Investigation of a Hall MHD channel with an ionization-unstable plasma of inert gases

We investigate a promising scheme for using ionization-unstable plasmas of pure inert gases as the working medium for a magnetohydrodynamic (MHD) closed-cycle generator. Our experiments were carried out using a disc Hall MHD channel, with the flux of ionized gas created in a shock tube. Our working gas was xenon. In these experiments we measured the gas pressure, the flow velocity, the concentration and temperature of the electrons, the azimuthal current density, the distribution of potential in the channel, and the value of the near-electrode voltage drop. We recorded voltage-current characteristics for various values of magnetic field and load resistances. The results of these experiment showed that in an ionization-unstable plasma of inert gases without admixtures of alkali metal, the effective conductivity in the Hall channel increases significantly with increasing degree of criticality of the magnetic field, and the value of the maximum specific power extracted increases more rapidly than the specific power calculated by assuming “frozen” ionization. Zh. Tekh. Fiz. 67, 6–11 (December 1997)     

MHD modeling of conductors at ultrahigh current density

In conjunction with ongoing high-current experiments on Sandia National Laboratories' Z accelerator (Albuquerque, NM) we have revisited a problem first described in detail by Heinz Knoepfel (1970). Unlike the 1-Tesla MITL's of pulsed power accelerators used to produce intense particle beams, Z's disk, transmission line (downstream of the current addition) is in a 100-1200-Tesla regime; so its conductors cannot be modeled simply as static infinite conductivity boundaries. Using the MHD code MACH2 we have been investigating the conductor hydrodynamics, characterizing the joule heating, magnetic field diffusion, and material deformation, pressure, and velocity over a range of current densities, current rise-times, and conductor materials. The three purposes of this work are 1) to quantify power flow losses owing to ultrahigh magnetic fields, 2) to model the response of VISAR diagnostic samples in various configurations on Z, and 3) to incorporate the most appropriate equation of state and conductivity models into our magnetohydrodynamics (MHD) computations. Certain features are strongly dependent on the details of the conductivity model     

Calculations of the parameters of the air plasma produced by an electron beam in the channel of an MHD generator with a nonequilibrium conductivity

Approximate analytic expressions for calculating the electron density in both steady and unsteady plasmas produced by pulsed electron beams are derived and proved to agree well with numerical calculations. It is shown that the algorithm for calculating the parameters of a nonequilibrium plasma in the channel of an MHD plasma generator depends on the type of generator. The effect of the magnetic field strength on the electron density and electric conductivity of the air plasma produced by an electron beam in the channel of a Faraday MHD generator is investigated. The influence of the parameters of the flow and ionizer on the efficiency of an MHD generator with a nonequilibrium conductivity is analyzed.     

Design of Closed-Cycle MHD Generator with Nonequilibrium Ionization and System

A closed-cycle MHD generator topping a steam bottoming plant is analyzed. The combined power plant involves three working fluids in three loops. The MHD loop is investigated more thoroughly since it is the least conventional of the three. Equations are developed to determine the geometric and thermodynamic variables throughout the MHD channel for inlet conditions of mass flow, temperature, pressure, and velocity. Limiting design parameters are output power, channel length, channel aspect ratio, Hall parameter, and interaction parameter. The basic closed-cycle MHD loop working fluid can consist of either argon or helium seeded with cesium. Both non-equilibrium ionization produced by the elevation of the electron temperature from joule heating of the plasma and thermal ionization are considered. Equations used to calculate the electrical conductivity and the elevation of electron temperatures are derived. These equations are coupled with the one-dimentional differential equations applicable to an MHD generator. The chief interest is in determining those MHD channel conditions which result in the most thermodynamically efficient MHD-steam plantcombination. Thus an overall heat balance forthe system is required. Equations are developed to calculate the gas properties at the various stations of the closed loop and to determine the overall efficiency of the cycle. A rather flexible computer program written in Fortran is used to solve the MHD generator equations and to make the overall heat balance. Some typical results presented demonstrate the feasibility and adaptability of the analysis for optimizing the thermal efficiency and the sensitivity of thermal efficiency to various parameters.     

Performance Analysis of a Diagonal MHD Accelerator for Space Propulsion

The performance of a diagonal magnetohydrodynamic (MHD) accelerator has been numerically investigated. Studies were carried out using air plasma as a working gas in an equilibrium condition based on the MHD Augmented Propulsion Experiment channel designed by NASA. The MacCormack scheme is employed in order to solve the set of differential equations with MHD approximations. The fundamental performance of a diagonal MHD accelerator considering both flow performance along the channel and propulsion performance has been evaluated under various applied input currents and magnetic fields. The optimum performance is dominated by ${bf j} times {bf B}$ Lorentz body force acceleration, while it is increased with Joule heating and the ${bf u} times {bf B}$ term's contribution, which are detrimental to the propulsion performance. Moreover, friction forces resist the flow performance, particularly near the channel exit.      

