Flow in coronal loops with a mass source

This research studies the flow of plasma inside a coronal loop in which an injection of plasma through the lateral surface is permitted. The flow is assumed steady and polytropic. The problem covers two cases: (a) upflow at one footpoint, downflow at the other; (b) downflow at both footpoints. The first case can be shown to be quite similar to that of a mass-conserving flow with variable cross section; the second, instead, is characterized by solutions with a different type of topology; its main new feature is the obvious fact that all the solutions pass through a single point going from negative to positive velocities. In this second case the density ratio between footpoints and top can be much smaller than in a mass conserving flow. This can explain some properties of observed loops.     

Tripolar vortex in plasma flow

Strongly nonlinear processes in a two-component plasma with sheared flow, in the low-frequency limit, in comparison with the ion gyro frequency Ω_i, and for perturbations propagating perpendicularly to the ambient magnetic field are studied. In the linear domain such a system is prone to the development of instability of the Kelvin–Helmholtz type. In the nonlinear regime this instability can saturate into stationary travelling solutions of the form of vortex chains and tripolar vortices, which are found in this paper.     

Resonant Absorption of Nonlinear Slow MHD Waves in Isotropic Steady Plasmas – II. Application: Resonant Acoustic Waves

Nonlinear theory of driven magnetohydrodynamic (MHD) waves in the slow dissipative layer in isotropic steady plasmas developed by Ballai and Erdélyi (Solar Phys. 180 (1998)) is used to study the nonlinear interaction of sound waves with one-dimensional isotropic steady plasmas. An inhomogeneous magnetic slab with field-aligned plasma flow is sandwiched by a homogeneous static magnetic-free plasma and by a homogeneous steady magnetic plasma. Sound waves launched from the magnetic-free plasma propagate into the inhomogeneous region interacting with the localised slow dissipative layer and are partially reflected, dissipated or transmitted by this region. The nonlinearity parameter, introduced by Ballai and Erdélyi, is assumed to be small and a regular perturbation method is used to obtain analytical wave solutions. Analytical studies of resonant absorption of sound waves show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We also find that a steady equilibrium shear flow can significantly influence the nonlinear resonant absorption in the limits of thin inhomogeneous layer and weak nonlinearity. The presence of an equilibrium flow may therefore be important for the nonlinear resonant MHD wave phenomena. A parametric analysis also shows that the nonlinear part of resonant absorption can be strongly enhanced by the equilibrium flow.     

Two-dimensional MHD equilibria in the solar corona

Using a combined analytical and numerical Method we have treated the question of two-dimensional MHD equilibriam in an inviscid compressible, perfect conducting plasma with an embedded magnetic field in the spherically symmetric gravitational field of the sun. Two solutions are obtained. (1) A steady, self-consistent plasma flow in a magnetic field with both a closed and an open region. In the open region, beyond a few solar radii, the plasma velocity exceeds the local sound and Alfvén velocities. (2) The plasma velocity is everywhere smaller than the local sound and Alfvén velocities and tends to zero at large radial distances.     

Chemically reacting flow of a compressible thermally radiating two-component plasma

The paper studies the compressible flow of a hot two-component plasma in the presence of gravitation and chemical reaction in a vertical channel. For the optically thick gas approximation, closed form analytical solutions are possible. Asymptotic solutions are also obtained for the general differential approximation when the temperatures of the two bounding walls are the same. In the general case the problem is reduced to the solution of standard nonlinear integral equations which can be tackled by iterative precedure. The results are discussed quantitatively. The problem may be applicable to the understanding of explosive hydrogen-burning model of solar flares.     

Expansion of the solar wind from a two-hole corona

A one-fluid model is employed to study the global expansion of the solar wind from a two-hole corona, under the assumptions that the holes are confined to polar caps within 30° of heliographic colatitude, the flow is steady and axisymmetric, and the geometry of streamlines is prescribed. The boundary conditions are adjusted in such a way that the calculated solar wind properties at 1 AU are in a reasonable agreement with observational results. A series of numerical solutions are obtained, the series produces a maximum terminal speed of 829 km s^?1 at the pole. The calculated solar wind speeds are strongly latitude dependent and are positively correlated with local divergence factor of a stream tube. The solutions imply that most plasma properties are highly inhomogeneous at the polar caps. The flow velocity, the temperature, the proton number flux and the conduction heat flux all increase towards the hole center.     

A class of semi-analytical solutions for a rotating toroidal plasma

In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P _s andf ² are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.     

Models of flux tubes from constrained relaxation

We study the relaxation of a compressible plasma to an equilibrium with flow. The constraints of conservation of mass, energy, angular momentum, cross-helicity and relative magnetic helicity are imposed. Equilibria corresponding to the energy extrema while conserving these invariants for parallel flows yield three classes of solutions and one of them with an increasing radial density profile, relevant to solar flux tubes is presented.     

