Ion Slip Research Articles

Influence of hall effect and ion slip on velocity and temperature fields in an MHD channel

The combined influence of viscosity, Hall effect and ion slip on hydrodynamic fields and on heat transfer is investigated. The exact solutions for velocity, induced magnetic field and temperature are derived for the laminar MHD flow in a flat channel assuming a small magnetic Reynolds number, finely segmented electrodes, fully developed flow and uniform heat flux at channel walls. The internal generation of heat is not considered. The Kantorowitsch method of variational calculus is employed to approximate the complicated velocity distribution.

Electron and ion momentum transfer from plasma electrical conductivity in a magnetic field

The electrical conductivity of a partially to strongly (Coulomb collision-dominated) ionized dc plasma in a dc magnetic field was investigated at low frequency by two experimental methods, one utilizing the Hall effect and the other a plasma interaction with an induced solenidal electric field. Electron-ion and electron-atom momentum transfer collision frequencies and ion mobility in the magnetic field (ion slip) were inferred. The helium abnormal negative glow plasma was used at pressures of 0.5 to 2.5 Torr, electron densities of 1 to 32 × 1017m−3 and temperature ≈ 600 °K; the magnetic field ranged up to 675 G. The data support Shkarofsky's theory of partial ionization. When ion motion becomes dominant, the resulting ion mobility is 75% larger that He+ mobility in helium taken from drift tube measurements. This disagreement suggests that further theoretical work on ion mobility in a plasma is needed.

Dispersive waves in a slightly ionized nonequilibrium plasma

The equations giving the response of a slightly ionized plasma with monatomic components to sinusoidal perturbations are formulated. Included in the model equations are the electron Hall effect, electron thermal diffusion, radiation and electron-atom rate processes. Plasma conditions are limited to those where viscous effects, the induced magnetic field, ion slip and atom-atom inelastic processes can be neglected. The limiting cases of frozen and equilibrium electron excited state populations are discussed. Presented are results of calculations for MHD generators with a working fluid of potassium seeded argon and with a Boltzmann distribution of electron quantum states of the seed in steady state.

Incompressible Magnetohydrodynamic Entrance Flow in a Plane Channel

The hydromagnetic flow of a conducting, incompressible fluid in the entrance section of a plane channel is analyzed. The problem is generalized to include a small cross-flow, small wall injection, Hall currents, and ion slip. The solution is carried out using two methods. The first is the generalized Kármán-Pohlhausen momentum integral method, and the second utilizes asymptotic power series in the small parameter ξ = (x/LRe)1/2. The equations are solved numerically, and the two results compared with one another, as well as with similar studies in the literature.

Electrical equivalent circuits of D.C. MHD generators

In the paper the equivalent circuits of generators with the segmented electrodes electrically connected in various ways are determined (generators with the electrodes connected in series, with Halland Faraday-connected electrodes). Constant gas dynamic parameters, constant generator cross-section, constant magnetic field and uniformity of current density and electric field are assumed. Electrode effects, end effects and “ion slip” are neglected. From the equivalent circuits the electrical terminal values of the generator as a function of the geometric dimensions of the generator, the Hall parameter and the connexions system of electrodes can easily be determined.

Physical property distributions in a low- pressure crossed-field plasma accelerator.

The physical phenomena that occur in a steady crossed-field accelerator were studied both experimentally and analytically. Experiments were conducted on a crossed-field accelerator of conventional design employing a single electrode pair and operated with argon at a channel static pressure of about 1-mm Hg and a magnetic field of up to 5000 gauss. Measurements of the current distribution over the anode and cathode surfaces and the potential and electron temperature distributions between the anode and cathode were obtained. An approximate theoretical analysis of the accelerator was developed which accounts for Hall effects, ion slip, viscosity, and elevated electron temperature. From this analysis, the potential, current density, and electron and atom temperature distributions were calculated. The calculations agreed reasonably well with the measurements except in the region near the electrode surfaces. As expected, at large values of the Hall parameter, the current distribution was found to be unsuitable for producing a high accelerator efficiency.

Shock Structure in a Partially Ionized Gas

The structure of a steady plane shock in a partially ionized gas is investigated using the Navier-Stokes equations for the atom, electron, and ion fluids. Across the shock, quasi-neutrality and frozen ionization is assumed. For all degrees of ionization there is shown to be a broad thermal layer of elevated electron temperature ahead of the shock front and a precursor and imbedded axial electric field induced by the charge separation. Because of the large atom-ion charge exchange cross section, ion slip is small for less than 30% ionization. In a weakly ionized plasma, the atom flow is unaffected by the ionized particles and the structure consists of an ordinary atom shock imbedded in the thermal layer. For substantial ionization, the heavy particles are compressed and heated in the thermal layer and in the shock the ion and atom temperatures overshoot their downstream values. The induced electric fields increase with degree of ionization and free stream Mach number while the shock thickness decreases. A measurement in partially ionized hydrogen of potential variation in a strong shock gives a potential rise across the imbedded shock and thickness in good agreement with the calculated values.

