Euler potentials for two layers with non-constant current densities in the ambient magnetic field aligned to the layers

Vandas, M.; Romashets, E.

doi:10.5194/angeo-34-1165-2016

Cited by 2 publications

(3 citation statements)

References 26 publications

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“…To investigate an influence of FAC on fluxes of energetic particles, we follow the approach by Vandas and Romashets (2016). We consider an anisotropic gyrotropic monoenergetic particle distribution function, which at the equator has the form

f_{e} false(v, δ false) = \frac{n_{0}}{4 π v_{0}^{2}} false(1 + A_{1} normalcos δ false) δ_{normalD} false(v - v_{0} false),

where n 0 is the particle number density; v 0 and δ are the particle velocity and pitch angle, respectively; A 1 is a coefficient of anisotropy; and δ D is the Dirac delta function.…”

Section: Effects Of Fac On Energetic Particlesmentioning

confidence: 99%

“…In our previous papers (Romashets & Vandas, 2011, 2012; Vandas & Romashets, 2014, 2016), we have studied motion of charged particles in the magnetic field induced by various systems of surface or volume currents superimposed by an ambient uniform magnetic field. In this paper we model a three‐dimensional Earth's dipole magnetic field with FACs.…”

Section: Introductionmentioning

confidence: 99%

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Euler Potentials for the Earth Magnetic Field With Field‐Aligned Currents

Romashets

Vandas

2020

JGR Space Physics

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Euler potentials of the Earth's dipole magnetic field with field‐aligned currents are found. The results generalize ones obtained earlier for systems of plane currents parallel to an ambient uniform magnetic field. A real current system corresponding to an observed increase of the magnetic field measured by a low‐altitude spacecraft is used in this modeling. Parameters of charged particle trajectories, such as length and period, are determined for typical and strongly disturbed conditions. A particle distribution function is calculated.

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f_{e} false(v, δ false) = \frac{n_{0}}{4 π v_{0}^{2}} false(1 + A_{1} normalcos δ false) δ_{normalD} false(v - v_{0} false),

where n 0 is the particle number density; v 0 and δ are the particle velocity and pitch angle, respectively; A 1 is a coefficient of anisotropy; and δ D is the Dirac delta function.…”

Section: Effects Of Fac On Energetic Particlesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Euler Potentials for the Earth Magnetic Field With Field‐Aligned Currents

Romashets

Vandas

2020

JGR Space Physics

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“…The Euler potentials for two parallel and antiparallel current-carrying wires in the homogeneous ambient magnetic field were found in Romashets and Vandas (2011). The magnetic field and Euler potentials of two parallel and antiparallel current sheets in homogeneous ambient magnetic field, with uniform and non-uniform distribution of currents on sheets of zero thickness were studied in Romashets and Vandas (2012) and Vandas and Romashets (2016). The current sheets of finite thickness in the ambient magnetic field, and combined magnetic field with the Euler potentials were determined in Vandas and Romashets (2014).…”

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confidence: 99%

Exact Alpha‐Beta Mapping of IGRF Magnetic Field in the Ionosphere

Romashets,

Vandas

2024

JGR Space Physics

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Finding the magnetic flux mapping in the ionosphere is very important. It would not only divide the surface into the elements with the same flux, but also indicate locations of conjugated points. It is important for studies of field aligned currents and bouncing of energetic charged particles and their precipitation. The existing methods involve numerical magnetic field lines tracing in the entire volume of the magnetosphere or numerical integration along assumed contour lines of the Euler potentials on the surface of the ionosphere. It is possible to determine the mapping with these methods near the magnetic equator, but not on middle latitudes and near and inside the polar caps. Our approach is to search for the Euler potentials as a sum of basic functions with their coefficients. Each basic function is a product of a sine or cosine of longitude multiplied by m and the Legendre polynomial of the colatitude angle cosine and of the order n. Maxima of m and n in this calculation were set to 13. The difference between the radial component from the cross product of the Euler potentials gradients and from International Geomagnetic Reference Field is less than 0.01 percent. We discuss the possibility of using orthogonal coordinates defined on the sphere's surface, which remain finite functions of θ and φ everywhere except for the vicinities of the North and South poles. The issues with numerical errors accumulated on long tracing are avoided when using this approach.

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Euler potentials for two layers with non-constant current densities in the ambient magnetic field aligned to the layers

Cited by 2 publications

References 26 publications

Euler Potentials for the Earth Magnetic Field With Field‐Aligned Currents

Euler Potentials for the Earth Magnetic Field With Field‐Aligned Currents

Exact Alpha‐Beta Mapping of IGRF Magnetic Field in the Ionosphere

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