Generalized Ohm's law in multifluid systems
Generalized Ohm law from Boltzmann equation for multifluid systems under nonlocal thermodynamic equilibrium
Wu, S.-T.↗
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Ohm's law for a current sheet
The paper derives an Ohm's law for single-particle motion in a current sheet, where the magnetic field reverses in direction across the sheet. The result is considerably different from the resistive Ohm's law often used in MHD studies of the geomagnetic tail. Single-particle analysis is extended to obtain a self-consistency relation for a current sheet which agrees with previous results. The results are applicable to the concept of reconnection in that the electric field parallel to the current is obtained for a one-dimensional current sheet with constant normal magnetic field. Dissipated energy goes directly into accelerating particles within the current sheet.
Lyons, L. R.↗
Plasma Jet Simulations Using a Generalized Ohm's Law
Plasma jets are important physical phenomena in astrophysics and plasma propulsion devices. A currently proposed dual jet plasma propulsion device to be used for ISS experiments strongly resembles a coronal loop and further draws a parallel between these physical systems [1]. To study plasma jets we use numerical methods that solve the compressible MHD equations using the generalized Ohm s law [2]. Here, we will discuss the crucial underlying physics of these systems along with the numerical procedures we utilize to study them. Recent results from our numerical experiments will be presented and discussed.
Ebersohn, Frans↗
Estimates of Terms in Ohm's Law During an Encounter with an Electron Diffusion Region
We present measurements from the Magnetospheric Multiscale (MMS) mission taken during a reconnection event on the dayside magnetopause which includes a passage through an electron diffusion region (EDR). The four MMS satellites were separated by about 10 km such that estimates of gradients and divergences allow a reasonable estimate of terms in the generalized Ohm's law, which is key to investigating the energy dissipation during reconnection. The strength and character of dissipation mechanisms determines how magnetic energy is released. We show that both electron pressure gradients and electron inertial effects are important, but not the only participants in reconnection near EDRs, since there are residuals of a few mVm (approximately 30-50%) of E+ U(sub e) x B (from the sum of these two terms) during the encounters. These results are compared to a simulation, which exhibits many of the observed features, but where relatively little residual is present.
Torbert, R. B.↗
Magnetospheric Multiscale measurements of turbulent electric fields in earth's magnetosheath: How do plasma conditions influence the balance of terms in generalized Ohm's law?
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Harry C. Lewis↗
Generalized Ohm's Law Decomposition of the Electric Field in Magnetosheath Turbulence: Magnetospheric Multiscale Observations
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Julia E. Stawarz↗
Ohm's law in the fast lane: general relatiivistic charge dynamics
Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, as well as the evolution of the electromagnetic field, in highly dynamical relativistic environments on timescales much shorter than the collapse time (GM/c3).
magnetic fields black holes↗
Effect of Hall current on Rayleigh-Taylor instability of a plasma.
Rayleigh-Taylor instability of plasma is unaffected by inclusion of Hall current and electron-inertia terms in generalized Ohm law
PLASMA INSTABILITY↗
Magnetic Reconnection and Modification of the Hall Physics Due to Cold Ions at the Magnetopause
Observations by the four Magnetospheric Multiscale spacecraft are used to investigate the Hall physics of a magnetopause magnetic reconnection separatrix layer. Inside this layer of currents and strong normal electric fields, cold (eV) ions of ionospheric origin can remain frozen-in together with the electrons. The cold ions reduce the Hall current. Using a generalized Ohms law, the electric field is balanced by the sum of the terms corresponding to the Hall current, the v x B drifting cold ions, and the divergence of the electron pressure tensor. A mixture of hot and cold ions is common at the subsolar magnetopause. A mixture of length scales caused by a mixture of ion temperatures has significant effects on the Hall physics of magnetic reconnection.
