Effect of ion temperature and plasma density on an ion-acoustic soliton in a collisionless relativistic plasma: An application to radiation belts

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Abstract
The effect of ion temperature and plasma density on the behavior of an ion‐acoustic soliton in a collisionless relativistic plasma is studied. Based on an appropriate set of coordinate transformations, a reductive perturbation analysis is carried out to obtain the Korteweg–de Vries (KdV) equation for the one‐dimensional soliton motion. By solving this equation for a single soliton, simple expressions for the soliton phase velocity, soliton amplitude, soliton width, peak soliton ion density, and peak soliton potential are derived. These results are applied to the plasma parameters of the radiation belts. The soliton phase velocity λ0 increases with an increase in the relativistic effect. The effect of the ion temperature on λ0 is, however, negligible. It is shown that for the constant ion temperature and plasma density, the soliton amplitude, soliton phase velocity, peak soliton ion density, and peak soliton potential increase, and the soliton width decreases as the relativistic effect increases. With the increasing ion temperature, however, the soliton behaves in an entirely different way. It is further shown that for a constant value of the ion temperature, the amplitude and peak ion density increase and the width decreases, whereas the peak potential remains unchanged as the plasma density increases.