Analytical solution for constant enthalpy mhd accelerator

Abstract : A closed form solution is obtained for a constant enthalpy, crossed field accelerator. The onedimensional inviscid equations of motion are integrated, assuming that the axial variation of electrical energy addition and the area variation are specified. The accelerator is assumed to be segmented, and ion slip effects are ig nored. The solution is useful for a parametric study of a hypervelocity wind tunnel which employs an MHD accelerator. (Author)

The performance of a magnetohydro-dynamic re-entry vehicle channel

The performance of a magneto-hydrodynamic (MHD) channel is discussed. Solutions of the MHD equations are evaluated through the channel as a function of inlet Mach number, voltage parameter, magnetic-interaction parameter, and channel aspect ratio. The over-all performance of a re-entry vehicle channel throughout the trajectory is described for various vehicle applications as a function of the trajectory, the channel, and the vehicle geometry. Various design aspects are discussed including the coil channel, electrodes, seeding requirements, Hall and ion slip effects. A typical MHD channel and coil design is included.

The Effects of Hall and Ion Slip on the Electrical Conductivity of Partially Ionized Gases for Magnetohydrodynamic Re-Entry Vehicle Application

The presence of a partially ionized gas around a hypersonic vehicle permits the application of magnetohydrodynamic (MHD) devices during re-entry. The operation of such MHD devices on a re-entry vehicle will largely depend on the magnitude of the electrical conductivity of the gas between the electrodes. In some cases it may be necessary to seed the air in order to insure high conductivity. The operation of the re-entry vehicle at relatively low gas densities and high magnetic fields will produce Hall and ion slip effects which may materially reduce the effective conductivity between the electrodes. The electrical conductivity including Hall and ion slip effects for air is presented for a wide range of pressures and temperatures and for a typical re-entry vehicle, with and without seeding. The electrical conductivity is evaluated for equilibrium conditions considering the number density and collision cross sections for electrons, neutrals, and ions. The Hall and ion slip effects are evaluated from the degree of ionization, the cyclotron frequency, and the time between collisions for electrons, neutrals, and ions.

Some Consequences of Ion Slip in a Plasma flowing through a Magnetic Field

DIRECT generation of electrical power can be achieved by driving a conducting gas through a magnetic field transverse to the direction of flow. The necessary conductivity is obtained by heating the gas to a temperature at which appreciable thermal ionization occurs, the latter in accordance with the Saha equation. The conducting gas will be considered to consist of neutral particles and charged particles, no distinction being made between ions and electrons. It is the purpose of this communication to discuss the behaviour of this system as it flows along a duct (neglecting wall effects) through a uniform transverse magnetic field as shown in Fig. 1.

One-dimensional flow of an ionized gas through a magnetic field

As a primary step towards understanding the flow of a partially ionized gas in a magnetic field, we have studied both theoretically and experimentally the problem in which the gas flow is one-dimensional. This simplification permits a detailed calculation of the flow field and a quantitative comparison of the theory with observations made in a shock tube.An ionized gas is composed of three species: electrons, ions and neutral particles. To take complete account of all the phenomena occurring when the high-velocity gas interacts with the magnetic field, the motion of all three species must be considered. When this is done, it is found that the electrical conductivity of the gas is a tensor dependent on both the magnitude and geometry of the magnetic field. However, when the collision frequency for the electrons is greater than their cyclotron frequency in a magnetic field, the gas may be treated as a continuum with a scalar conductivity. For such gas states, all of the observed effects for two experimental geometries in which the gas current forms closed loops in the magnetic field can be explained with a simple theory. The interaction produces a flow completely analogous to pipe flow with friction and no heat transfer, where the wall friction force is replaced by the magnetic body force which can choke the flow if the body forces are larger than a certain minimum value.Using the same experimental geometries, the gas state is then adjusted so that the electrical conductivity is a tensor. Outstanding among the observed effects are ion slip, where the ions and neutrals travel through the field at different velocities, and Hall currents, generated by the drift of the charged particles across magnetic field lines. The observed effects again agree with the predicted values.

Two-dimensional incompressible magneto-hydrodynamic flow across an elliptical solenoid

An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.