Magnetized Plasma Configurations Research Articles

BORAY: A ray tracing code for various magnetized plasma configurations

Ray tracing codes are useful to study the electromagnetic wave propagation and absorption in the geometrical optics approximation. In magnetized fusion plasma community, most ray tracing codes assume the plasma density and temperature be functions of the magnetic flux and study waves only inside the last closed flux surface, which are sufficient for the present day tokamak. However, they are difficult to be used for configurations with open magnetic field line plasmas, such as mirror machine and field-reversed-configuration (FRC). We develop a ray tracing code in cylindrical coordinates (r,ϕ,z) to support arbitrary axisymmetric configurations with both closed and open field lines plasmas. For wave propagation, the cold plasma dispersion relation is usually sufficient, and we require the magnetic field B(r,z) and species densities ns0(r,z) profiles as input. For wave absorption, we require a further temperature Ts0(r,z) profile to solve a hot kinetic plasma dispersion relation. In difference to other ray tracing codes which calculate the imaginary part of wave vector k⊥,i for wave absorption, we calculate the imaginary part of wave frequency ωi, which is shown to be equivalent with the former technique under weak damping approximation. The code can use either numerical or analytical equilibrium. Examples and benchmarks with electron cyclotron wave, lower hybrid wave and ion cyclotron wave for tokamak, spherical tokamak (ST), FRC and mirror machine are shown. Program summaryProgram Title: BORAYCPC Library link to program files:https://doi.org/10.17632/tnkrjdbcz8.1Code Ocean capsule:https://codeocean.com/capsule/6205646Licensing provisions: BSD 3-clauseProgramming language: MatlabNature of problem: Solve the plasmas electromagnetic wave propagation and absorption in the geometrical optics approximation for magnetized plasmas based on ray tracing of plasma dispersion relation. In axisymmetric (r,z) coordinates, the code can be used for both closed and open field lines plasmas of various configurations such as tokamak, spherical tokamak, FRC and mirror machine.Solution method: Runge-Kutta time integral to solve ray tracing equations for wave propagation, and integral the imaginary part of the wave frequency in hot kinetic dispersion relation for wave absorption.Additional comments including restrictions and unusual features: Kinetic relativistic effects and collisional damping are not included in the present version yet. Only axisymmetric two-dimensional (2D) profiles are support in present version.

Pressure anisotropy generation in a magnetized plasma configuration with a shear flow velocity

The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth’s magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this complex nonlinear dynamics.

Barriers to field line transport in 3D magnetic configurations

The transport properties of magnetized plasma configurations are studied that arise from a one-dimensional, current layer that is unstable to reconnecting modes. These magnetic configurations are partially stochastic. It is shown that ridges in the Finite Time Lyapunov Exponents (FTLE) distribution are aligned with the invariant manifolds related to the lines of uniform hyperbolicity. It is shown that these ridges form approximate Lagrangian Coherent Structures (LCS) and act as barriers to the transport of magnetic field lines.

Evidence of low-dimensional chaos in magnetized plasma turbulence

We analyze probe data obtained from a toroidal magnetized plasma configuration suitable for studies of low-frequency gradient-driven instabilities. These instabilities give rise to field-aligned convection rolls analogous to Rayleigh-Benard cells in neutral fluids, and may theoretically develop similar routes to chaos. When using mean-field dimension analysis, we observe low dimensionality, but this could originate from either low-dimensional chaos, periodicity or quasi-periodicity. Therefore, we apply recurrence plot analysis as well as estimation of the largest Lyapunov exponent. These analyses provide evidence of low-dimensional chaos, in agreement with theoretical predictions. Our results can be applied to other magnetized plasma configurations, where gradient-driven instabilities dominate the dynamics of the system.

Model of the symmetry evolution of a nonlinear continuous system

A simple algebraic model is constructed with the aim of investigating the time evolution of the symmetry properties of a nonlinear continuous system. The model is constructed so as to mimic the dynamics of a two-dimensional inviscid flow bounded by periodic conditions, but can easily generalized to more complex dynamics involving magnetized plasma configurations.

