Theoretical Study on the Nonlinear Waves in Space Plasmas

Abstract: In space physics, the study of substorms and magnetic storms has a great importance in transferring the energy from solar wind to the magnetosphere-ionosphere coupling system and atmosphere, where this energy take an important role in different processes such as, generating plasma instabilities, ion acceleration, plasma heating and so on. Plasma waves play a significant role in the transfer of mass, momentum and energy in tenuous, collisionless space plasmas and experience substantial attenuation during their propagation. This collisionless damping is caused by resonant wave-particle interaction as proposed by Landau; therefore, the study of Landau damping has significant importance in understanding the propagation characteristics of waves in space plasmas and provides insight into the basic plasma wave modes. When wave amplitude gets larger, nonlinear effects have to be considered. The nonlinear waves including the bipolar electric field solitary (EFS) structures are of great interest, as they are partially responsible for the acceleration of local plasma to produce magnetic-field-aligned electron and ion beams that produce discrete auroras and populate the magnetosphere with plasma of ionospheric origin.Therefore, in this dissertation, first we reviewed all the possible sources of energy entering the magnetosphere from solar wind and the energy release in the Magnetosphere-Ionosphere-coupling (MI Coupling) system during substorms and magnetic storms. As damping is an important characteristic of the wave which determines whether the wave will grow or damp out as it propagates in space, we will then studied the Landau damping of small amplitude electron plasma and ion-acoustic waves. At the last, we studied the characteristics of bipolar EFS structures which are a special type of nonlinear waves. For the energy budget studies, we concluded that the Akasofu’sε-parameter in its original form remains the most widely used parameter in the energy budget studies and gives a reasonable estimate of the total energy transferred into the magnetosphere from the solar wind. Although, some authors have found thatε-parameter underestimated the energy entered the magnetosphere. Furthermore, for the energy sinks in the MIC system, still there are three most important energy dissipation rates; the ring current injection rate UR, the Joule heat production rate in the ionosphere UJ, and the auroral particles precipitation rate UA, however, there are other minor energy sinks too.In this dissertation, Landau damping of small amplitude electron plasma (Langmuir) and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is investigated. As the space plasmas posses non-Maxwellian distributions, therefore, for the first time we have used a non-Maxwellian distribution function, such as the generalized distribution function in this investigation. Our numerical results showed that the damping rate is strongly dependent on the spectral indices r and q; and increases if the value of either q or r decreases or the percentage of the high energy particles increases. Although, as compared to the Langmuir ( r,q) waves, the dependence of damping rate on the spectral indices r and q for the ion-acoustic waves is weak. The Landau damping for such waves is strongly dependent on the ion temperature and experience only moderate Landau damping as long as T_i < 1. The bipolar EFS structures can be of polarities, first negative then positive, and first positive then negative, depending on the initial value of electric field. The amplitude of the continuous bipolar EFS structure decreases with phase velocity but for the separated bipolar EFS structure, it first decreases when M < 0.4 and then increases with velocity when M > 0.4. The amplitude of the continuous as well as separated bipolar EFS structures increases with the increase of initial value of electric field. Using the values of the parameters observed by satellites in appropriate positions in the auroral zone for calculations with our model, the amplitude and the duration of the bipolar EFS waves can be from 35 to 330 mV/m and range from 7 ms to about 23 ms, respectively. These values are in good agreement with observation. Therefore, our model can interpret the continuous and separated bipolar EFS structures with both polarities in the auroral ionosphere in particular and other space plasmas in general by using the corresponding observed parameter values.The results for oblique propagation from our model are: We obtain the nonlinear density periodic waves and density hump soliton corresponding to the different plasma conditions, respectively. The bipolar EFS waves corresponding to the density hump soliton can develop from ion acoustic waves when the plasma parameters satisfy certain conditions. The bipolar EFS structures can have both polarities, first negative then positive or first positive then negative, depending upon the initial conditions. The amplitude of the bipolar EFS structure increases with wave velocity and with the angle of propagation of the wave, which is consistent with the observations. The rate of increase of the amplitude of the bipolar EFS structures increases with the higher values of the angle of propagation. Depending on Mach number M, bipolar EFS structures can propagate in a certain range of angles of propagation that shifts towards the higher values of angles with the decrease in wave velocity…
Key words: discontinuous shallow water flow; Qiantang River; tidal bore; Godunov scheme; KFVS scheme; “well-balanced” scheme; sediment mathematical model; moving boundary

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