Relativistic fluid equations for intense electron beams

Abstract

A general, covariant, four-space relativistic fluid formulation has been obtained that is not limited to small thermal effects. The four-space formulation has been transformed to a three-space formulation which further reduces to the set of relativistic fluid equations given by Newcomb [Phys. Fluids 25, 846 (1982)] for the case of small thermal effects. A new and important relativistic macroscopic fluid parameter has been defined and evaluated in general. This is the thermal velocity relativistic rest mass factor λ, first introduced approximately by Newcomb. The factor λ plays a role similar to the single particle relativistic rest mass factor γ and the fluid velocity relativistic rest mass factor Γ. For a relativistic fluid the effective relativistic rest mass factor is the product of λ and Γ. The factor λ has been expressed in terms of the normalized beam emittance, thereby permitting direct evaluation of λ from beam experimental data. High-quality beams are characterized by extremely low emittance values, thereby resulting in values for λ of order 1. The regime of λ large is also an interesting one, particularly in cases where beam directed energy is rapidly being converted, through elastic collisional interactions, to beam thermal energy such as in beam–solid target or beam–dense plasma interactions.