Problems In Plasma Physics Research Articles

Introduction

This issue of Journal of Physics: Conference Series includes 18 articles submitted by the participants of the XLVII International Zvenigorod Conference on Plasma Physics and Controlled Fusion (March 16–20, 2020). The conference is named after the town of Zvenigorod, Moscow region, where it has been held annually for 47 years. More than 500 scientists took part in the conference this year. The presented articles showcase a wide range of topical issues in the field of plasma physics that were discussed at the conference.Leading foreign scientists have participated in Zvenigorod conferences from the very first time they were organized. They were invited by the conference organizers to give talks on the challenging problems of plasma physics. By now several dozen of foreign scientists from the USA, Europe and Japan take part in the conference annually. They represent approximately 30 leading research centers working in different fields of plasma physics.Nowadays, the conference has expanded to include a large number of topics. It includes sessions on the magnetic confinement of high-temperature plasma, inertial fusion, processes in low-temperature plasma, physical principles of plasma and beam technologies, and topical issues of the ITER project. About 90 Russian research centers are usually represented at the conference. Among them are institutes of the Russian Academy of Sciences, research centers of Russian universities, institutes of the State Corporation ROSATOM, and other scientific organizations of the Russian Federation.

Ontological approach to formalization of knowledge in computational plasma physics

Computational plasma physics is a wide area of research, which includes a certain set of physical phenomena, mathematical equations, numerical methods, programming strategies, and hardware architectures that directly follow each other. To design an efficient code for solving a computational plasma physics problem, the researcher should have a clear understanding of the relationships between the concepts of physics, mathematics, computer science, and computer architecture. Ontology is one of the effective ways to realize (provide) such an understanding. Authors propose an approach to design an ontology which will show how physical phenomena determine mathematical equations being used, how the equations define numerical methods, and how methods enable programming strategies to form an architecture-efficient implementation of problem solution.

Dynamic load balancing with enhanced shared-memory parallelism for particle-in-cell codes

Furthering our understanding of many of today’s interesting problems in plasma physics – including plasma based acceleration and magnetic reconnection with pair production due to quantum electrodynamic effects – requires large-scale kinetic simulations using particle-in-cell (PIC) codes. However, these simulations are extremely demanding, requiring that contemporary PIC codes be designed to efficiently use a new fleet of exascale computing architectures. To this end, the key issue of parallel load balance across computational nodes must be addressed. We discuss the implementation of dynamic load balancing by dividing the simulation space into many small, self-contained regions or “tiles,” along with shared-memory (e.g., OpenMP) parallelism both over many tiles and within single tiles. The load balancing algorithm can be used with three different topologies, including two space-filling curves. We tested this implementation in the code Osiris and show low overhead and improved scalability with OpenMP thread number on simulations with both uniform load and severe load imbalance. Compared to other load-balancing techniques, our algorithm gives order-of-magnitude improvement in parallel scalability for simulations with severe load imbalance issues.

Robert May, 1936–2020: A man for all disciplines

Robert (Bob) May, Baron May of Oxford, a long-time International Member of the National Academy of Sciences, passed away on April 28, 2020, in Oxford, United Kingdom, from “frailties of old age, Alzheimer's disease, and pneumonia,” at the age of 84. He is survived by his wife Judith, his daughter Nome, and legions of students and colleagues. Across six decades, Bob had a transformative impact on myriad fields: mathematical biology, ecology, epidemiology, public policy, and finance. His intellect, sense of loyalty to colleagues and students, and commitment to humanity made him a towering giant in science and science policy. Robert M. May, c. 2004. Image credit: Royal Society/Laurence Bulaitis. Bob May was born in Sydney, Australia, where his talents as a mathematician were evident from an early age. Bob was trained in theoretical physics at the University of Sydney by the distinguished physicist Robbie Schafroth, receiving his PhD at 24 years old for his work on bosons and superconductivity. Nonetheless, May traced his good luck in mentorships back to his high school chemistry teacher Lenny Basser and was always quick to give accolades to the many influences on his development, from teachers and colleagues alike. For those who knew him, it was clear that he made it a point to pay forward this debt through his investment in his own students and others. After a postdoctoral stint with Max Krook at Harvard University—during which he met his future wife, Judith—Bob accepted a faculty position at the University of Sydney, and within a few years had risen to one of the first “Personal Professorships” at the university. In his early work, he focused on problems in plasma physics and related fields and quickly rose to prominence. However, soon after, concerned for the fate of the planet and feeling he had a … [↵][1]1To whom correspondence may be addressed. Email: slevin{at}princeton.edu. [1]: #xref-corresp-1-1

