Ion-acoustic solitons in a relativistic Fermi plasma at finite temperature

Abstract

Abstract The theory of ion-acoustic solitons in nonrelativistic fully degenerate plasmas and nonrelativistic and ultra-relativistic degenerate plasmas at low temperatures is known. We consider a multi-component relativistic degenerate electron-positron-ion plasma at finite temperatures. Specifically, we focus on the intermediate region where the particle’s thermal energy $$(k_BT)$$ ( k B T ) and the rest mass energy $$(mc^2)$$ ( m c 2 ) do not differ significantly, i.e., $$k_BT\sim mc^2$$ k B T ∼ m c 2 . However, the Fermi energy $$(k_BT_F)$$ ( k B T F ) is larger than the thermal energy and the normalized chemical energy ( $$\xi =\mu /k_BT$$ ξ = μ / k B T ) is positive and finite. Two different parameter regimes with $$\beta \equiv k_BT/mc^21$$ β > 1 , relevant for astrophysical plasmas, are defined, and the existence of small amplitude ion-acoustic solitons in these regimes are studied, including the critical cases where the known KdV (Korteweg–de Vries) theory fails. We show that while the solitons with both the positive (compressive) and negative (rarefactive) potentials coexist in the case of $$\beta 1)$$ ( β > 1 ) . Furthermore, while the rarefactive solitons within the parameter domains of $$\beta$$ β and $$\xi$$ ξ can evolve with increasing amplitude and hence increasing energy, the energy of compressive solitons reaches a steady state.