Abstract
The drift resonance of relativistic equatorial electrons with ultra low-frequency (ULF) waves in the dipole magnetic field is considered as a nonlinear resonance in a Hamiltonian system. There are no waves in the undisturbed system. An expression for the undisturbed Hamiltonian as a function of drift action I is obtained. The corresponding oscillator is nonlinear. Waves represent a periodical disturbance. The case of resonance with a monochromatic wave having a single value of the azimuthal wave number is studied. The equation for resonant L is solved analytically in the ultra-relativistic approximation. The applicability of this approximation to description of the considered observed events is demonstrated. Formulas for resonant values of the action and energy are given. At small changes in I(L), an analytical expression is found for a conserving Hamiltonian that makes it possible to draw phase trajectories of particles. It is noticed that, for resonant interaction with equatorial electrons, the waves with the electrostatic potential whose amplitude is independent of L are most important. The phase portrait of the nonlinear resonance qualitatively agrees with the results of numerical calculations. At small changes in L, the quantitative agreement takes place as well. The maximum dimensions of the nonlinear resonance in I, L, energy, and drift frequency, and also the phase oscillations frequency are obtained. The results agree with measurements onboard the SAMPEX spacecraft.
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Original Russian Text © Yu.I. Gubar’, 2010, published in Kosmicheskie Issledovaniya, 2010, Vol. 48, No. 4, pp. 308–316.
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Gubar’, Y.I. Drift resonance of relativistic electrons with ULF waves as a nonlinear resonance. Cosmic Res 48, 300–307 (2010). https://doi.org/10.1134/S0010952510040039
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DOI: https://doi.org/10.1134/S0010952510040039