Problems In Plasma Physics Research Articles

Three-Dimensional Direct-Implicit Particle-in-Cell Model Using Trilinear Anisotropic Immersed-Finite-Element for Plasma Propulsion

Efficiently and accurately calculating the plasma transport process is one of the difficulties in aerospace plasma application simulation, especially in the magnetic sail spacecraft applications that have a huge size. This paper develops a three-dimensional trilinear anisotropic immersed-finite-element direct-implicit particle-in-cell (IFE-DIPIC) model to solve the problem of large-scale, long-term evolution plasma with complex interfaces. The model uses the DIPIC method to track the motion of particles in the plasma while simulating the anisotropic electric field containing an interface by using a modified trilinear anisotropic IFE method. Compared to the previous models, the developed model in this paper allows for the use of larger spatial and time steps in the Cartesian meshes without inducing numerical divergence. Using an interface-independent mesh avoids redundant interpolation in the PIC method, further improving efficiency. These advantages significantly improve the efficiency in solving actual complex three-dimensional plasma physics problems. The accuracy, efficiency, stability, and applicability of the proposed model are proved through numerical examples and the application in magnetic sail. The simulation results indicate that the developed model can efficiently simulate the actual working conditions of magnetic sails. The performance is significantly influenced by both the direction and magnitude of the magnetic moment.

Demonstration of metaplectic geometrical optics for reduced modeling of plasma waves.

The Wentzel, Kramers, and Brillouin (WKB) approximation of geometrical optics is widely used in plasma physics, quantum mechanics, and reduced wave modeling, in general. However, it is well-known that the approximation breaks down at focal and turning points. In this paper, we present an unsupervised numerical implementation of the recently developed metaplectic geometrical optics framework, which extends the applicability of geometrical optics beyond the limitations of WKB, such that the wave field remains finite at caustics. The implementation is in 1D and uses a combination of Gauss-Freud quadrature and barycentric rational function inter- and extrapolation to perform an inverse metaplectic transform numerically. The capabilities of the numerical implementation are demonstrated on Airy's and Weber's equations, which both have exact solutions to compare with. Finally, the implementation is applied to the plasma physics problem of linear conversion of X mode to electron Bernstein waves at the upper hybrid layer and a comparison is made with results from fully kinetic particle-in-cell simulations. In all three applications, we find good agreement between the exact results and a reduced wave modeling paradigm of metaplectic geometrical optics.

Hybrid Kinetic Modeling of the Magnetosheath Impulsive Plasma Cloud Penetration Through the Magnetopause and Comparison With MMS and Other Spacecraft Observations

AbstractThis research examines the plasma processes under penetration of the plasma clouds (plasmoids) across the magnetopause which is modeled as a tangential discontinuity (TD). Cases with the parallel magnetic field in both sides out of the TD are under investigation. Plasma parameters and magnetic field were chosen from the MMS mission and other spacecraft observations. The results are important for understanding the following basic space plasma physics problems: (a) plasma cloud deformation and strong phase mixing with magnetospheric plasma; (b) the transfer of mass, momentum and energy of magnetosheath and magnetic cloud plasma into magnetospheric plasmas; (c) necessary conditions for plasma cloud penetration via the magnetopause; (d) wave generation by plasma clouds inside the magnetopause.

Enhanced Energy Conversion by Turbulence in Collisionless Magnetic Reconnection

Abstract Magnetic reconnection and turbulence are two of the most significant mechanisms for energy dissipation in collisionless plasma. The role of turbulence in magnetic reconnection poses an outstanding problem in astrophysics and plasma physics. It is still unclear whether turbulence can modify the reconnection process by enhancing the reconnection rate or energy conversion rate. In this study, utilizing unprecedented high-resolution data obtained from the Magnetospheric Multiscale spacecraft, we provide direct evidence that turbulence plays a vital role in promoting energy conversion during reconnection. We reached this conclusion by comparing magnetotail reconnection events with similar inflow Alfvén speed and plasma β but varying amplitudes of turbulence. The disparity in energy conversion was attributed to the strength of turbulence. Stronger turbulence generates more coherent structures with smaller spatial scales, which are pivotal contributors to energy conversion during reconnection. However, we find that turbulence has negligible impact on particle heating, but it does affect the ion bulk kinetic energy in these two events. These findings significantly advance our understanding of the relationship between turbulence and reconnection in astrophysical plasmas.