Magnetohydrodynamics of a viscous spherical layer rotating in a strong potential field

An analytic solution is given for classical magnetohydrodynamic (MHD) problem of almost rigid-body rotation of a viscous, conducting spherical layer of liquid in an axisymmetric potential magnetic field. Large-scale flows bounded by rigid spheres are described for the first time in a new approximation. Two problems are solved: (1) in which both spheres are insulators and (2) in which the outer sphere is an insulator and the inner sphere a conductor. Axially symmetric flows and azimuthal magnetic fields are maintained by a slightly faster rotation of the inner sphere. The primary regeneration takes place in the boundary and shear MHD layers. The shear layers, described here for the first time, smooth out the large gradients at the boundaries of the MHD structures encompassed by them. There is essentially no azimuthal magnetic field inside these original structures, which are bounded by potential contours tangent to the spheres. An applied constant magnetic field creates a rigid MHD structure outside an axial cylinder tangent to the inner sphere. Inside the cylinder the rotation is faster and the meridional flux depends on height. A magnetic dipole forms a structure tangent to the outer equator. Outside the structure, the rotation is also rigid-body when both spheres are insulators. When a conducting sphere is present, the liquid rotates differentially everywhere, while near the axis and inside the MHD structure, it rotates even faster than the inner sphere. The last example of a general solution is a quadrupole magnetic field. In this case, two equatorially symmetric MHD structures are formed which rotate together with the inner sphere. Outside the structures, as in the most general case, the rotation is differential, the azimuthal magnetic field falls off as the first power of the applied field, and the meridional flux falls off as the square of the field in the first problem, and as the cube in the second. Zh. éksp. Teor. Fiz. 112, 2056–2078 (December 1997)     

SILEP-1 COMPUTER SYSTEM FOR MEASURING ELECTRICAL CONDUCTIVITY OF PLASMA IN THE CHANNELS OF MHD GENERATORS

Abstract

The development of devices capable of measuring the elctrical conductivity of plasma is a complex task that requires solution of a number of problems, including high flow velocities and high plasma temperatures, aggressive media, strong magnetic fields, and large Hall potentials. At the Institute for High Temperatures we have solved these problems in the course of developing we have solved these problems in the course of developing a computer system, SILEP-1, for measuring the electrical conductivity of plasma in the U-25B MHD generator.     

The role of helicity in turbulent MHD flows

We have studied the behavior of a helical homogeneous small-scale MHD turbulent flow under the influence of a weak inhomogeneous large-scale disturbance. We have shown that turbulent energy redistribution in the presence of nonzero helicity occurs mainly over large scales. Helicity increases correlation time, leading to the weakening of a direct cascade and to the formation of steep spectra over small scales, with simultaneous turbulent energy growth over large scales. Furthermore, an expression for the effective viscosity of the mean flow is derived. It is shown that the magnetic field, in addition to the helicity, reduces the effective viscosity of the medium. This may be important in the study of MHD flow around obstacles in the presence of an external magnetic field. Zh. éksp. Teor. Fiz. 114, 171–181 (July 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Local effect of electric and magnetic fields on the position of an attached shock in a supersonic diffuser

Effective ways for controlling shock wave configurations by means of external actions are sought. One such way is a local effect of electric and magnetic fields. In this paper, the local effect of external fields is implemented by current localization in a limited region of a diffuser. The experiment is carried out in a diffuser providing the complete internal compression of the gas with a Mach number at the inlet M=4.3. As a working medium, a xenon plasma is used. The plasma flow is formed in a shock tube equipped with an accelerating nozzle. Two ways of current localization are tested. In the first one, the diffuser inlet is a short channel of Faraday generator type. In this case, the ponderomotive force basically decelerates or accelerates the flow depending on the direction of the electric field. In the second way, the current flows through a narrow near-wall region between adjacent electrodes. In this case, the ponderomotive force compresses or expands the gas. In both cases, it is shown that the angle of an attached shock due to MHD interaction can be both decreased and increased. The central problem with the MHD control of shock waves is near-electrode and near-wall phenomena.     