Andre, M.↗
First-Principles Modeling of IAT-Driven Anomalous Resistivity in Hollow Cathode Discharges II: Numerical Simulations and Comparisons with Experiments
We present a model that quantifies the magnitude of the ion-acoustic turbulence (IAT) in the plume of hollow cathodes and its effect on the resistivity and ion heating. The model takes the form of a partial differential equation (PDE) that can be solved concurrently with the equations of motion for a partially ionized plasma already included in our numerical code for the simulation of the plasma discharge in hollow cathodes, OrCa2D. We also determine that self-induced magnetic fields are not negligible in hollow cathodes operating at large discharge currents and implement in our code Ampere’s law and modifications to Ohm’s law that account for this effect. Numerical simulations that employed these models show large improvements in our agreement with experimental measurements with respect to a previous model, which assumed complete saturation of the IAT and did not account for the growth stage of the waves. In particular, the model is able to accurately predict the location and magnitude of the maximum resitivity to the electron current along the cathode centerline.
Lopez Ortega, Alejandro↗
Performance Theory of Diagonal Conducting Wall MHD Accelerators
The theoretical performance of diagonal conducting wall crossed field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm's law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm's law by imposing appropriate configuration and loading constraints. A current dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities lead to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed field accelerator operation.
Litchford, R. J.↗
Performance Theory of Diagonal Conducting Wall Magnetohydrodynamic Accelerators
The theoretical performance of diagonal conducting wall crossed-field accelerators is examined on the basis of an infinite segmentation assumption using a cross-plane averaged generalized Ohm s law for a partially ionized gas, including ion slip. The desired accelerator performance relationships are derived from the cross-plane averaged Ohm s law by imposing appropriate configuration and loading constraints. A current-dependent effective voltage drop model is also incorporated to account for cold-wall boundary layer effects, including gasdynamic variations, discharge constriction, and electrode falls. Definition of dimensionless electric fields and current densities leads to the construction of graphical performance diagrams, which further illuminate the rudimentary behavior of crossed-field accelerator operation.
Litchford, R. J.↗
Thermoelectric effects in decaying homogeneous magneto-gas turbulence
In the formulation of compressible MHD (i.e., magneto-gas dynamics), a 'generalized Ohm's law is required. In particular, an electron pressure term and a 'Hall effect' term may appear as non-negligible additions to the Ohm's law that is conventionally used for incompressible MHD. In 'high-beta' (i.e., relatively low magnetic energy) situations, the Hall term may be neglected (at least initially) but, as it turns out, the electron pressure term cannot be neglected. Here, three-dimensional, high-beta, homogeneous, decaying, magneto-gas turbulence is examined with regard to this additional term. Through numerical simulation, it is found that 'thermoelectric effects' are produced that significantly alter the evolution of the magnetic field and electric current strengths.
Shebalin, John V.↗
Electrothermal oscillations and the quasilinear theory of electron enthalpy fluctuations in magnetohydrodynamic generators and magnetoplasmadynamic arc thrusters
Flucturations in electron density and temperature coupled through OHM's Law are studied for MHD power generator and MPD arc thruster applications. The dispersion relation based on linear theory is derived, and the two limiting cases of infinite ionization rate and frozen flow are examined. The nonlinear effects of the frozen flow case are then studied in the quasilinear limit. Equations are derived for the amplitude of the fluctuation and its effect upon Ohm's Law and the electron temperature equation. Conditions under which a steady state can exist in the presence of the fluctuation are examined, and effective transport properties are determined.
Smith, J. M.↗
Electric Currents Through Ion Tracks in Silicon Devices
A modified form of Ohm's law, describing electric currents through ion tracks, is presented as a tool for future theoretical modeling efforts related to charge collection from ion tracks in silicon devices.
Ohm's↗
Hall-Effect Thruster Simulations with 2-D Electron Transport and Hydrodynamic Ions
A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.
plasma↗
Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters
Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.
Smith, M.↗
Quasi-linear theory of electron density and temperature fluctuations with application to MHD generators and MPD arc thrusters.
Fluctuations in electron density and temperature coupled through Ohm's law are studied for an ionizable medium. The nonlinear effects are considered in the limit of a third order quasi-linear treatment. Equations are derived for the amplitude of the fluctuation. Conditions under which a steady state can exist in the presence of the fluctuation are examined and effective transport properties are determined. A comparison is made to previously considered second order theory. The effect of third order terms indicates the possibility of fluctuations existing in regions predicted stable by previous analysis.
Smith, J. M.↗