A Korteweg–de Vries (KdV) equation for fully relativistic one dimensional plasmas of arbitrarily large streaming speed and temperature is derived by using the reductive perturbation method. For plasmas with more than two species of particles, the coefficient representing quadratic nonlinearity in KdV can vanish at critical values of certain parameters. To describe the nonlinear evolution at this critical parameter, a modified KdV (mKdV) equation that contains a cubic nonlinear term is obtained. Furthermore, a mixed mKdV equation pertaining to parameters in the vicinity of the critical values is also derived, in which the quadratic and cubic nonlinearities are both present. As an illustration of the results, the mixed mKdV equation is applied to a plasma comprised of cold ions and electrons having cold (T=0) and finite temperature components. For warm temperature T⪡mec2, it is found that electron-acoustic nonlinear waves in the shape of double layer (kink) and solitary waves can exist, which have phase speed 3T/(4+α)me in the rest frame of plasma, where α is the polytropic index of the equation of state of the warm electrons. The thickness of the transitional layer of the kink structure is of the order of Debye length λD. For extremely high temperature T⪢mec2, it is also found that double layer and soliton-type solutions can exist with phase speed α−1c, which is equal to the well known relativistic sound speed c/3 for α=4/3. The thickness of the transition layer scales as δ∼T−1/4, which is different from the T⪡mec2 case.
A second order Korteweg–deVries (KdV) equation that describes the evolution of nonlinear electrostatic waves in fully relativistic two-fluid plasmas is derived without any assumptions restricting the magnitudes of the flow velocity and the temperatures of each species. In the derivation, the positive and negative species of plasmas are treated with equal footings, not making any species specific assumptions. Thus, the resulting equation, which is expressed in transparent form symmetric in particle species, can be applied to any two-fluid plasmas having arbitrarily large flow velocity and ultrarelativistically high temperatures. The phase velocity of the nonlinear electrostatic waves found in this paper is shown to be related to the flow velocity and the acoustic wave velocity through the Lorentz addition law of velocities, revealing the relativistic nature of the formulation in the present study. The derived KdV equation is applied to some limiting cases, and it is shown that it can be reduced to existing results in nonrelativistic plasmas, while there are some discrepancies from the results in the weak relativistic approximations.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.