Causality and stability conditions of a conformal charged fluid

In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To do this, I take a charged conformal matter in the flat and 3 + 1 dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I observe that in a dense medium having a finite U(1) charge with chemical potential μ0, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $$ {\tilde{\upgamma}}_{1,2}, $$ γ ˜ 1 , 2 , coefficients of the dissipative terms of the current, is of negative values.

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave number. Rigorous matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic sense. Simulated examples are given to illustrate the conclusion.

Effect of beam pre-bunching on gain and efficiency in a surface wave-pumped free electron laser

A pre-bunched relativistic electron beam (REB) counter-propagating to the surface wave in the vacuum region Compton backscatters the surface wave into a high-frequency coherent radiation. Plasma supports the surface wave that acquires a large wave number k0z around pump wave frequency $\omega _0 = {{\omega _p } {/ {\vphantom {{\omega _p } {\sqrt 2 }}} \kern-\nulldelimiterspace} {\sqrt 2 }}$, where ωp is the plasma frequency. The surface wave extends into the vacuum region and can be employed as a wiggler for the generation of sub-millimeter waves. The growth rate, efficiency, and gain were evaluated based on experimentally known parameters relevant to free electron laser (FEL). It was found that the growth rate, efficiency, and gain of the surface wave-pumped FEL increase with the modulation index Δ, which has the maximum value when approaching unity in addition to when the frequency and wave number of the pre-bunched beam are comparable to that of the radiation wave, i.e., ω01 ~ ω1 and k01 ~ k1. The growth rate of FEL instability scales as one-third power of beam density in the Compton regime.