Electron Heating by Magnetic Pumping and Whistler-mode Waves

The investigation of mechanisms responsible for the heating of cold solar wind electrons around the Earth’s bow shock is an important problem in heliospheric plasma physics because such heating is vitally required to run the shock drift acceleration at the bow shock. The prospective mechanism for electron heating is magnetic pumping, which considers electron adiabatic (compressional) heating by ultralow-frequency waves and simultaneous scattering by high-frequency fluctuations. Existing models of magnetic pumping have operated with external sources of such fluctuations. In this study, we generalize these models by introducing the self-consistent electron scattering by whistler-mode waves generated due to the anisotropic electron heating process. We consider an electron population captured within a magnetic trap created by ultralow-frequency waves. Periodical adiabatic heating and cooling of this population drives the generation of whistler-mode waves scattering electrons in the pitch-angle space. The combination of adiabatic heating and whistler-driven scattering provides electron acceleration and the formation of a suprathermal electron population that can further participate in the shock drift acceleration.

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. We believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

Equilibria as boundary value problems under Lie transformations

The use of transformations recently gained attention in obtaining invariant solutions to the equilibrium problem of plasma physics. In all of the cases considered, the new solutions were related to a (Generalized) Grad–Shafranov equation. In the same context, the present study focuses on the issue of an axisymmetric, toroidal plasma equilibrium as a boundary value problem associated with new solutions obtained by means of Lie group transformations. It appears that in all the cases examined, only a single infinitesimal generator of the symmetry group permits closed boundary that remains invariant under the transformation. The respective equilibrium, in addition to a peculiar axisymmetric magnetically confined plasma with current hole reaching the axis of symmetry, describes a planet's magnetosphere for low heights.

A detailed numerical study of field line random walk in magnetic turbulence

ABSTRACT A fundamental problem in space plasma physics and astrophysics is to understand the behaviour of magnetic field lines in turbulence. In the past it was controversial what aspects of turbulence are most important in field line random walk theory. In the current paper we employ numerical tools, commonly referred to as simulations, to gain more insight. In particular, we explore the importance of the energy range of the turbulence spectrum, spectral anisotropy, as well the existence of a component of the turbulent magnetic field parallel with respect to the mean magnetic field. The latter point is directly related to the question whether field line random walk in compressible turbulence behaves differently compared to random walk in incompressible turbulence.

Estimates of Proton and Electron Heating Rates Extended to the Near-Sun Environment

A central problem of space plasma physics is how protons and electrons are heated in a turbulent, magnetized plasma. The differential heating of charged species due to dissipation of turbulent fluctuations plays a key role in solar wind evolution. Measurements from previous heliophysics missions have provided estimates of proton and electron heating rates beyond 0.27 au. Using Parker Solar Probe (PSP) data accumulated during the first 10 encounters, we extend the evaluation of the individual rates of heat deposition for protons and electrons to a distance of 0.063 au (13.5 R ⊙) in the newly formed solar wind. The PSP data in the near-Sun environment show different behavior of the electron heat conduction flux from what was predicted from previous fits to Helios and Ulysses data. Consequently, the empirically derived proton and electron heating rates exhibit significantly different behavior than previous reports, with the proton heating becoming increasingly dominant over electron heating at decreasing heliocentric distances. We find that the protons receive about 80% of the total plasma heating at ≈13 R ⊙, slightly higher than the near-Earth values. This empirically derived heating partition between protons and electrons will help to constrain theoretical models of solar wind heating.