Electrostatic waves in bounded dusty magnetoplasma

Electrostatic perturbations propagating obliquely to the magnetic field lines are studied in a cylindric magnetized dusty plasma configuration. A set of two coupled equations describing the perturbed electrostatic and gravity potentials in a radially nonuniform plasma is derived. The equations are discussed and solved in two limits, without and with the self-gravity effects included. Without the gravity the corresponding equation for the electrostatic potential is solved analytically for a Gaussian-type equilibrium density profile. The general solution, which can be applied to various plasma situations, is expressed in terms of the Kummer confluent hypergeometric functions. In the self-gravitating case the equations are solved analytically for a homogeneous plasma and the general solutions are written in terms of the Bessel functions, describing well-behaving radially localized wave amplitudes.

Nonsolid rotation of structures in isothermal magnetized atmospheres

Possible equilibrium rotating magnetized plasma configurations in which angular asymmetry due to a nonuniform distribution of the molecular weight is absent are studied. The viscosity of the medium is assumed to be negligible. The variables in exact nonlinear equations are separated by representing the vector fields as series in orthogonal vector spherical harmonics. These series are normally divergent. However, the truncation of the series is also possible. Equilibrium models corresponding to the truncated series are generalizations of a simple rigidly rotating model. They are studied below. It is shown that nonaxisymmetric equilibrium structures with the magnetic field of a tilted dipole are possible. In the case of an isothermal atmosphere, conditions for the superrotation of the medium and meridional circulation of the matter may arise. The feasibility of such conditions in the Earth’s upper atmosphere is discussed.

Physics issues in the design of high-beta, low-aspect-ratio stellarator experiments

High-beta, low-aspect-ratio (“compact”) stellarators are promising solutions to the problem of developing a magnetic plasma configuration for magnetic fusion power plants that can be sustained in steady state without disrupting. These concepts combine features of stellarators and advanced tokamaks and have aspect ratios similar to those of tokamaks (2–4). They are based on computed plasma configurations that are shaped in three dimensions to provide desired stability and transport properties. Experiments are planned as part of a program to develop this concept. A β=4% quasi-axisymmetric plasma configuration has been evaluated for the National Compact Stellarator Experiment (NCSX). It has a substantial bootstrap current and is shaped to stabilize ballooning, external kink, vertical, and neoclassical tearing modes without feedback or close-fitting conductors. Quasi-omnigeneous plasma configurations stable to ballooning modes at β=4% have been evaluated for the Quasi-Omnigeneous Stellarator (QOS) experiment. These equilibria have relatively low bootstrap currents and are insensitive to changes in beta. Coil configurations have been calculated that reconstruct these plasma configurations, preserving their important physics properties. Theory- and experiment-based confinement analyses are used to evaluate the technical capabilities needed to reach target plasma conditions. The physics basis for these complementary experiments is described.

Interaction of sound waves with an inhomogeneous magnetized plasma in a strongly nonlinear resonant slow-wave layer

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.

Nonlinear theory of the interaction of sound waves with an inhomogeneous magnetized plasma in the resonant slow wave layer

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in the resonant slow wave dissipative layer developed by Ruderman, Hollweg, and Goossens [Phys. Plasmas 4, 75 (1997)] is used to study the interaction of sound waves with a static one-dimensional planar magnetic plasma configuration. This configuration is a nonhomogeneous magnetic slab (region II) sandwiched by a homogeneous magnetic field free plasma (regions I) and a homogeneous magnetic plasma (region III). The equilibrium magnetic field is unidirectional. An incoming sound wave is launched from region I, and the equilibrium quantities and the parameters of the incoming sound wave are chosen in such a way that the wave is evanescent in region III and resonates with a slow local MHD wave in region II. The analysis is restricted to incoming sound waves with wave vectors in the plane determined by the equilibrium magnetic field and the direction of inhomogeneity, so that there is no resonance with a local Alfvén wave. Partial reflection of the incoming sound wave from region II generates an outgoing sound wave in region I. The nonlinearity parameter introduced by Ruderman et al. is assumed to be small, and a regular perturbation analysis is used to determine the wave solution. The present analysis shows that nonlinearity in the resonant slow wave dissipative layer causes the following new effects in comparison with results obtained on the basis of linear theory: (i) higher harmonic contributions are generated in the wave solution in the dissipative layer and also in the outgoing sound wave in addition to the fundamental harmonic. Outside the dissipative layer the amplitude of each harmonic contribution is of a higher order with respect to the small nonlinearity parameter than inside the dissipative layer. This property reflects the fact that nonlinearity is only taken into account in the dissipative layer, so that the higher harmonic contributions to the outgoing wave are only due to the interaction of the external plasma motions with the plasma motions in the dissipative layer; (ii) the coefficient of wave energy absorption and the absolute value of the jump in the normal velocity are decreased.

