scholarly journals Time evolution of electric fields and currents and the generalized Ohm's law

2005 ◽  
Vol 23 (4) ◽  
pp. 1347-1354 ◽  
Author(s):  
V. M. Vasyliūnas
Keyword(s):  
Electric Field ◽  
Electric Current ◽  
Time Evolution ◽  
Time Scales ◽  
Current Density ◽  
Time Derivative ◽  
Electron Plasma ◽  
Displacement Current ◽  
Ohm’S Law ◽  
Ohm's Law

Abstract. Fundamentally, the time derivative of the electric field is given by the displacement-current term in Maxwell's generalization of Ampère's law, and the time derivative of the electric current density is given by the generalized Ohm's law. The latter is derived by summing the accelerations of all the plasma particles and can be written exactly, with no approximations, in a (relatively simple) primitive form containing no other time derivatives. When one is dealing with time scales long compared to the inverse of the electron plasma frequency and spatial scales large compared to the electron inertial length, however, the time derivative of the current density becomes negligible in comparison to the other terms in the generalized Ohm's law, which then becomes the equation that determines the electric field itself. Thus, on all scales larger than those of electron plasma oscillations, neither the time evolution of J nor that of E can be calculated directly. Instead, J is determined by B through Ampère's law and E by plasma dynamics through the generalized Ohm's law. The displacement current may still be non-negligible if the Alfvén speed is comparable to or larger than the speed of light, but it no longer determines the time evolution of E, acting instead to modify J. For theories of substorms, this implies that, on time scales appropriate to substorm expansion, there is no equation from which the time evolution of the current could be calculated, independently of ∇xB. Statements about change (disruption, diversion, wedge formation, etc.) of the electric current are merely descriptions of change in the magnetic field and are not explanations.

A three-dimensional, iterative mapping procedure for the implementation of an ionosphere-magnetosphere anisotropic Ohm's law boundary condition in global magnetohydrodynamic simulations

1995 ◽  
Vol 13 (8) ◽  
pp. 843-853 ◽  
Author(s):  
M. L. Goodman
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Electric Field ◽  
Current Density ◽  
Time Step ◽  
Mhd Simulation ◽  
Ohm’S Law ◽  
Field Aligned Current ◽  
Ohm's Law ◽  
The Magnetic Field

Abstract. The mathematical formulation of an iterative procedure for the numerical implementation of an ionosphere-magnetosphere (IM) anisotropic Ohm's law boundary condition is presented. The procedure may be used in global magnetohydrodynamic (MHD) simulations of the magnetosphere. The basic form of the boundary condition is well known, but a well-defined, simple, explicit method for implementing it in an MHD code has not been presented previously. The boundary condition relates the ionospheric electric field to the magnetic field-aligned current density driven through the ionosphere by the magnetospheric convection electric field, which is orthogonal to the magnetic field B, and maps down into the ionosphere along equipotential magnetic field lines. The source of this electric field is the flow of the solar wind orthogonal to B. The electric field and current density in the ionosphere are connected through an anisotropic conductivity tensor which involves the Hall, Pedersen, and parallel conductivities. Only the height-integrated Hall and Pedersen conductivities (conductances) appear in the final form of the boundary condition, and are assumed to be known functions of position on the spherical surface R=R1 representing the boundary between the ionosphere and magnetosphere. The implementation presented consists of an iterative mapping of the electrostatic potential ψ the gradient of which gives the electric field, and the field-aligned current density between the IM boundary at R=R1 and the inner boundary of an MHD code which is taken to be at R2>R1. Given the field-aligned current density on R=R2, as computed by the MHD simulation, it is mapped down to R=R1 where it is used to compute ψ by solving the equation that is the IM Ohm's law boundary condition. Then ψ is mapped out to R=R2, where it is used to update the electric field and the component of velocity perpendicular to B. The updated electric field and perpendicular velocity serve as new boundary conditions for the MHD simulation which is then used to compute a new field-aligned current density. This process is iterated at each time step. The required Hall and Pedersen conductances may be determined by any method of choice, and may be specified anew at each time step. In this sense the coupling between the ionosphere and magnetosphere may be taken into account in a self-consistent manner.

Motion of Electron Gas and the Induced Nanofilm Electromigration

2007 ◽  
Author(s):  
Bing-Yang Cao ◽  
Qing-Guang Zhang ◽  
Zeng-Yuan Guo
Keyword(s):  
Kinetic Energy ◽  
Electric Current ◽  
Current Density ◽  
Electron Gas ◽  
Electric Current Density ◽  
Electric Resistance ◽  
Energy Effect ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Electron Wind