THREE-LAYER SCHEME FOR SOLVING THE RADIATION DIFFUSION EQUATION

A method has been developed for the numerical solution of a nonlinear equation describing the diffusion transfer of radiation energy. The method is based on the introduction of the second time derivative with a small parameter into the parabolic equation and an explicit difference scheme. Explicit approximation of the initial equation makes it possible to implement on its basis an algorithm that is effectively adapted to the architecture of high-performance computing systems. The new scheme provides, in comparison with the original scheme, a larger time integration step and a sufficiently high resolution quality of the solution structure, providing the second order of accuracy. A heuristic algorithm for choosing the parameters of a three-layer difference scheme is proposed. A promising field of application of the method can be problems of plasma physics and astrophysics.

Hybrid-VPIC: An open-source kinetic/fluid hybrid particle-in-cell code

Hybrid-VPIC is an extension of the open-source high-performance particle-in-cell (PIC) code VPIC incorporating hybrid kinetic ion/fluid electron solvers. This paper describes the models that are available in the code and gives an overview of applications of the code to space and laboratory plasma physics problems. Particular choices in how the hybrid solvers were implemented are documented for reference by users. A few solutions for handling numerical complications particular to hybrid codes are also described. Special emphasis is given to the computationally taxing problem of modeling mix in collisional high-energy-density regimes, for which more accurate electron fluid transport coefficients have been implemented for the first time in a hybrid PIC code.

Some new soliton solutions to the (3 + 1)-dimensional generalized KdV-ZK equation via enhanced modified extended tanh-expansion approach

In this article, The (3 + 1)-dimensional generalized Korteweg-de-Vries-Zakharov-Kuznetsov equation (gKdV-ZKe) which explains the influence of the magnetic field on the weak nonlinear ion-acoustic waves investigated in the field of plasma conjured up including both cold and hot electrons. GKdV-zk techniques solutions are obtained using the improved modified extended tanh expansion method, which is one of the most efficient algebraic methods for obtaining accurate solution to nonlinear partial differential equations. We aim to show how the analyzed model’s parameter impact soliton behavior by choosing different bright and single soliton forms and by developing various analytical optical soliton solutions for the explored equation. MethodologyIn order to apply the suggested method, we used a complex wave transform to derive the nonlinear ordinary differential form of the analyzed equation. Then, using the method, we were able to obtain the polynomial form, leading to a set of linear equations. The conclusion of solving the linear equations problem, the outcomes of the analyzed model, and the suggested strategy are all included in different solution sets. After choosing the appropriate set from these sets, using the solution functions, and utilizing the wave transformation provided by the approach, we were able to arrive at the optical soliton solutions by providing the central equation. FindingThe proposed method has successfully produced a number of soliton solutions and several analytical optical solutions to such model. The research shows that the parameters of the model may have a variety of effects on the behavior of solitons, categories based on the soliton type. The findings we get in this article can be used to research and compare numerical and experimental data with analytical solving problems in plasma physics. OriginalityThis study differs from others in that it assessed the impact that parameters of the model have on the actions of solitons, despite the fact that the proposed technique was applied for the first time on the topic under investigation and numerous soliton types were created. This study focuses on the influence of model parameters on solitons behavior.

In search of a data-driven symbolic multi-fluid ten-moment model closure

The inclusion of kinetic effects into fluid models has been a long standing problem in magnetic reconnection and plasma physics. Generally, the pressure tensor is reduced to a scalar which is an approximation used to aid in the modelling of large scale global systems such as the Earth's magnetosphere. This unfortunately omits important kinetic physics which have been shown to play a crucial role in collisionless regimes. The multi-fluid ten-moment model, however, retains the full symmetric pressure tensor. The ten-moment model is constructed by taking moments of the Vlasov equation up to second order, and includes the scalar density, the vector bulk-flow and the symmetric pressure tensor for a total of ten separate components. Use of the multi-fluid ten-moment model requires a closure which truncates the cascading system of equations. Here we look to leverage data-driven methodologies to seek a closure which may improve the physical fidelity of the ten-moment multi-fluid model in collisionless regimes. Specifically, we use the sparse identification of nonlinear dynamics (SINDy) method for symbolic equation discovery to seek the truncating closure from fully kinetic particle-in-cell simulation data, which inherently retains the relevant kinetic physics. We verify our method by reproducing the ten-moment model from the particle-in-cell (PIC) data and use the method to generate a closure truncating the ten-moment model which is analysed through the nonlinear phase of reconnection.