Numerical simulations of rotating axisymmetric sunspots

A numerical model of axisymmetric convection in the presence of a vertical magnetic flux bundle and rotation about the axis is presented. The model contains a compressible plasma described by the non-linear MHD equations, with density and temperature gradients simulating the upper layer of the Sun's convection zone. The solutions exhibit a central magnetic flux tube in a cylindrical numerical domain, with convection cells forming collar flows around the tube. When the numerical domain is rotated with a constant angular velocity, the plasma forms a Rankine vortex, with the plasma rotating as a rigid body where the magnetic field is strong, as in the flux tube, while experiencing sheared azimuthal flow in the surrounding convection cells, forming a free vortex. As a result, the azimuthal velocity component has its maximum value close to the outer edge of the flux tube. The azimuthal flow inside the magnetic flux tube and the vortex flow is prograde relative to the rotating cylindrical reference frame. A retrograde flow appears at the outer wall. The most significant convection cell outside the flux tube is the location for the maximum value of the azimuthal magnetic field component. The azimuthal flow and magnetic structure are not generated spontaneously, but decay exponentially in the absence of any imposed rotation of the cylindrical domain.     

Bifurcations of electron acoustic traveling waves in an unmagnetized quantum plasma with cold and hot electrons

Bifurcations of nonlinear electron acoustic solitary waves and periodic waves in an unmagnetized quantum plasma with cold and hot electrons and ions has been investigated. The one dimensional quantum hydrodynamic model is used to study electron acoustic waves (EAWs) in quantum plasma. Applying the well known reductive perturbation technique (RPT), we have derived a Korteweg-de Vries (KdV) equation for EAWs in an unmagnetized quantum plasma. By using the bifurcation theory and methods of planar dynamical systems to this KdV equation, we have presented the existence of two types of traveling wave solutions which are solitary wave solutions and periodic traveling wave solutions. Under different parametric conditions, some exact explicit solutions of the above waves are obtained.     

Two-dimensional guiding-center model of the solar wind-moon interaction

This paper presents a continued study of the two-dimensional guiding-center model of the solar wind interaction with the Moon. The characteristics theory and the computational method are discussed. The magnetic permeability of plasma is (1 + /2)^–1 in the solar wind flow upstream of the Moon, and it changes to 1 in the void region of the lunar wake. The gradual change of the magnetic permeability in the penumbral region from the interplanetary condition to the void condition is explained as the source of field perturbations in the lunar wake. Perturbations of the magnetic field propagate as magnetoacoustic waves in a frame of reference moving with the plasma flow. Computer solutions were obtained to show that (i) the two principal perturbations of the magnetic field in the lunar wake (the umbral increase and the penumbral decrease) are confined to a region bounded by a Mach cone tangent to the lunar body, and (ii) the penumbral increases occur outside the lunar Mach cone. Computer solutions are also used to identify the source of field perturbations and to simulate the solar wind-moon interaction under varying interplanetary conditions.     

The structure of the hydrodynamic plasma flow near the heliopause stagnation point

The plasma flow in the vicinity of the heliopause stagnation point in the presence of the H atom flow is studied. The plasma at both sides of the heliopause is considered to be a single fluid. The back reaction of the plasma flow on the H atom flow is neglected, and the density, temperature and velocity of the H atom flow are taken to be constant. The solution describing the plasma flow is obtained in the form of power series expansions with respect to the radial distance from the symmetry axis. The main conclusion made on the basis of the obtained solution is that the heliopause is not the surface of discontinuity anymore. Rather, it is the surface separating the flows of the solar wind and interstellar medium with all plasma parameters continuous at this surface.     

The interaction of the solar wind with a comet

The flow of plasma on the sunward side of a comet is investigated by means of an axialsymmetric model based on hydrodynamics modified by source terms. The model assumes a given curvature of the isobaric surfaces, which corresponds to paraboloids around the nucleus of the comet. The flow on the axis can be represented by a solution of a system of seven ordinary differential equations (respectively five in case of pure photo-ionization). The flow pattern always contains a widely detached bow shock and a contact discontinuity separating a cavity with purely cometary plasma from the transition region containing also solar wind ions. The model is applied to the special case where the cometary gas is ionized by the solar UV radiation only. Numerical solutions are integrated for five levels of production of neutral gas by the comet and for seven typical situations in the undisturbed solar wind. The results imply standoff distances of the stagnation point from the nucleus of the order of 10 000 km or more, and distances of the bow shock of the order of 10⁶–10⁷ km.     

