Abstract
Distinctive features of the drift motion of a nonrelativistic charged particle in slowly varying magnetic and strong electric fields, for which the assumption that the electric drift velocity is small as compared to the total particle velocity is non-applicable, are studied. The variational principles of the drift motion are extended to the case of the strong electric field. The generalized Littlejohn’s Lagrangian is obtained and the extended set of drift equations is derived. The possibility of particle acceleration due to the drift motion along the strong electric field is demonstrated.
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Notes
An alternative method for deriving the expression (11) is based on the fundamental property of invariance of the equations of motion with respect to the substitution \(L \to L + dF{\text{/}}dt\), where F is an arbitrary scalar function. The choice of such a function in the form of \(F({\mathbf{R}},t) = - \frac{{m{{u}^{2}}}}{{2\Omega B}}{{{\mathbf{e}}}_{2}} \cdot ({{{\mathbf{e}}}_{2}} \cdot \nabla ){\mathbf{A}}\) results in the cancellation of “unnecessary” terms in expression (9).
In Eq. (12), the \({{v}_{\parallel }}\) and R variables are considered to be independent, and, in the subsequent derivation of the drift equations of motion, their independent variation is used; to derive the drift equations from expression (1) for the Lagrangian \(L{\text{*}}\), it is necessary to consider \({{v}_{\parallel }}\) as a function of R: \({{v}_{\parallel }} = {{v}_{\parallel }}({\mathbf{R}})\).
In the case of the strong electric field, one should also set \({\mathbf{b}} \cdot \nabla \times {{{\mathbf{V}}}_{{\text{E}}}} = 0\).
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Funding
The work was supported in part by the Ministry of Education and Science of the Russian Federation (contract no. 3.2223.2017/4.6, Section 3) and the RUDN University Program 5-100 (Section 2).
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Marusov, N.A., Sorokina, E.A. & Ilgisonis, V.I. Drift Motion of Charged Particles in Inhomogeneous Magnetic and Strong Electric Fields. Plasma Phys. Rep. 46, 724–731 (2020). https://doi.org/10.1134/S1063780X20070065
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DOI: https://doi.org/10.1134/S1063780X20070065