About one boundary-value problem arising in modeling dynamics of groundwater

Modeling the movement of moisture in the soil is of great importance for assessing the impact of agricultural land on surface water bodies and, consequently, on the natural environment and humans. This is because huge volumes of pollutants from the fields (pesticides, mineral fertilizers, nitrates, and nutrients contained in them) are transferred to reservoirs by filtering moisture. Different methods solve all these tasks. The method of natural analogies is based on the analysis of graphs of fluctuations in groundwater level. To apply this method on irrigated lands, it is necessary to have a sufficiently studied irrigated area with similar natural, organizational and economic conditions. The successful application of this method, based on the fundamental theory of physical similarity, mainly depends on the availability of a sufficiently close comparison object, which is quite rare in practice. Physical modeling is often used to construct dams and other hydraulic structures. Previously, the method of electrical modeling was also widely used. It was further found that nonlocal boundary conditions arise in the problems of predicting soil moisture, modeling fluid filtration in porous media, mathematical modeling of laser radiation processes, and plasma physics problems, as well as mathematical biology.

Анализ процессов формирования θ-пинча в лабораторных и природных условиях

The processes that occur during the formation of pinch discharges have been intensively studied and are being studied in programs for the implementation of controlled thermonuclear fusion, however, it is still far from a complete understanding of the mechanisms during the discharge. There are significant achievements on the way to the implementation of CTS in magnetic traps, but the final conclusion about the advantages of this solution is still far away. This work is aimed at improving one of the problems of plasma physics, namely, explaining the fact of twisting and compression of the plasma flow in the θ-pinch. At the same time, an analysis is given of the possible reasons for the formation of this type of ionized air flows in natural conditions, namely, during tornadoes and similar phenomena (tornadoes and others). As one of the arguments for such a generalization, the fact of the existence of a deafening crack on the surface of the earth at the bases of a tornado is used, which is typical only for a stream of water droplets with a high potential, that is, a vertical current. As a basis for the analysis, the results of the experimental and theoretical analysis of a periodic discharge in a liquid flow (PDLF), which were thoroughly studied earlier, were taken.

Quadrature-based moment methods for kinetic plasma simulations

Quadrature-based moment methods (QBMM) are applied to rarefied gas flow and plasma physics problems represented by the Boltzmann equation or the Vlasov-Poisson system of equations. QBMM are a computationally advantageous alternative to both direct Eulerian and Lagrangian particle solvers, able to provide a noise-free solution to the Boltzmann equation and capture non-equilibrium velocity distribution functions (VDF) without excessive computational cost. To provide a closure of the moment equations, the VDF is assumed to be represented by the sum of weighted kernel functions that are placed at given velocity abscissas. Three QBMM approaches, QMOM (Dirac delta kernels), HyQMOM (hyperbolic QMOM), and EQMOM (Gaussian kernels), are applied to canonical one-dimensional rarefied gas flow and plasma physics problems. A new algorithm for EQMOM that is able to treat pathological VDFs and provide control over large abscissas for more than two nodes is developed. QMOM and EQMOM are suitable for problems where the flow does not have shock-like features (for QMOM) or a discontinuity in the VDF (for EQMOM) and where the VDF is far from non-equilibrium and features strong phase-mixing. HyQMOM is generally applicable to all test problems and yields good representations of both the moments and the VDF. HyQMOM also provides significant wall-time improvement (factor of 10–100) compared to other direct Eulerian solvers.