Space-Time Geometry of Quark and Strange Quark Matter

We study quarkand strangequarkmatter in the contextof generalrelativity.For this purpose,we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times,thus we are able to obtain the space-time geometries of quark and strange quark matter. Also,we discuss the features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory,i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).     

Excitation of Electromagnetic Flute Modes in the Process of Interaction of Plasma Flow with Inhomogeneous Magnetic Field

Laboratory experiments on the interaction of a plasma flow, produced by laser ablation of a solid target with the inhomogeneous magnetic field from the Zebra pulsed power generator demonstrated the presence of strong wave activity in the region of the flow deceleration. The deceleration of the plasma flow can be interpreted as the appearance of a gravity-like force. The drift due to this force can lead to the excitation of flute modes. In this paper a linear dispersion equation for the excitation of electromagnetic flute-type modes with plasma and magnetic field parameters, corresponding to the ongoing experiments is examined. Results indicate that the wavelength of the excited flute modes strongly depends on the strength of the external magnetic field. For magnetic field strengths ∼0.1 MG the excited wavelengths are larger than the width of the laser ablated plasma plume and cannot be observed during the experiment. But for magnetic field strengths ∼1 MG the excited wavelengths are much smaller and can then be detected.     

A linear MHD instability analysis of solar mass ejections with gravitation

Solar mass ejections seem, on the basis of many observations, to be divided into two categories: stable and unstable. We use linear magnetohydrodynamic (MHD) instability of a cylindrical plasma in an attempt to search for a theoretical explanation for this phenomenon. The dispersion relation is obtained and solved numerically. It is found that the initial plasma-flow velocity has a significant effect on the instability criteria and growth rate. Also found is that the instability growth-rate is much larger in those cases where plasma flow exists in comparison with the static case. The wave number range where the instability may occur also becomes wider with plasma flow. Further, it is shown that the region of the instability shifts to the short wavelength region with increasing plasma-flow velocity. Therefore, the plasma column may break into small pieces, resembling the melon seed phenomenon that has been suggested as a mechanism for mass ejection in the solar atmosphere. Under the assumption of a thin-tube approximation we show that gravity has little effect on the instability of quasi-horizontal ejection, but it has considerable effect for the vertical ejection. In order to deal with the gravitational force it is convenient to divide the problem into three cases: horizontal, vertical, and oblique. The exact analytical solution exists only in the vertical case. Asymptotic solutions are given in the horizontal and oblique cases.     

Relativistic expansion of magnetic loops at the self-similar stage

We obtained self-similar solutions of relativistically expanding magnetic loops taking into account the azimuthal magnetic fields. We neglect stellar rotation and assume axisymmetry and a purely radial flow. As the magnetic loops expand, the initial dipole magnetic field is stretched into the radial direction. When the expansion speed approaches the light speed, the displacement current reduces the toroidal current and modifies the distribution of the plasma lifted up from the central star. Since these self-similar solutions describe the free expansion of the magnetic loops, i.e.  d v /d t = 0  , the equations of motion are similar to those of the static relativistic magnetohydrodynamics. This allows us to estimate the total energy stored in the magnetic loops by applying the virial theorem. This energy is comparable to that of the giant flares observed in magnetars.     

On continuous transitions between discontinuous MHD solutions in the magnetic reconnection problem

The possibility that the type of magnetohydrodynamic (MHD) discontinuity changes as the plasma flow conditions gradually change is investigated in a general form. The conservation laws in MHD admit such transitions if there exist the so-called transition solutions that simultaneously satisfy two types of discontinuities. These solutions have been sought for. The system of possible transitions between MHD discontinuities obtained on their basis is presented in a clear schematic form. The ultimate general scheme of transitions includes all of the previously described schemes of transitions known to us. The system of discontinuities and transitions between them is studied in a self-consistent solution of the analytical problem of reconnection in a strong magnetic field.     

On the equilibrium of a cylindrical plasma supported horizontally by magnetic fields in uniform gravity

We consider the mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity. This configuration is what may be expected if a quiescent prominence were to condense in a region initially filled with a uniform magnetic field. A set of exact solutions describing the equilibrium situation is presented. Although the plasma distribution is assumed to be cylindrically symmetric to obtain tractibility of the problem, exact force balance between plasma pressure, the Lorentz force and gravity is achieved everywhere in space. The set of solutions covers a particular case of a uniform temperature as well as cases where the temperature rises from zero at the center of the plasma cylinder to rapidly reach a constant asymptotic value outside the cylinder. The physical properties of these solutions are described. A suggestion is made for future development, based on the present work, to construct a prominence model in which the requirements of both mechanical and radiative equilibrium are satisfied.