Steady Plasma Flow Research Articles

Steady plasma flows in a periodic non-symmetric domain

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Phys. Plasmas, vol. 21, 2014, p. 022515) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by Hameiri (J. Math. Phys., vol. 22, 1981, pp. 2080–2088, § III), to obtain a generalized Grad–Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we can obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

Magnetically coupled atmosphere, fast sausage MHD waves, and forced magnetic field reconnection during the SOL2014-09-10T17:45 flare

Aims.We study the physical properties and behaviour of the solar atmosphere during the GOES X1.6 solar flare on 2014 September 10.Methods.The steady plasma flows and the fast sausage MHD waves were analysed with the wavelet separation method. The magnetically coupled atmosphere and the forced magnetic field reconnection were studied with the help of the Vertical-Current Approximation Non-linear Force-Free Field code.Results.We studied a mechanism of MHD wave transfer from the photosphere without dissipation or reflection before reaching the corona and a mechanism of the wave energy distribution over the solar corona. We report a common behaviour of (extreme)ultraviolet steady plasma flows (speed of 15.3 → 10.9 km s−1) and fast sausage MHD waves (Alfvén speed of 13.7 → 10.3 km s−1and characteristic periods of 1587 → 1607 s), propagating in cylindrical plasma waveguides of the individual atmospheric layers (photosphere → corona) observed by SDO/AIA/HMI and IRIS space instruments. A magnetically coupled solar atmosphere by a magnetic field flux tube above a sunspot umbra and a magnetic field reconnection forced by the waves were analysed. The solar seismology with trapped, leakage, and tunnelled modes of the waves, dissipating especially in the solar corona, is discussed with respect to its possible contribution to the outer atmosphere heating.Conclusions.We demonstrate that a dispersive nature of fast sausage MHD waves, which can easily generate the leaky and other modes propagating outside of their waveguide, and magnetic field flux tubes connecting the individual atmospheric layers can distribute the magnetic field energy across the active region. This mechanism can contribute to the coronal energy balance and to our knowledge on how the coronal heating is maintained.

Analytical Model of an Asymmetric Sunspot with a Steady Plasma Flow in its Penumbra

A new exact analytical solution to the stationary problem of ideal magnetohydrodynamics is derived for an unipolar asymmetric sunspot immersed in a realistic solar atmosphere. The radial and vertical profiles of pressure, plasma density, and temperature in the visible layers of the sunspot are calculated. The reduction in plasma density in the magnetic funnel of the sunspot, corresponding to the Wilson depression, is also obtained. The magnetic structure of the sunspot is given analytically in a realistic way: a part of the magnetic flux of the sunspot approaches the surrounding photosphere at the outer edge of the penumbra. The magnetic field of the sunspot is not assumed to be axially symmetric. For the first time, the angular dependence of the physical variables in this model allows us to simulate not only a deviation from the circular shape of the sunspot, but also a fine filamentary structure of the sunspot penumbra. The Alfven Mach number (the ratio of the plasma speed to the Alfven speed) is zero at the center of the sunspot and rises slowly toward the periphery of the sunspot; this corresponds to the structure of the Evershed flow in the penumbra. The Evershed flow in our model is mainly concentrated in dark penumbral filaments, as is observed.

Role of equilibrium plasma flow on damping of slow MHD waves

In the solar corona waves and oscillatory activities are observed with modern imaging and spectral instruments. These oscillations are interpreted as slow magneto-acoustic waves excited impulsively in coronal loops. This study explores the effect of steady plasma flow on the dissipation of slow magneto-acoustic waves in the solar coronal loops permeated by uniform magnetic field. We have investigated the damping of slow waves in the coronal plasma taking into account viscosity and thermal conductivity as dissipative processes. On solving the dispersion relation it is found that the presence of plasma flow influences the characteristics of wave propagation and dissipation. We have shown that the time damping of slow waves exhibits varying behavior depending upon the physical parameters of the loop. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 106 erg cm−2 s−1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region.

Dynamics of rotating flows in plasma accelerator channels with a longitudinal magnetic field

Results are presented from numerical simulations of axisymmetric plasma flows that occur in a coaxial accelerator with a longitudinal magnetic field. The simulations were carried out based on a two-dimensional MHD plasma dynamic model for the general case of a three-component magnetic field. The steady plasma flows are calculated in solving the time-dependent MHD problem by the relaxation method. The results of simulations of steady transonic flows are compared with the solutions that were obtained in the smooth accelerator channel approximation. The main regular features of plasmodynamic processes are revealed. It is found that current sheets arise in the plasma flow in a comparatively strong longitudinal magnetic field.