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

Data-driven discovery of reduced plasma physics models from fully kinetic simulations

At the core of some of the most important problems in plasma physics---from controlled nuclear fusion to the acceleration of cosmic rays---is the challenge to describe nonlinear, multiscale plasma dynamics. The development of reduced plasma models that balance between accuracy and complexity is critical to advancing theoretical comprehension and enabling holistic computational descriptions of these problems. Here we report the data-driven discovery of accurate reduced plasma models, in the form of partial differential equations, directly from first-principles particle-in-cell simulations. We achieve this by using an integral formulation of sparsity-based model-discovery techniques and show that this is crucial to robustly identify the governing equations in the presence of discrete particle noise. We demonstrate the potential of this approach by recovering the fundamental hierarchy of plasma physics models---from the Vlasov equation to magnetohydrodynamics. Our findings show that this data-driven methodology offers a promising route to accelerate the development of reduced theoretical models of complex nonlinear plasma phenomena and to design computationally efficient algorithms for multiscale plasma simulations.

Optical spectrograph for the Takhomag-International Space Station space-based spectromagnetograph

Subject of study. This paper is the second part of a series devoted to the development of the optical spectrograph designed for the Takhomag-International Space Station space-based spectromagnetograph planned to be deployed in the Russian segment of the International Space Station. The first paper of the series published in this journal describes a solar optical telescope in the spectromagnetograph. Aim of study. This study aimed to design an optical spectrograph for the Takhomag-International Space Station spectromagnetograph with properties required for the measurement of the Zeeman effect at selected spectral lines under magnetic fields characteristic of the solar photosphere. Method. The design of the Takhomag-International Space Station spectrograph is a classic variation of the off-axis lens scheme of the Littrow spectrograph. FeI 6301.5 Å and FeI 6302.5 Å lines were chosen as working spectral lines. The lens-based spectrograph design enabled it to satisfy the requirements of its limited size without optical elements with aspherical surface shapes. Main results. Despite the hard constraints on mass and dimensions owing to the conditions of operation, the spectrograph enables the formation of almost aberrationless images (Marechal parameter exceeding λ/20) of the solar photosphere spectrum with an angular resolution of 0.35″ by the Rayleigh criterion that corresponds to the angular resolution of the solar optical telescope of the Takhomag-International Space Station spectromagnetograph with a spectral range of 2.52 Å and spectral resolution of approximately 30 mÅ. The spectral resolution is smaller than the widths of the spectral lines used in the range of 42.4 mÅ in intense spots to 49.1 mÅ in a calm photosphere that results from the chaotic motion of atoms along the line of sight and the unresolvable structure of microturbulent velocities. Practical significance. The development of the Takhomag-International Space Station spectromagnetograph will facilitate the solution of relevant problems of solar and plasma physics and provide the groundwork for preparing more complex missions involving solar research from small distances.

An implicit monolithic AFC stabilization method for the CG finite element discretization of the fully-ionized ideal multifluid electromagnetic plasma system

This study considers an implicit finite element formulation for an ideal fully-ionized multifluid electromagnetic plasma system. The formulation is based on fully-implicit Runge-Kutta time discretizations and a monolithic discrete algebraic flux corrected (AFC) continuous Galerkin (CG) spatial discretization of the coupled system. The AFC approach adds scalar artificial diffusion to the high-order, semi-discrete Galerkin method and uses mass lumping in the time derivative term. The result is a low-order method that attempts to enforce local-extremum-diminishing properties for the hyperbolic system. An element-based iterative limiter is applied to reduce the amount of artificial diffusion that is used in regions where the solution is smooth and the additional stabilization is not required. Two models are considered for the electromagnetics portion of the system: an electrostatic model, and a full Maxwell system with a parabolic divergence cleaning approach that enforces the required involutions on the electric and magnetic fields. Results are presented that demonstrate the accuracy and robustness of the formulation for smooth and discontinuous solutions to challenging plasma physics problems. This includes a demonstration that the solution of the full multifluid system yields the expected behavior in the ideal shock-MHD limit.