اثر الکترون‌های غیرگرمایی و به‌دام‌افتاده بر روی امواج سالیتونی و آشوب در نواحی شتاب‌دار شفق قطبی

در این مقاله با استفاده از روش اختلال کاهش‌یافته، انتشار امواج سالیتونی غیرخطی و پدیده آشوب و پایداری آن در نواحی شتاب‌دار شفق قطبی در حضور الکترون‌های با تابع توزیع کایرنزگورویچ مطالعه ‌شد. با استفاده از دو مدل مختلف، معادلات کورته وگدی وری (kdv) و kdv تغییر شکل‌یافته به‌دست‌‌آمده و نشان دادیم که جواب‌های این معادلات به شکل امواج سالیتونی هستند. اثر الکترون‌های غیرگرمایی و به‌دام‌افتاده و سرعت موج برروی این امواج مطالعه شد. نتایج نشان دادند که با افزایش سرعت موج، اندازه دامنه موج سالیتونی افزایش می‌یابد. در ضمن اثر این کمیت‌ها برروی انرژی کل بررسی شد. با در نظر گرفتن یک عامل شبه‌دوره‌ای، معادلات kdv و kdv تغییر شکل‌یافته مورد بازبینی قرار گرفته و مسئله آشوب و پایداری آن مطالعه شد. نتایج نشان دادند که با افزایش سرعت موج و پارامتر غیرگرمایی و به‌دام‌افتاده، نگاشت بازگشتی پوانکاره دچار تغییر شده به‌طوری‌که برای برخی حالات سیستم شبه‌پایدار و برای برخی حالات دیگر پایدار است. در نهایت به این نتیجه رسیدیم که نتایج کار اخیر در توافق خوبی با نتایج به‌دست‌‌آمده از ماهواره‌های وایکینگ، فرجا و s3-3 است.

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

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 CairnsGurevich distribution function. Using the continuity, momentum transfer, and Poisson equations, and considering the density of electrons as the CairnsGurovich 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 nonthermal and trapped electrons and wave velocity on these waves were studied. In the next section, pseudopotentials and total mechanical energy are obtained. Considering a quasiperiodic 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 nonthermal 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 nonthermal 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. Threedimensional graphs of total mechanical energy were also plotted for different values of the wave velocity and nonthermal 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 quasistable state to a stable state. By increasing the quasiperiodic frequency, the Poincaré return map goes from steadystate to quasisteady 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