Steady 2D prominence-like solutions of the MHD equations with field-aligned compressible flow

An exact two-dimensional solution of the ideal magnetohydrodynamic (MHD) equations with compressible flow in a uniform gravitational field is presented and applied to solar prominences. The solution is constructed via a systematic nonlinear separation of variables method used to calculate several classes of MHD equilibria in Cartesian geometry and uniform gravity. This simple model of steady plasma flow along the dipped field lines of a solar prominence is the first 2D MHD model with a nonisothermal temperature distribution which selfconsistently also examines the required heating. Although the model is 2D, a third magnetic/velocity vector field component is included and the highly sheared fields observed in prominences are reproduced. A description is given of the balance of gas pressure gradient, gravity, Lorentz and inertial forces acting along and across the prominence. It is found that the flow may significantly influence the energy balance as in a similar application of this class of solutions to solar coronal loops.

Recombining processes in a steady plasma flow penetrating into hydrogen gas

A numerical investigation of recombining process in a high-temperature plasma flow in a quasi-steady state (electron temperature about 10 eV, electron density about 1014 cm-3 and flow velocity about 106 cm s-1) was performed under gas contact cooling conditions using the collisional-radiative model, in which gas cooling is mainly due to surrounding gas particles freely coming into the plasma column. The calculation has shown that the electron temperature relaxes in accord with experimental results and also that the occurrence of the recombining region and the inverted populations almost agree with the experimental ones. Atomic processes responsible for gas cooling are discussed.

Production and flow of plasma in ion beams

Steady plasma flow is analyzed for the case where a positive- or negative-ion beam penetrates and ionizes background gas (or vapor). The work of previous authors is extended to treat nonuniform beam densities that fall to low values at the transverse plasma boundary, and to include gas densities that are nonuniform along the beam axis. These nonuniformities give a two-dimensional plasma flow problem that is analyzed using a fluid model. The effect of unusually low gas density on the plasma flow is discussed; for negative-ion beams, the electron density becomes much smaller than the beam density and space-charge neutralization is maintained by a reduction in plasma flow. When there is a large local gas density, as in a gas cell, the resulting high electron density is also localized to the same region by the nature of the flow.

Steady plasma flow with a shock in a mirror

Based on scaled version of the equations of ideal magnetohydrodynamics it is shown how to construct a steady flow with a shock in a mirror. The upstream state is supersonic, but essentially arbitrary. The shock must be Mach number one on axis although the Mach number may rise rapidly off axis. The shock is extremely effective in converting the directed streaming energy of flow into randomized thermal energy. Such flow patterns may be of interest in very long theta pinches where quasi-steady flow may obtain or in plasma gun devices where the gun injects a plasma along a magnetic field.

Nonlinear Modulation of Spatial Waves in a Steady Plasma Flow

Nonlinear modulation of strongly dispersive ion-acoustic standing wave produced by some obstacle in a uniform plasma flow, is investigated by means of the reductive perturbation method. The two fluid equations composed of cold ions and isothermal electrons are used, which in the specific ranges of Mach number and wavenumber permit the spatial waves. Consequently, the system is reduced to the nonlinear Schrödinger equation expressed in terms of three independent variables which are responsible for slow two-dimensional spatial variation and slower temporal change. It is further shown that in general the nonlinear Schrödinger equation derived from the Korteweg-de Vries equation is always stable as to the modulational instability.

Shocks and Solitions in a Steady Plasma Flow

The present paper investigates weakly nonlinear, dissipative and dispersive hydromagnetic waves of small but finite amplitudes standing or slowly propagating in the aligned-(parallel-)transverse flow, which consists of a two-dimensional aligned flow with superposed third components of flow-velocity and magnetic field. The two-fluid plasma model is used. In a certain range of the flow-velocity the system of equations in the ideal limit becomes spatially hyperbolic, and for the specific ranges the system is reduced by means of the reductive perturbation method to the Korteweg-de Vries Burgers equation which describes slow two-dimensional spatial variation and slower temporal change. Shock-like and solitary wave solutions are obtained even without the time-dependence, and conspicuous properties of those solutions are exhibited.

Similarities between Ion Waves in Plasmas and Gravity Waves in Incompressible Fluids

Some similarities between ion waves in plasmas and gravity waves in incompressible fluids are investigated. It is shown that for zero ion temperature the ion-wave dispersion relation is similar to that of gravity waves in a stratified liquid between rigid, horizontal walls; for large wavelength the ion waves behave as the surface gravity waves of shallow-water theory. The general character of the pattern of ion waves arising in steady plasma flows is analyzed for arbitrary ion temperature, wavelength, and acoustic Mach number (which is based on the ion-acoustic speed), and is compared to the pattern of surface gravity waves in steady water flows when surface tension is taken into account.