Non-standard magnetohydrodynamics equations and their implications in sunspots

In this work, we study the physics of plasma waves and magnetohydrodynamic (MHD) equilibrium of sunspots based on the concept of non-standard Lagrangians which play an important role in several branches of science. We derived the modified fluid equations from the Maxwell–Vlasov equation using the moment conventional procedure. Several new interaction terms between physical quantities arise in the non-standard MHD (NS-MHD) equations that give rise to additional features in plasma MHD. A number of fundamental problems in plasma physics are discussed including the non-relativistic dynamics of inviscid fluid subject to the gravitational field, linear waves in plasma MHD and MHD equilibrium of sunspots. For the case of magnetoacoustic wave, it was observed that the NS-MHD equations modify the dispersion relation and its corresponding velocity depends on the sign (positive or negative) of the free parameters introduced in the theory. The non-standard Alfvén velocity is greater than the standard Alfvén velocity for the negative sign and smaller for the positive sign. Besides, in the MHD equilibrium of sunspots, non-standard MHD extends the conventional problem by adding several constraints that lead to an emergence of very low temperature inside the magnetic flux tube comparable to what is observed in low-temperature superconductors. Additional consequences are discussed accordingly.

Abundant new analytical and approximate solutions to the generalized Schamel equation

An exact solution of partial differential equations provides a lot of information for a model. Since obtaining such answers is generally very difficult or in some cases impossible, having powerful analytical methods in determining them seems very necessary. Unlike numerical methods, these methods have fewer constraints such as stability, convergence, and approximation error. This paper aims to consider the generalized Schamel equation which arises in the modeling of some problems in plasma physics. Fortunately, by applying a new analytical method, a large number of exact solutions to the model are obtained. The structure used in the solutions specified in this method uses Jacobi elliptic functions. In another part of the paper, an effective numerical method, namely the reproducing kernel method is used to approximate the solutions of the equation. Numerical simulations of some acquired exact and approximate solutions are also included. It seems that the employed methods can be considered as effective, powerful, and straightforward methods of studying equations. The methods can also be utilized to investigate other partial differential equations.

Accurate Prediction of Clock Transitions in a Highly Charged Ion with Complex Electronic Structure.

We develop a broadly applicable approach that drastically increases the ability to predict the properties of complex atoms accurately. We apply it to the case of Ir^{17+}, which is of particular interest for the development of novel atomic clocks with a high sensitivity to the variation of the fine-structure constant and to dark matter searches. In general, clock transitions are weak and very difficult to identify without accurate theoretical predictions. In the case of Ir^{17+}, even stronger electric-dipole (E1) transitions have eluded observation despite years of effort, raising the possibility that the theoretical predictions are grossly wrong. In this work, we provide accurate predictions of the transition wavelengths and E1 transition rates for Ir^{17+}. Our results explain the lack of observations of the E1 transitions and provide a pathway toward the detection of clock transitions. The computational advances we demonstrate in this work are widely applicable to most elements in the periodic table and will allow us to solve numerous problems in atomic physics, astrophysics, and plasma physics.

Sensitivity-driven adaptive sparse stochastic approximations in plasma microinstability analysis

Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance – and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse grid approximations are an established approach to overcome these challenges. However, standard adaptivity is based on global information, thus properties such as lower intrinsic stochastic dimensionality or anisotropic coupling of the input directions, which are common in practical applications, are not fully exploited. We propose a novel structure-exploiting dimension-adaptive sparse grid approximation methodology using Sobol' decompositions in each subspace to introduce a sensitivity scoring system to drive the adaptive process. By employing sensitivity information, we explore and exploit the anisotropic coupling of the stochastic inputs as well as the lower intrinsic stochastic dimensionality. The proposed approach is generic, i.e., it can be formulated in terms of arbitrary approximation operators and point sets. In particular, we consider sparse grid interpolation and pseudo-spectral projection constructed on (L)-Leja sequences. The power and usefulness of the proposed method is demonstrated by applying it to the analysis of gyrokinetic microinstabilities in fusion plasmas, one of the key scientific problems in plasma physics and fusion research. In this context, it is shown that a 12D parameter space can be scanned very efficiently, gaining more than an order of magnitude in computational cost over the standard adaptive approach. Moreover, it allows for the uncertainty propagation and sensitivity analysis in higher-dimensional plasma microturbulence problems, which would be almost impossible to tackle with standard screening approaches.

