Effect of non-thermal and trapped electrons on solitary waves and chaos in auroral acceleration regions

Document Type : Research Article


Assistant Professor, Department of Plasma Physics and Basic Particle, Faculty of Physics, Shahrood University of Technology, Shahrood, Iran


In this paper, using the reductive perturbation method, the propagation of nonlinear solitary waves and chaos phenomenon and its stability were studied in auroral acceleration regions in the presence of electrons with the Cairns-Gurevich distribution function. Using the continuity, momentum transfer, and Poisson equations, and considering the density of electrons as the Cairns-Gurovich distribution function, and using two different models, Korteweg–De Vries (KdV) and modified KdV equations were obtained. It was shown that the solutions of these equations are in the form of solitary waves. The effect of non-thermal and trapped electrons and wave velocity on these waves were studied. In the next section, pseudo-potentials and total mechanical energy are obtained. Considering a quasi-periodic factor, KdV and modified KdV equations were reviewed and the chaos and its stability were studied in the auroral acceleration regions. Results showed that by increasing the wave velocity and non-thermal and trapped parameters, the size of the field increased, and the depth of the potential well was also increased. These results confirmed each other. It was indicated that in the case of b=0, this distribution function became as the Maxwellian distribution function. In the case b>0, in addition to free particles, the trapped and non-thermal particles also affect the distribution function. In this case, the width of the distribution function became larger, which indicated that the more energetic electrons existed in this case. It is also concluded that for both nonlinear equations, the solutions can exist in the form of rarefactive and compressive solitons. Three-dimensional graphs of total mechanical energy were also plotted for different values of the wave velocity and non-thermal and trapped parameters. Results for this case also showed that for the total energy of E1, by increasing the b parameter, the energy deviated from the uniform function and reached the saddle state. It was also shown that the wave velocity was similar to the b parameter. It was found that for different values of U and b parameters, the behavior of the total energy of E2 was different from the total energy diagram of E1. Poincaré return mapping diagrams confirmed the existence of a closed cycle indicating chaos in these plasmas. Results of this section also showed that for solitons with function ψ1, by increasing the U parameter, the Poincaré return mapping cycle region increased. Poincaré return mapping lines were also more focused in this case. For solitons with ψ1 functions, by increasing the wave velocity, Poincaré's return map goes from a quasi-stable state to a stable state. By increasing the quasi-periodic frequency, the Poincaré return map goes from steady-state to quasi-steady state so that a cycle converts to two cycles with a certain overlap. Finally, it was concluded that using real parameters, the wave velocity was in the interval 13km/s<v'<52km/s and the electric field was approximately 5mV/m and the Debye length became 15m. It was also concluded that the results of the recent work were in good agreement with the results obtained from the Viking, Freja and S3-3 satellites.


Main Subjects

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