Group properties and invariant solutions of equations of an electric field in the case of nonlinear ohm's law

1974 ◽  
Vol 13 (3) ◽  
pp. 285-292
Author(s):  
Yu. P. Emets ◽  
V. B. Taranov
Keyword(s):  
Electric Field ◽  
Invariant Solutions ◽  
Ohm’S Law ◽  
Ohm's Law ◽  
Solutions Of Equations

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.

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 Calculation of the radial electric field from a modified Ohm's law

2017 ◽  
Vol 24 (1) ◽  
pp. 012505 ◽  
Author(s):  
T. M. Wilks ◽  
W. M. Stacey ◽  
T. E. Evans
Keyword(s):  
Electric Field ◽  
Radial Electric Field ◽  
Ohm’S Law ◽  
Ohm's Law

scholarly journals A Comparison of Sparse and Non-sparse Techniques for Electric-Field Inversion from Normal-Component Magnetograms

Solar Physics ◽  
2021 ◽  
Vol 296 (12) ◽  
Author(s):  
Duncan H. Mackay ◽  
Anthony R. Yeates
Keyword(s):  
Electric Field ◽  
Magnetic Energy ◽  
Normal Component ◽  
Detailed Comparison ◽  
Solar Photosphere ◽  
Magnetic Vector Potential ◽  
Ohm’S Law ◽  
Spatially Resolved ◽  
Ohm's Law ◽  
Field Lines

AbstractAn important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm’s law. Yeates (Astrophys. J.836(1), 131, 2017) put forward a new “sparse” technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm’s law compared to previously used “non-sparse” techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen (Astrophys. J.729(2), 97, 2011). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen (2011) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates (2017) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates (2017) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen (2011) method produces consistent results using either approach. The sparse technique of Yeates (2017) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise.

scholarly journals Generalized Ohm's Law Decomposition of the Electric Field in Magnetosheath Turbulence: Magnetospheric Multiscale Observations

2020 ◽  
Author(s):  
Julia E. Stawarz ◽  
Lorenzo Matteini ◽  
Tulasi N. Parashar ◽  
Luca Franci ◽  
Jonathan P. Eastwood ◽  
...  
Keyword(s):  
Electric Field ◽  
Ohm’S Law ◽  
Magnetospheric Multiscale ◽  
Ohm's Law

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.

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