Effect of unstable MHD modes on the confinement of a stellarator plasma

The results of an experimental study of the influence of unstable MHD modes on plasma confinement in an L-2M stellarator are presented. The spectral and statistical characteristics of turbulent plasma simultaneously at both the edge and center of the plasma are investigated. It is shown that at constant power of electron-cyclotron heating of the plasma the energy content of the plasma depends strongly on the strength of the externally applied vertical magnetic field used to adjust the position of the plasma column. Appreciable degradation of plasma confinement is observed for values of the vertical field such that ideal MHD modes become unstable in the greater part of the plasma column. This in turn is due to the formation of a magnetic configuration with a magnetic “hump.” At the same time, in the edge plasma the instability of resistive-balloon modes grows, and turbulent particle transport increases. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 407–412 (25 March 1999)     

Experimental studies on isentropic efficiency of a nonequilibriumMHD disk generator

Isentropic efficiency of the nonequilibrium MHD power generator was studied by a shock tube driven disk generator. Cesium seeded helium was used as a working gas. From the measurements of Faraday current density distribution, it was possible to estimate the general tendency of Joule dissipation in the generator. The Joule dissipation did not decrease due to the occurrence of nonuniformity of the plasma when external load resistance was low, although it decreased with the decrease in the load resistance when the load resistance was high. The electrical efficiency increased with the increase in applied magnetic flux density. This fact is thought to be caused by high Hall parameter and the stabilization of the plasma due to high degree of seed ionization     

Measurements of turbulent magnetic diffusivity in a liquid-gallium flow

Direct measurements of the effective conductivity (magnetic diffusivity) in the turbulent flow of a liquid metal have been performed. An nonstationary turbulent flow of a gallium alloy has been excited in a closed toroidal channel with dielectric walls. The Reynolds number reaches a maximum value of Re ≈ 10⁶, which corresponds to the magnetic Reynolds number Rm ≈ 1. The conductivity of the metal in the channel has been determined from the phase shift of forced harmonic oscillations in a series RLC circuit whose inductance is a toroidal coil wound around the channel. The maximum deviation of the effective conductivity of the turbulent medium from the ohmic conductivity of the metal is about 1%.     

Contribution to the theory of “incompressible” regions in an inhomogeneous magnetized 2D electronic system

A modification of the theory of “incompressible” regions in an ideal spinless inhomogeneous magnetized 2D electronic system near points on the electron density profile n(x) with an integer filling factor is proposed. Such regions leads to the appearance of a finite capacitance between the parts of the 2D system that are separated by an incompressible channel, so that capacitive methods can be used to investigate such a system. The Corbino configuration is especially convenient for these purposes. The parameters of the “incompressible” channel in a Corbino disk with a spatially inhomogeneous 2D electronic system in the presence of an individual point, near the channel, on the electron density profile with an integer magnetic filling factor are determined. The magnetocapacitance between the edges of the Corbino disk separated by an incompressible interlayer is found for cases of practical interest. It is shown that this magnetocapacitance contains direct information about the width of the integer strip. Fiz. Tverd. Tela (St. Petersburg) 41, 1103–1109 (June 1999)     

Study of MHD dynamo effect at the outlet from plasma accelerator in the presence of longitudinal magnetic field

Properties of compressible flows in the quasi-stationary plasma accelerator have been studied in the presence of an additional longitudinal magnetic field and the arising rotation of plasma flow. Numerical study was carried out within the framework of two-dimensional magnetic hydrodynamics (MHD) model of the axisymmetric plasma flows taking into account the finite conductivity of medium and radiation transport. Dynamics of compressible plasma flows is accompanied by the MHD dynamo effect or generation of magnetic field on a conical shock wave forming at the outlet from the accelerator.     

Structure of the magnetic field of the Jovian magnetosphere

We exactly solved the problem of the interaction between the rotating magnetic field of Jupiter and the equatorial plasma disk formed by the gases flowing from the Jovian satellite Io. The disk is shown to expel the Jovian magnetic field in both directions, inward, toward Jupiter, compressing its dipole magnetic field, and outward. Jupiter spins up the disk up to velocities that correspond to nearly constant angular rotation, but with an angular frequency lower than the angular frequency of Jupiter itself. The radial velocity of the plasma in the disk approaches its azimuthal velocity. We determined the power of Jupiter’s rotational energy losses. Part of this energy is transferred to the disk, and the other part goes into heating the Jovian ionosphere. We show that the Pedersen surface conductivity of the Jovian ionosphere must have a lower limit to maintain the electric current that arises in the disk-rotating magnetic field system. This current in the Jovian magnetosphere flows only along the preferential magnetic surfaces that connect the inner and outer edges of the disk to the ionosphere.     