Understanding how electron gas moves and induces electromigration is highly desirable in micro- and nano-electronic devices. Based on introducing some novel concepts of electron gas momentum, kinetic energy and resisting force, we establish the continuum, momentum and energy conservation equations of the electron gas in this paper. Through analyzing the control equations, the Ohm’s law can be derived if the inertial force or the kinetic energy of the electron gas is ignored. Thus, the Ohm’s law is no longer applicable if the variation of the electron gas momentum is too large to be ignored. For instance, the kinetic energy variation can not be ignored for the electron gas with a high velocity flowing along the conductor with variable cross-sections. Under such conditions, the electric resistance of the section-variable conductors is a function of the electric current density and direction, which is referred to as a kinetic energy effect on the electric resistance. Based on the control equations of the electron gas motion, the electron wind force and the kinetic energy can also be calculated. The kinetic energy transferred from the electron wind to metallic atoms increases greatly with the increasing electric current density. It may be comparable with the activated energy of the metallic atoms in nanofilms. Thus, the electromigration induced by the electron wind can be regarded as another kind of kinetic energy effect of the electron gas, i.e. kinetic energy effect on the electromigration.

scholarly journals Electric Currents Connected With the Proton Flares of 7 July and 2 September, 1966

1971 ◽  
Vol 43 ◽  
pp. 417-421
Author(s):  
A. B. Severny
Keyword(s):  
Active Region ◽  
Field Strength ◽  
Magnetic Flux ◽  
Electric Field ◽  
Electric Field Strength ◽  
Electric Conductivity ◽  
Electric Current ◽  
Current Density ◽  
High Energy ◽  
Electric Currents

It is observed that the change of the net magnetic flux associated with flares can exceed 1017 Mx/s, which corresponds according to Maxwell's equation to the e.m.f. ∼ 109 V which is specific for the high energy protons generated in flares. It is shown that this value of e.m.f. can hardly be compensated by e.m.f. of inductance which should appear due to the actually measured motions in a flare generating active region. The values of electric field strength thus found, together with measured values of electric current density (from rotH), leads to an electric conductivity which is 103 times smaller than usually adopted.

The Electric Field in Maxwell's Equations

1978 ◽  
Vol 15 (2) ◽  
pp. 169-171 ◽  
Author(s):  
Z. L. Budrikis
Keyword(s):  
Electric Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Coulomb Force ◽  
Maxwell’S Equation ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Maxwell's Equation

The field E in Maxwell's equation curl E = – δB/δ t is limited to induction and Coulomb force. It does not extend to all phenomena that are included in E of Ohm's law, J = σE. Maxwell's equation would need another term to account for additional vorticity of the E in Ohm's law.

scholarly journals Comparative Analysis of the Various Generalized Ohm's Law Terms in Magnetosheath Turbulence as Observed by Magnetospheric Multiscale

2021 ◽  
Author(s):  
Julia Stawarz ◽  
Lorenzo Matteini ◽  
Tulasi Parashar ◽  
Luca Franci ◽  
Jonathan Eastwood ◽  
...  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Electron Mass ◽  
Turbulent Fluctuation ◽  
Electron Pressure ◽  
Ohm’S Law ◽  
Magnetospheric Multiscale ◽  
Ohm's Law ◽  
Turbulent Plasmas ◽  
The Impact

<p><span>Electric fields (<strong>E</strong>) play a fundamental role in facilitating the exchange of energy between the electromagnetic fields and the changed particles within a plasma. </span>Decomposing <strong>E</strong> into the contributions from the different terms in generalized Ohm's law, therefore, provides key insight into both the nonlinear and dissipative dynamics across the full range of scales within a plasma. Using the unique, high‐resolution, multi‐spacecraft measurements of three intervals in Earth's magnetosheath from the Magnetospheric Multiscale mission, the influence of the magnetohydrodynamic, Hall, electron pressure, and electron inertia terms from Ohm's law, as well as the impact of a finite electron mass, on the turbulent electric field<strong> </strong>spectrum are examined observationally for the first time. The magnetohydrodynamic, Hall, and electron pressure terms are the dominant contributions to <strong>E</strong> over the accessible length scales, which extend to scales smaller than the electron gyroradius at the greatest extent, with the Hall and electron pressure terms dominating at sub‐ion scales. The strength of the non‐ideal electron pressure contribution is stronger than expected from linear kinetic Alfvén waves and a partial anti‐alignment with the Hall electric field is present, linked to the relative importance of electron diamagnetic currents within the turbulence. The relative contributions of linear and nonlinear electric fields scale with the turbulent fluctuation amplitude, with nonlinear contributions playing the dominant role in shaping <strong>E</strong> for the intervals examined in this study. Overall, the sum of the Ohm's law terms and measured <strong>E</strong> agree to within ∼ 20% across the observable scales. The results both confirm a number of general expectations about the behavior of <strong>E</strong> within turbulent plasmas, as well as highlight additional features that may help to disentangle the complex dynamics of turbulent plasmas and should be explored further theoretically.</p>

scholarly journals Relation between magnetic fields and electric currents in plasmas

