Solving procedure for the dynamics of charged particle in variable (time-dependent) electromagnetic field

Ershkov, Sergey V.; Leshchenko, Dmytro

doi:10.1007/s00033-020-01298-5

Cited by 8 publications

(2 citation statements)

References 20 publications

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“…One of the most important and old problems in the dynamics of charged particles governed by Lorentz force [1][2][3][4][5][6][7] in outer EM-field (at least, magnetic time-dependent field) is the Störmer problem, which refers to the magnetic-binary case when external magnetic field is considered to be as in classical dipole magnetic field (here, Earth's magnetic field) for further tracing the charged micro-particles along with portraying their trajectories (e.g., in case of solar wind attacking the outer atmosphere of Earth [2,3]). It is a well-known fact that this problem, despite it having a simple mathematical formulation presented in the governing equations, is unlikely to be solved even in semianalytical code [6].…”

Section: Introduction Equations Of Motionmentioning

confidence: 99%

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

Ershkov,

Prosviryakov,

Leshchenko

et al. 2023

Math Methods in App Sciences

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In this semianalytical research, we present a new ansatz in solving the Störmer problem with numerical findings in graphical representations of solutions where dynamics of the charged particle in the classical dipole magnetic field (here, Earth's magnetic field) was investigated in detail. We have fully solved the Störmer problem for partial class of the charged particle's motion close to the equatorial plane of Earth; this result is the main important theoretical finding presented here with prescribed symmetry. Aforementioned motions, determined by Lorentz force in nonrelativistic case, thereby are explored in polar coordinates to present them in a quasi‐periodic motions in a general case (in equatorial plane of Earth). Thus, the system of momentum equations has been successfully solved numerically or semianalytically in each case and the resulting semianalytical solving algorithm can clarify the quasi‐periodic structure of such family of solutions (with reduction of their geometric symmetry around the Earth in an equatorial plane).

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Section: Introduction Equations Of Motionmentioning

confidence: 99%

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

Ershkov,

Prosviryakov,

Leshchenko

et al. 2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similarly, with the imposition of a magnetic field, it is possible to deal with the heat transfer rates in waterways, tubes, etc., adequately. The driving force of MHD is essentially the electromagnetic force, which can also be used to energize the transport of charged particles [21]. Magnetohydrodynamic flow with all its characteristics is still complex in the field of atomic coolant pumping [22] and tokamak liquid metal structures [23].…”

Section: Introductionmentioning

confidence: 99%

Stefan Blowing Impacts on Unsteady MHD Flow of Nanofluid over a Stretching Sheet with Electric Field, Thermal Radiation and Activation Energy

et al. 2021

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In this paper, a mathematical model is established to examine the impacts of Stefan blowing on the unsteady magnetohydrodynamic (MHD) flow of an electrically conducting nanofluid over a stretching sheet in the existence of thermal radiation, Arrhenius activation energy and chemical reaction. It is proposed to use the Buongiorno nanofluid model to synchronize the effects of magnetic and electric fields on the velocity and temperature fields to enhance the thermal conductivity. We utilized suitable transformation to simplify the governing partial differential equation (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The obtained equations were solved numerically with the help of the Runge–Kutta 4th order using the shooting technique in a MATLAB environment. The impact of the developing flow parameters on the flow characteristics is analyzed appropriately through graphs and tables. The velocity, temperature, and nanoparticle concentration profiles decrease for various values of involved parameters, such as hydrodynamic slip, thermal slip and solutal slip. The nanoparticle concentration profile declines in the manifestation of the chemical reaction rate, whereas a reverse demeanor is noted for the activation energy. The validation was conducted using earlier works published in the literature, and the results were found to be incredibly consistent.

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A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy

Jabeen

Mushtaq

et al. 2023

Numerical Heat Transfer, Part A: Applications

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Solving procedure for the dynamics of charged particle in variable (time-dependent) electromagnetic field

Cited by 8 publications

References 20 publications

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

Stefan Blowing Impacts on Unsteady MHD Flow of Nanofluid over a Stretching Sheet with Electric Field, Thermal Radiation and Activation Energy

A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy

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