A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability,implementation and tests

The ideal MHD equations are a central model in astrophysics, and their solution relies upon stable numerical schemes. We present an implementation of a new method, which possesses excellent stability properties. Numerical tests demonstrate that the theoretical stability properties are valid in practice with negligible compromises to accuracy. The result is a highly robust scheme with state-of-the-art efficiency. The scheme’s robustness is due to entropy stability, positivity and properly discretised Powell terms. The implementation takes the form of a modification of the MHD module in the FLASH code, an adaptive mesh refinement code. We compare the new scheme with the standard FLASH implementation for MHD. Results show comparable accuracy to standard FLASH with the Roe solver, but highly improved efficiency and stability, particularly for high Mach number flows and low plasma β. The tests include 1D shock tubes, 2D instabilities and highly supersonic, 3D turbulence. We consider turbulent flows with RMS sonic Mach numbers up to 10, typical of gas flows in the interstellar medium. We investigate both strong initial magnetic fields and magnetic field amplification by the turbulent dynamo from extremely high plasma β. The energy spectra show a reasonable decrease in dissipation with grid refinement, and at a resolution of 512³ grid cells we identify a narrow inertial range with the expected power law scaling. The turbulent dynamo exhibits exponential growth of magnetic pressure, with the growth rate higher from solenoidal forcing than from compressive forcing. Two versions of the new scheme are presented, using relaxation-based 3-wave and 5-wave approximate Riemann solvers, respectively. The 5-wave solver is more accurate in some cases, and its computational cost is close to the 3-wave solver.     

Global energy balance and density limit on CASTOR tokamak

Total radiative power losses have been measured by a pyroelectric detector on the CASTOR tokamak in a broad range of plasma parameters. It has been shown that while for the low density operation (n _e <10 ¹⁹ m ^–3 ) the most important channel of energy losses is a thermal conductivity, the high density regimes are radiation dominated. Using a simple analytic energy balance model, the connection between such a high level of radiation and shrinking of the current channel resulting in an enhanced MHD activity is discussed.The authors would like to thank Dr. R. Klíma for many helpful and stimulating discussions.     

Integer quantum Hall effect on an interface with disclinations

The Hall conductivity of an electron gas on an interface showing topological defects as disclinations in the presence of an orthogonal constant magnetic field is investigated. This kind of defect induces either positive or negative singular curvature in the medium. It is shown that the positive curvature decreases the quantum Hall plateau widths and shifts the steps in the Hall conductivity to lower magnetic fields. In contrast, the negative one leaves to the existence of two types of plateaus, one with higher widths and the other one with lower widths in comparison to the flat case. In this case, the shift in the steps of the Hall conductivity goes to higher magnetic fields. We also investigate the Hall conductivity for electrons around a cylindrically symmetric distribution of disclinations and it turns out that it is the same as that corresponding to a single effective disclination.     

Conductance of a 2D Corbino disk under QHE conditions in the presence of contact phenomena

It is noted that contacts of a two-dimensional (2DEG) electronic system with “external” metallic electrodes destroy the spatial uniformity of the density of the system. This gives rise to specific dimensional effects for the conductance of an unscreened Corbino disk in a magnetic field sufficient for the appearance of local regions with an integer-valued filling factor in the electron density profile. The overall pattern of the transport voltage distribution along the disk is seriously transformed. It becomes possible to explain the large (compared with the cyclotron energy) values of the critical transport voltage, leading to breakdown of the QHE regime. The experiment qualitatively confirms the predictions of the theory. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 1, 64–69 (10 January 1999)     

Formation of tight plasma pinches and generation of high-power soft x-ray radiation pulses in fast Z-pinch implosions

Argon K-shell plasma radiation source experiments were carried out on the GIT-12 generator [Bugaev, S.P. et al., 1997, Russian Phys. Journal, 40, 38] for a long (300 ns) implosion regime. The performance of a shell-on-solid-fill double gas puff was characterized in the experiments with and without an external axial magnetic field. The maximum Ar K-shell radiation yield registered in the experiments without an axial magnetic field was at the level of 1100 J/cm. This yield is consistent with the theoretically predicted yield for a short (100 ns) implosion regime. The experiments showed that the initial magnetic field which provides stabilization of the shell-on-solid-fill double gas puff was lower than that required for stabilization of a single annular gas puff. Satisfactory stabilization of the double gas puff was observed at an initial axial magnetic field of 1.4 kG. The maximum Ar K-shell radiation yield registered in the experiments with the axial magnetic field did not exceed 400 J/cm. A sharp reduction of the K-shell yield cannot be explained only by taking into account the energy losses associated with the compression of the axial magnetic field. Original Text ? Astro, Ltd., 2006.