Modulation of electromagnetic waves in a relativistic degenerate plasma at finite temperature

We study the modulational instability (MI) of a linearly polarized electromagnetic (EM) wave envelope in an intermediate regime relativistic degenerate plasmas at finite temperature (T≠0) where thermal energy (KBT) and rest-mass (mec2) electrons do not differ significantly, i.e., βe≡KBT/mec2≲ (or ≳) 1, but Fermi (KBTF) chemical potential (μe) are still bit higher than energy, TF>T ξe=μe/KBT≳1. Starting from set fluid equations for temperature, coupled to EM equation using multiple scale perturbation expansion scheme, one-dimensional nonlinear Schödinger (NLS) is derived, which describes evolution slowly varying amplitudes envelopes. Then, we MI latter two different regimes, namely, βe<1 βe>1. Like unmagnetized classical cold plasmas, modulated always unstable region βe>4. However, βe≲1 1<βe<4, can be stable or depending on values frequency, ω, parameter ξe. also obtain growth rate find significant reduction by increasing either βe Finally, present profiles traveling waves form bright (envelope pulses) dark (voids) solitons, as well (other waves) Kuznetsov–Ma breather, Akhmediev Peregrine solitons rogue (freak) waves, discuss their characteristics regimes