Precise Derivation of the Intermediate Scale

A classical problem of plasma physics is the treatment of the plasma-wall transition. This can be reached in the presheath with a presheath scale, in the sheath with a sheath scale and between presheath and sheath with an “intermediate scale”. Riemann (J Tech Phys 41:89–121, 2000) published a derivation of the intermediate scale. In our calculation we take the non-quasineutral values for the ion density and the ion velocity at the point where the non-quasineutral solution of the potential is zero. This approach is consistent and valid also for small but finite values of the smallness parameter of the theory. An effect of taking the non-quasineutral values is that the potential is shifted, dependent on the magnitude of the smallness parameter. But this shifting has no consequences on the intermediate scale and so we get a similar result as K.-U. Riemann. Furthermore, we show that it is not necessary to take into account the temperature change in the vicinity of the sheath edge and that it is possible to work always strictly with the complete and normalized basic equations of the problem and not only with orders on the left or right hand side of these equations.

Screening potential and continuum lowering in a dense plasma under solar-interior conditions

An accurate description of the screening potential induced by a hot, dense plasma is a fundamental problem in atomic physics and plasma physics, and it plays a pivotal role in the investigation of microscopic atomic processes and the determination of macroscopic physical properties, such as opacities and equations of state as well as nuclear fusion cross sections. Recent experimental studies show that currently available analytical models of plasma screening have difficulty in accurately describing the ionization-potential depression, which is directly determined by the screening potential. Here, we propose a consistent approach to determine the screening potential in dense plasmas under solar-interior conditions from the free-electron micro-space distribution. It is assumed that the screening potential for an ion embedded in a dense plasma is predominately determined by the free electrons in the plasma. The free-electron density is obtained by solving the ionization-equilibrium equation for an average-atom model to obtain the average degree of ionization of the plasma. The proposed model was validated by comparing the theoretically predicted ionization-potential depression of a solid-density Si plasma with recent experiments. Our approach was applied to investigate the screening potential and ionization-potential depression of Si plasmas under solar-interior conditions over a temperature range of 150–500 eV and an electron-density range of 5.88 × 1022–3.25 × 1024 cm−3. It can be easily incorporated into atomic-structure codes and used to investigate basic atomic processes, such as photoionization, electron-ion collisional excitation and ionization, and Auger decay, in a dense plasma.

Development strategy for steady-state fusion volumetric neutron source based on the gas-dynamic trap

The paper presents the project and the development strategy of a continuously operating high-flux (>) fusion volumetric neutron source. The proposed facility is based on the gas-dynamic magnetic plasma confinement device with high-power () neutral beam injection. Project roadmap includes construction of several prototype installations addressing a specific set of physics and engineering problems, starting from the continuous operation of critical subsystems and ending with advanced plasma physics problems specific to axisymmetric mirror-based plasma confinement machines. The project aims to build the widest possible international collaboration to create a multi-purpose experimental facility, which could solve a set of problems most critical to deployment of economical fusion power worldwide. The paper details on the core principles of operation of a gas-dynamic neutron source, presents the parameters, expected performance and basic construction principles of intermediate and final devices, and outlines the ways to resolve the scientific and engineering challenges that constitute the project.

Matrix-Based Rational Interpolation for New Coupling Scheme Between MHD and Eddy-Current Numerical Models

In this article, a matrix-based Pade rational interpolation is used to couple a 3-D eddy-current code with a linear magneto-hydrodynamic (MHD) solver. This approach is a general methodology viable for multiphysics problems involving the coupling of an electromagnetic model with another nonalgebraic physical model, which has to be solved in a certain region of space. The matrix-based Pade interpolation has been applied to a typical plasma physics problem of modeling the plasma response to external perturbation, providing an accurate and reliable mathematical model viable for the feedback stabilization of resistive wall modes (RWMs) in fusion plasmas. The choice of matrix-based Pade interpolation gives a reliable approach for the considered problem and can be viewed as a convenient formalism for the coupling strategy in this class of multi-physics problems.