Alfvén wave current drive

The resonant and nonresonant current drive produced by the Alfvén and fast waves are discussed both for collision and collisionless magnetized plasmas. The magneto-hydrodynamics approach is used to study collision plasma regimes, and the purely kinetic model, with the Landau and transit time magnetic pumping (TTMP) damping, is considered in the weak collision plasma case. The general form of the time-averaged ponderomotive force (and current drive as a result) generated by waves in magnetized plasma configurations is presented. It has been shown that standing Alfvén waves can drive non-inductive and nonresonant current in a magnetized plasma through Landau and TTMP damping. If all oscillations of the solar corona loops are related to standing Alfvén waves, which can introduce the density of dissipated wave power that is necessary to keep the plasma hot, the axial nonresonant current drive has been estimated to be enough for equilibrium and stability of corona loops. Experimental evidence of the Alfvén wave current drive in tokamaks and stellarators is demonstrated.

Radial plasma transport and toroidal current driven by nonresonant ponderomotive forces

A general form of the time-averaged ponderomotive force produced by radio frequency waves in magnetized plasma configurations is treated. Included in the ponderomotive force are components that result from plasma flow, the dynamo effect, and wave helicity. A detailed description of effects of individual components in the ponderomotive force on radio frequency (RF) driven transport and current is given.

Reconnection of stressed magnetic fields

It is shown that magnetized plasma configurations under magnetic stress relax irreversibly to the state of minimum stress at a rate that is essentially Alfvenic provided a magnetic null is present. The relaxation is effected by the reconnection at the field null and proceeds at a rate proportional to the absolute value of ln(eta) exp-1, where eta is the resistivity. An analytic calculation in the linear regime is presented.

Anomalous temperature equilibria due to E × B drive and the nuclear dynamo

On reversal of the magnetic field of a mirror confined plasma (or minimum B mirror confined plasma) the electric fields will also reverse, forming a nuclear dynamo configuration, and lead to E × B drive of the nuclei to energies higher than those of the electrons. For small gyro-orbit radii, a, the E × B drift velocity is V d = cE/ B and the maximum drift energy is W = 1 2 M(2V d ) 2 = 2Mc 2E 2/B 2 . For nonsmall a, the drift velocity is more complicated and the maximum drift energy is reduced but still much larger than that of the electrons. Since this E × B heating occurs in about one-fourth of an ion cyclotron period it is much faster than ion-electron slowing down and the mean ion energy may be much higher than that of the electrons, leading to increased nuclear reaction rates and relatively reduced radiation loss rate. The nuclear dynamo, a reversed magnetic field plasma configuration with inwardly pointing electric fields, will have maximum ion collision velocity at or near the axis and minimum ion velocities nearer the periphery. This will ensure higher reaction rates near the axis and maximum loss rates of lower energy ions near the periphery where the mirror is open ended. This may permit some direct electrical conversion of charged particle power since electrons will preferably exist at smaller radii and positive ions at larger radii. A major technological problem associated with fuel feed to a reacting plasma, such as the tokamak, is resolved in the nuclear dynamo configuration since fuel ions will be accelerated by the negative potential to the core of the plasma where further ionization and scatter will lead to irreversible trapping of fuel nuclei.

Toroidal plasma configuration with anisotropic pressure

The relation between various surface quantities required in hydrodynamic calculations, and the relation between the parallel and perpendicular currents in an arbitrary magnetic toroidal plasma configuration with scalar pressure, are generalized to the case of anisotropic pressure. Magnetic co-ordinates for hydrodynamic equilibria in this configuration are defined. A general expression for the mean velocity of diffusion through a magnetic surface, on the basis of the one-fluid magnetohydrodynamic equation with anisotropic pressure, is derived.

Toroidal plasma configuration with non-planar magnetic axis

The ideal MHD equilibrium, stability, classical diffusion, effective thermal conductivity, and Ohmic heating of a zero-shear toroidal plasma configuration with a single non-planar magnetic axis of variable torsion and curvature are investigated. The plasma has a circular cross-section through which a longitudinal current density with arbitrary profile flows. In this type of magnetic configuration, the magnetic surfaces arbitrarily rotate around the magnetic axis. This magnetic toroidal configuration is of a stellarator type with a non-planar magnetic axis. The present work also covers as special cases tokamak and a magnetic toroidal plasma configuration with a magnetic axis of arbitrarily modulated curvature.