2005 ◽  
Vol 23 (7) ◽  
pp. 2589-2597 ◽  
Author(s):  
V. M. Vasyliunas
Keyword(s):  
Electric Field ◽  
Time Scales ◽  
Electric Fields ◽  
Spatial Scales ◽  
Charged Particles ◽  
Displacement Current ◽  
Plasma Dynamics ◽  
Electric Fields And Currents ◽  
The One ◽  
The Magnetic Field

Abstract. Maxwell's equations allow the magnetic field B to be calculated if the electric current density J is assumed to be completely known as a function of space and time. The charged particles that constitute the current, however, are subject to Newton's laws as well, and J can be changed by forces acting on charged particles. Particularly in plasmas, where the concentration of charged particles is high, the effect of the electromagnetic field calculated from a given J on J itself cannot be ignored. Whereas in ordinary laboratory physics one is accustomed to take J as primary and B as derived from J, it is often asserted that in plasmas B should be viewed as primary and J as derived from B simply as (c/4π)∇×B. Here I investigate the relation between ∇×B and J in the same terms and by the same method as previously applied to the MHD relation between the electric field and the plasma bulk flow vmv2001: assume that one but not the other is present initially, and calculate what happens. The result is that, for configurations with spatial scales much larger than the electron inertial length λe, a given ∇×B produces the corresponding J, while a given J does not produce any ∇×B but disappears instead. The reason for this can be understood by noting that ∇×B≠4π/c)J implies a time-varying electric field (displacement current) which acts to change both terms (in order to bring them toward equality); the changes in the two terms, however, proceed on different time scales, light travel time for B and electron plasma period for J, and clearly the term changing much more slowly is the one that survives. (By definition, the two time scales are equal at λe.) On larger scales, the evolution of B (and hence also of ∇×B) is governed by ∇×E, with E determined by plasma dynamics via the generalized Ohm's law; as illustrative simple examples, I discuss the formation of magnetic drift currents in the magnetosphere and of Pedersen and Hall currents in the ionosphere. Keywords. Ionosphere (Electric fields and currents) – Magnetospheric physics (Magnetosphere-ionosphere interactions) – Space plasma physics (Kinetic and MHD theory)

scholarly journals Use of filtration and electricity analogy in simulation of underflooding protection in urban construction

2021 ◽  
Vol 18 (4) ◽  
pp. 450-462
Author(s):  
V. I. Sologaev
Keyword(s):  
Electric Current ◽  
New Technologies ◽  
Darcy’S Law ◽  
Underground Water ◽  
Darcy's Law ◽  
Water Filtration ◽  
Ohm’S Law ◽  
Balance Principle ◽  
Urban Construction ◽  
Ohm's Law

Introduction. The fight against underflooding remains an urgent problem. The application of the analogy between water filtration and electric current has the goal of protecting the environment, built-up areas and, in particular, highways in cities from underflooding. Writing Ohm’s law similarly to Darcy’s filtration law, we achieve a better match to their analogy. This, in turn, makes it possible to develop new technologies for protection against underflooding in urban construction, for example, electroosmotic dewatering and its modeling. Such technologies make it possible to drain clayey soils.Methods and materials. Darcy’s law, Ohm’s law and the law of electroosmotic filtration are considered together. A methodology for modelling construction dewatering is given, taking into account the combined effect of the two physical laws of water filtration and electroosmosis, optimally combining the high-altitude geometric arrangement of drainage bases and contact electrodes. The options for draining clay soil under the action of an electric field are presented. With the combined use of gravitational forces and electric direct current forces in the drained soil, the total filtration rate is the sum of the Darcy’s law component and another component of the water velocity – electroosmotic filtration. An additional feature of joint modelling in a porous medium of water filtration and electroosmosis is that the mass of the water-resistant part of the soil and its part related to the dielectric may not coincide. This complexity of the model is overcome by dividing it into modules, which can then be combined in compliance with the balance principle, stitching modules along the boundaries. To continue the scientific discussion, a short but informative overview of international publications on the topic under consideration is given.Discussion. The methodology for complex calculation and modelling of the joint processes of water filtration in soils, the flow of electric current and electroosmotic filtration can find useful application in the development of effective protection against underflooding in urban construction. a sequence of algorithmic modelling steps is recommended. initially, it is recommended to run rough spreadsheet simulations on personal computers and mobile phones. next, a different modelling approach should be applied. based on the initial rough models of the previous step, it is necessary to write the algorithms in the programming language. the compiled model of the investigated filtration and electroosmosis processes will significantly increase the reliability of the design of protection against underflooding.conclusion. a comparison is made of the joint use of construction dewatering means of different physical essence, with simultaneous processes of gravitational filtration of underground water and passing a direct electric current through the drained soil, which causes an additional effect of electroosmosis. it is proposed to apply in a new way the analogy of water filtration and electric current in order to achieve more effective results of engineering activities by modeling protection against underflooding of building areas, ensuring the safety of urban construction when the level of groundwater rises.

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