Introduction

This issue of Journal of Physics: Conference Series includes 31 articles submitted by the participants of the XLVI International Zvenigorod Conference on Plasma Physics and Controlled Fusion (March 18-22, 2019). The conference is named after the town of Zvenigorod, Moscow region, where it has been held annually for 46 years. More than 600 scientists took part in the conference this year. The presented articles showcase a wide range of topical issues in the field of plasma physics that were discussed at the conference.Leading foreign scientists have participated in Zvenigorod conferences from the very first time they were organized. They were invited by the conference organizers to give talks on the challenging problems of plasma physics. By now several dozen of foreign scientists from the USA, Europe, and Japan take part in the conference annually. They represent approximately 30 leading research centers working in different fields of plasma physics.Nowadays, the conference has expanded to include a large number of topics. It includes sessions on the magnetic confinement of high-temperature plasma, inertial fusion, processes in low-temperature plasma, physical principles of plasma and beam technologies, and topical issues of the ITER project. About 90 Russian research centers are usually represented at the conference. Among them are institutes of the Russian Academy of Sciences, research centers of Russian universities, institutes of the State Corporation ROSATOM, and other scientific organizations of the Russian Federation.The International Advisory Board of the International Zvenigorod Conference on Plasma Physics and Controlled Fusion consists of the leading scientists from around the world working in the field of plasma physics. The conference talks are selected by the Programming Committee comprised of leading Russian and foreign scientists.The full list of papers can be viewed on the conference website http://www.fpl.gpi.ru/Zvenigorod/XLVI/Zven_XLVI.html.The issue was edited by V.A. Ivanov, I.A. Grishina, and E.V. Voronova.

Hybrid numerical model of the plasma flow dynamics in open magnetic systems

The report provides a brief overview of the numerical models used to solve plasma physics problems. The necessity of using hybrid models is shown, and a hybrid model that can be used in computer modeling of plasma flows in open magnetic systems is considered in more detail. The features of using hybrid models in two-dimensional cylindrical coordinates are given. To solve the equations of particle motion, the Boris algorithm is considered and its improvement is proposed based on the analytical solution of equations at a time step. We present a number of results of numerical simulation of the interaction of plasma flows obtained on the basis of a hybrid model. The calculations were performed in relation to the conditions of laboratory experiments with laser plasma at the KI-1 facility of the ILF SB RAS and the conditions of the diamagnetic regime at the CAT facility of the INP SB RAS.

High-Energy-Density Physics and Laser Technologies

This paper is devoted to the jubilee of I.M. Khalatnikov, the founder and the first director of the Landau Institute for Theoretical Physics of the Russian Academy of Sciences. I.M. Khalatnikov organized a first-class institute the studies at which cover a broad spectrum of research directions. The plasma and lasers department of the Institute conducts research on plasma physics problems, laser–matter interaction, questions pertaining to laser applications, and hydrodynamics problems. Much attention is given to solid-state physics with an emphasis on the behavior of matter in extreme conditions under intense laser irradiation. A number of new results are presented: the behavior of metals in two-temperature states (when the temperature of the electron subsystem of a metal is much greater than the temperature of the ion subsystem due to ultrafast laser heating); determining the boundaries of existence of a single-wave propagation mode of elastoplastic shock waves in ductile metal crystals; the formation of a laser torch from target materials and liquids under metal laser ablation of a metal into the surrounding liquid; the physical–mechanical consequences (melting, capillarity, recrystallization) of nonuniform (along the irradiated surface) energy dissipation caused by the interference of plasmon–polariton and laser electromagnetic fields.

ViDA: a Vlasov–DArwin solver for plasma physics at electron scales

We present a Vlasov–DArwin numerical code (ViDA) specifically designed to address plasma physics problems, where small-scale high accuracy is requested even during the nonlinear regime to guarantee a clean description of the plasma dynamics at fine spatial scales. The algorithm provides a low-noise description of proton and electron kinetic dynamics, by splitting in time the multi-advection Vlasov equation in phase space. Maxwell equations for the electric and magnetic fields are reorganized according to the Darwin approximation to remove light waves. Several numerical tests show that ViDA successfully reproduces the propagation of linear and nonlinear waves and captures the physics of magnetic reconnection. We also discuss preliminary tests of the parallelization algorithm efficiency, performed at CINECA on the Marconi-KNL cluster. ViDA will allow the running of Eulerian simulations of a non-relativistic fully kinetic collisionless plasma and it is expected to provide relevant insights into important problems of plasma astrophysics such as, for instance, the development of the turbulent cascade at electron scales and the structure and dynamics of electron-scale magnetic reconnection, such as the electron diffusion region.

