPAÇO program, part of the Brazilian space activities program (PNAE) since 2004. The idea of using an array of permanent magnets, instead of an electromagnet, to produce a radial magnetic field inside the plasma channel of the thruster is very significant. It allows the development of a Hall thruster with power consumption low enough to be used in small- and medium-size satellites. The PHALL project consists on plasma source design, construction and characterization of the Hall-type propulsion engine using several plasma diagnostics sensors. PHALL is based on a plasma source in which a Hall current is generated inside a cylindrical channel with an axial electric field produced by a ring anode and a radial magnetic field produced by permanent magnets. In this work, a brief description of the plasma propulsion engine, its diagnostics instrumentation and measured plasma parameters with a focus for possible applications of PHALL on orbit transfer maneuvering for future Brazilian geostationary satellite space missions is shown. More specifically, we will show plasma density and temperature space profiles inside and outside the thruster channel, ion temperature measurements based on Doppler broadening of spectral lines and ion energy measurements. Based on the measured plasma parameters we construct an aptitude figure of the PHALL. It contains the specific impulse, total thrust, propellant flow rate and power consumption necessary for orbit raising of satellites. Based on previous studies of geosynchronous satellite orbit positioning we perform numerical simulations of satellite orbit raising from an altitude of 700-36,000 km using a PHALL operating in the 100-500 mN thrust range. To perform these calculations integration techniques were used. The main simulation parameters were orbit raising time, fuel mass, total satellite mass, thrust and exhaust velocity. We conclude by comparing our results with results obtained with known space missions performed with Hall thrusters. [ABSTRACT FROM AUTHOR]

In this paper, the Cauchy problem for the nonisentropic Euler-Maxwell system with a nonconstant background density is studied. The global existence of classical solution is constructed in three space dimensions provided the initial perturbation is sufficiently small. The proof is mainly based on classical energy estimate and the techniques of symmetrizer. And the time decay of the solution is also established by combining the decay estimate of the Green's function with some time-weighted estimate. [ABSTRACT FROM AUTHOR]

In this paper we study the quasineutral limit of the two-species Vlasov-Poisson system. For well-prepared initial data, we establish the convergence of the Vlasov-Poisson system to the pressureless Euler system as the Debye length tends to zero. [ABSTRACT FROM AUTHOR]

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa-Wakatani equations were proposed in 1983. In this paper, we consider the zero-resistivity limit for the Hasegawa-Wakatani equations in a cylindrical domain when the initial data are Stepanov-almost-periodic in the axial direction. We prove two results: one is the existence and uniqueness of a strong global in time Stepanov-almost-periodic solution to the initial boundary value problem for the Hasegawa-Mima-like equation; another is the convergence of the solution of the Hasegawa-Wakatani equations to that of the Hasegawa-Mima-like equation established at the first stage as the resistivity tends to zero. In order to obtain a priori estimates of the Stepanov-almost-periodic solutions to our problems, we have to overcome some difficulties. In the proof, we prepare some lemmas for the Stepanov-almost-periodic functions and then obtain a priori estimates. [ABSTRACT FROM AUTHOR]

We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption , namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile, we obtain the global existence of solutions based on energy method. [ABSTRACT FROM AUTHOR]

We discuss some general properties of the Landau kinetic equation. In particular, the difference between the 'true' Landau equation, which formally follows from classical mechanics, and the 'generalized' Landau equation, which is just an interesting mathematical object, is stressed. We show how to approximate solutions to the Landau equation by the Wild sums. It is the so-called quasi-Maxwellian approximation related to Monte Carlo methods. This approximation can be also useful for mathematical problems. A model equation which can be reduced to a local nonlinear parabolic equation is also constructed in connection with existence of the strong solution to the initial value problem. A self-similar asymptotic solution to the Landau equation for large v and t is discussed in detail. The solution, earlier confirmed by numerical experiments, describes a formation of Maxwellian tails for a wide class of initial data concentrated in the thermal domain. It is shown that the corresponding rate of relaxation (fractional exponential function) is in exact agreement with recent mathematically rigorous estimates. [ABSTRACT FROM AUTHOR]

We construct and analyze a numerical scheme for the two-dimensional Vlasov-Poisson system based on a backward-Euler (BE) approximation in time combined with a mixed finite element method for a discretization of the Poisson equation in the spatial domain and a discontinuous Galerkin (DG) finite element approximation in the phase-space variables for the Vlasov equation. We prove the stability estimates and derive the optimal convergence rates depending upon the compatibility of the finite element meshes, used for the discretizations of the spatial variable in Poisson (mixed) and Vlasov (DG) equations, respectively. The error estimates for the Poisson equation are based on using Brezzi-Douglas-Marini (BDM) elements in L and H, s>0, norms. [ABSTRACT FROM AUTHOR]

The stationary solutions of the Vlasov-Poisson system for a plasma are studied with general diffusive boundary conditions. The distribution function $$f(x,v)$$ , which depends on the local energy and angular momentum, is determined uniquely under certain integrability and decay assumptions on the diffusive kernels and the particle injection intensities. The resulting nonlinear Poisson equation is then solved for the electric potential $$\phi (x)$$ . We study the existence and uniqueness of its solutions in one and higher dimensions under a variety of settings. [ABSTRACT FROM AUTHOR]

We are concerned with global well-posedness of the three-dimensional Vlasov–Poisson system with radiation damping. First, we show that global C 1 solutions verifying specified decay conditions are stable under small perturbations. As a consequence, we obtain that a small perturbation of a monopolar and spherically symmetric plasma launches a global C 1 solution that preserves quasi-spherical symmetry at the macroscopic level. Second, we show that an initially quasi-neutral datum with C 1 regularity launches a global classical solution that propagates quasi-neutrality at the macroscopic level. Finally, we obtain better decay estimates for the radiation damping in both cases. [ABSTRACT FROM AUTHOR]