Trajectories of electrons with large longitudinal momenta in the phase plane during surfatron acceleration by an electro
- PDF / 639,934 Bytes
- 4 Pages / 612 x 792 pts (letter) Page_size
- 103 Downloads / 131 Views
E PLASMA
Trajectories of Electrons with Large Longitudinal Momenta in the Phase Plane during Surfatron Acceleration by an Electromagnetic Wave G. S. Mkrtichyan Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198 Russia e-mail: [email protected] Received October 28, 2014
Abstract—The trajectories of electrons with large longitudinal momenta in the phase plane in the course of their surfatron acceleration by an electromagnetic wave propagating in space plasma across the external magnetic field are analyzed. Electrons with large longitudinal momenta are trapped immediately if the initial wave phase Ψ(0) on the particle trajectory is positive. For negative values of Ψ(0), no electrons trapping by the wave is observed over the available computational times. According to numerical calculations, the trajectories of trapped particles in the phase plane have a singular point of the stable focus type and the behavior of the trajectory corresponds to the motion in a complex nonstationary effective potential well. For some initial phases, electrons are confined in the region of the accelerating electric field for relatively short time, the energy gain being about 50–130% and more. DOI: 10.1134/S1063780X15070041
1. INTRODUCTION Surfing of charge particles by electromagnetic waves that can be in the Cherenkov resonance with particles is one of the most probable mechanisms for the generation of ultrarelativistic particle fluxes in space plasma (see [1–11]). In order to correctly estimate conditions for the generation of fast particles fluxes and their parameters, it is necessary to analyze the mechanism of charged particle trapping into the regime of surfatron acceleration by an electromagnetic wave, determine the efficiency of such acceleration, and find optimum conditions for its implementation. Some of these problems were earlier considered, e.g., in [1–8]. Since there are a lot of free parameters, the total amount of required computations turns out to be very large; therefore, the problem should be studied step-by-step. In the present work, the structure of the phase plane is analyzed for electrons with large longitudinal momenta that are trapped into the surfing regime by an electromagnetic wave and experience ultrarelativistic acceleration. Earlier, it was shown (see, e.g., [6, 9, 12]) that, in the simplest model of surfatron acceleration, the problem is reduced to solving a nonlinear time-dependent second-order dissipative differential equation for the wave phase Ψ(τ) on the trajectory of a charged particle oscillating in an effective potential well in the region of the accelerating field. According to results of numerical calculations, the period of these oscillations increases substantially upon sufficiently
strong particle acceleration, while the oscillation amplitude decreases and asymptotically tends to zero. Such behavior correspond to the presence of a singular point of the stable focus type in the phase plane (Ψ(τ), dΨ/dτ). 2. EQUATIONS OF MOTION To describe surfatron acceleration of ele
Data Loading...