On stretching of plasma parameters and related open issues for the study of dust-ion-acoustic and dust-acoustic shock waves in dusty plasmas

To study the properties of the shock structures associated with dust-ion-acoustic (DIA) and dust-acoustic (DA) waves, the stretching of the plasma parameters [viz., kinematic or longitudinal viscosity coefficient ηi (ηd) for DIA (DA) waves and the plasma parameter δi (δd) associated with the dust charge fluctuation for DIA (DA) waves] has been used by many authors. It is argued that the stretching of such plasma parameters is not usually valid. The valid stretching coordinates for deriving the Burgers equation, which leads to the formation of DIA and DA shock waves, are provided. A few open issues related to the sources of dissipation [viz., different viscous forces giving rise to ηi and ηd and dust charge fluctuation giving rise to δi and δd] are also pinpointed. To remove the stretching of plasma parameters, which is not usually valid, from our future research work, and to address some related open issues will be able not only to enhance the quality of our future research work but also to help us in working on some challenging research problems in dusty plasma physics.

Temporal evolution of the velocity distribution in systems described by the Vlasov equation; Radiation Belts: Analytical and computational results

AbstractAn interesting problem in plasma physics, when approached from the point of view of Statistical Mechanics is to obtain properties of collisionless plasmas, which are described by the Vlasov equation. Through what we call the Ehrenfest procedure, which uses statistical mechanical relations we obtain expectation value relations for arbitrary observables, which allows us to study the dynamics of the Earth's Outer Radiation Belt. Focusing on the velocity fluctuations, the width of the distribution function and the pitch angle, a computer simulation was performed to describe the system in order to compare and test the Ehrenfest approach. Our results show that the change in the average width of the distribution follows the analytical relation. However, for the velocity fluctuation results are not conclusive yet and require more exploration. It remains as future work to verify the relation for the pitch angle.

Impact of Cosmic-Ray Physics on Dark Matter Indirect Searches

The quest for the elusive dark matter (DM) that permeates the Universe (and in general the search for signatures of physics beyond the Standard Model at astronomical scales) provides a unique opportunity and a tough challenge to the high energy astrophysics community. In particular, the so-called DMindirect searches—mostly focused on a class of theoretically well-motivated DM candidates such as the weakly interacting massive particles—are affected by a complex astrophysical background of cosmic radiation. The understanding and modeling of such background require a deep comprehension of an intricate classical plasma physics problem, i.e., the interaction between high energy charged particles, accelerated in peculiar astrophysical environments, and magnetohydrodynamic turbulence in the interstellar medium of our galaxy. In this review we highlight several aspects of this exciting interplay between the most recent claims of DM annihilation/decay signatures from the sky and the galactic cosmic-ray research field. Our purpose is to further stimulate the debate about viable astrophysical explanations, discussing possible directions that would help breaking degeneracy patterns in the interpretation of current data. We eventually aim to emphasize how a deep knowledge on the physics of CR transport is therefore required to tackle the DM indirect search program at present and in the forthcoming years.

The Lauricella hypergeometric function , the Riemann–Hilbert problem, and some applications

The problem of analytic continuation is considered for the Lauricella function , a generalized hypergeometric functions of complex variables. For an arbitrary a complete set of formulae is given for its analytic continuation outside the boundary of the unit polydisk, where it is defined originally by an -variate hypergeometric series. Such formulae represent in suitable subdomains of in terms of other generalized hypergeometric series, which solve the same system of partial differential equations as . These hypergeometric series are the -dimensional analogue of Kummer’s solutions in the theory of Gauss’s classical hypergeometric equation. The use of this function in the theory of the Riemann–Hilbert problem and its applications to the Schwarz–Christoffel parameter problem and problems in plasma physics are also discussed. Bibliography: 163 titles.