Stationary and nonstationary models of the global electric circuit: Well-posedness, analytical relations, and numerical implementation

Калинин, А. В.; Slyunyaev, N. N.; Mareev, E. A.; Zhidkov, A. A.

doi:10.1134/s0001433814030074

Cited by 22 publications

(30 citation statements)

References 20 publications

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“…i , then f (1) 5 f (2) and V (1) (Kalinin et al 2014). Therefore, V i can always be inferred from the solution of (8)-(10) and should not be specified explicitly.…”

Section: Problem Formulationmentioning

confidence: 95%

“…The question of to what extent it is possible to describe the global circuit by stationary equations is beyond the scope of this study; several aspects of this problem were discussed by Boström andFahleson (1976), Holzworth (1995), and Kalinin et al (2014). Equations (1)-(4) must be supplemented with Ohm's law:…”

Section: Problem Formulationmentioning

confidence: 99%

“…Therefore, V i can always be inferred from the solution of (8)-(10) and should not be specified explicitly. Furthermore, it can be proved that if some restrictions are imposed on the conductivity distribution and boundary surfaces, this problem is well posed; namely, there exists a solution to (8)-(10), which is unique in a certain class of functions [for more details, see Kalinin et al (2014) and references therein]. This also enables us to establish the connection between the equations for f [(8)-(10)] and the original equations [(1)-(6)] in terms of the fields.…”

Section: Problem Formulationmentioning

confidence: 99%

“…As in the steady-state case, one can introduce the electric potential, obtain a system of equations for it [from which the ionospheric potential is uniquely determined as a function of time V i (t)], prove that this problem is well posed, derive some explicit formulas for V i (t), and construct a numerical model calculating the distribution of the potential (Kalinin et al 2014).…”

Section: Explicit Formulas For the Ionospheric Potential And Numericamentioning

confidence: 99%

“…One of the most crucial advantages of our approach is that it is based on a well-posed problem formulation for a steady-state model of the global electric circuit, as discussed by Kalinin et al (2014), in which thunderstorm generators are treated as a continuous distribution of the external current and the ionospheric potential can always be uniquely determined from the solution. Under several simplifying assumptions about the conductivity distribution and thunderclouds, we obtain an approximate solution to the model equations and, whenever possible, compare it with the results of direct numerical simulations.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

Slyunyaev

Mareev

Калинин

et al. 2014

Journal of the Atmospheric Sciences

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Theoretical estimation of the influence of large-scale conductivity inhomogeneities on the global electric circuit and, in particular, on the ionospheric potential is considered. A well-posed formulation of this problem is presented, on the basis of which an approximate method is developed so as to take account of large-scale conductivity inhomogeneities. Under certain restrictions imposed on the distributions of the conductivity and the external current density, explicit approximate formulas for the ionospheric potential are derived. The approximation developed is shown to be equivalent to that of classical models of atmospheric electricity in which the atmosphere is divided into two or more columns and is replaced by a simple equivalent electric circuit. The effect of conductivity inhomogeneities located inside and outside thunderclouds is discussed and, in particular, it is demonstrated that taking account of the conductivity reduction inside thunderclouds leads to a substantial increase in the ionospheric potential. The results following from the approximate theory are compared with those obtained from direct numerical simulations. It is found that the suggested approximation qualitatively accounts for the dependence of the ionospheric potential on the parameters of the conductivity distribution, although the relative error may be significant, especially in the case of a substantial reduction in the conductivity inside thunderclouds.

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“…i , then f (1) 5 f (2) and V (1) (Kalinin et al 2014). Therefore, V i can always be inferred from the solution of (8)-(10) and should not be specified explicitly.…”

Section: Problem Formulationmentioning

confidence: 95%

Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

Section: Explicit Formulas For the Ionospheric Potential And Numericamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

Slyunyaev

Mareev

Калинин

et al. 2014

Journal of the Atmospheric Sciences

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Charge balance and ionospheric potential dynamics in time‐dependent global electric circuit model

Jánský

Pasko

2014

JGR Space Physics

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Citation:Jánský, J., and V. P. Pasko (2014), Charge balance and ionospheric potential dynamics in time-dependent global electric circuit model, J. Geophys. Res. Space Physics, 119, 10,184-10,203, doi:10.1002 An implicit time stepping is used to avoid a strict dielectric relaxation time step condition, and boundary conditions for Poisson's equation are implemented to allow accurate description of time evolution of the ionospheric potential. The concept of impulse response of GEC is introduced that allows effective representation of complex time dynamics of various physical quantities in the circuit using model results obtained for instantaneous deposition of a point charge. The more complex problems are then reconstructed using convolution and linearity principles. For a point charge instantaneously deposited at a typical thundercloud altitude the impulse response of the charge density shows induction of the same value and polarity charge at the ionospheric boundary, while charge of the same value but opposite sign is moving down logarithmically with time and neutralizes the source point charge on time scale corresponding to the dielectric relaxation time at altitude of the source point charge. The ionospheric potential is modified immediately with input of the source point charge based on free space solution of Poisson's equation. Then the ionospheric potential relaxes. It is shown that during formation of two main charge centers of the thundercloud, typically represented by a current dipole, the ionospheric potential can be determined from the difference of time integrals of two ionospheric potential impulse responses corresponding to charge locations at the opposite ends of the current dipole. For latitude-and longitude-independent conductivity model, the total charge on the Earth is exactly zero at all times. During cloud-to-ground lightning discharge, the ionospheric potential changes instantaneously by a value proportional to the charge moment change produced by lightning and then relaxes to zero. For a typical charge moment change of 35 C km and lightning frequency 10 s −1 , the ionospheric potential changes by 9.3 kV; this value agrees well with the results presented by Rycroft et al. (2007) and Rycroft and Odzimek (2010).

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On the variation of the ionospheric potential due to large‐scale radioactivity enhancement and solar activity

2015

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Sensitivity of the global electric circuit (GEC) to variations of atmospheric conductivity and current sources is analyzed and discussed. When the undisturbed exponential conductivity profile is assumed all over the Earth, the most substantial changes in the ionospheric potential (IP) are caused by conductivity perturbations inside thunderstorms; if, in addition, conductivity reduction inside thunderstorms and nonelectrified clouds is assumed, the IP becomes less sensitive to conductivity perturbations; besides, the IP is even more sensitive to source current variations than to conductivity. Current source and voltage source descriptions of GEC generators are compared; it is shown that the IP variation may critically depend on the chosen description. As an application, the IP variation due to nuclear weapons testing is studied; it is shown that neither local nor global increase of conductivity in the stratosphere could alone explain the observed 40% IP increase in the 1960s; at the same time this increase might be accounted for by a 40% increase in the source current density or a 46% reduction of the conductivity inside thunderstorms, provided that it was not reduced initially. The IP variation due to solar activity and, in particular, due to solar modulation of galactic cosmic ray flux is also discussed and modeled, which required an adequate parameterization of the rate of atmospheric ion pair production over the solar cycle. It is estimated that the maximum IP variation on the scale of the solar cycle does not exceed 5% of the mean value, unless source current perturbations are taken into account.

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Stationary and nonstationary models of the global electric circuit: Well-posedness, analytical relations, and numerical implementation

Cited by 22 publications

References 20 publications

Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

Influence of Large-Scale Conductivity Inhomogeneities in the Atmosphere on the Global Electric Circuit

Charge balance and ionospheric potential dynamics in time‐dependent global electric circuit model

On the variation of the ionospheric potential due to large‐scale radioactivity enhancement and solar activity

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