Cool electron beam steady flows

Abstract

An improved warm fluid model [Phys. Fluids 28, 949 (1985)] constructed from moments of the relativistic Vlasov equation is used to examine classes of cool electron steady flows. A new family of cool steady flows is identified which is distinguished from the Bennett profile by a far less restrictive set of assumptions. In a sense the generality of these cool flows is more typical of the freedom found in strictly cold beam steady flows. Some examples are provided. The Bennett pinch is reexamined on the basis of an extension of this warm fluid model. It is found that the conditions necessary for neglecting heat flow also restrict the Bennett radius to be no larger than a beam skin depth when the beam temperature is isotropic and low. This maximum Bennett radius is shown to yield the Alfvén current limit exactly. For anisotropic beams the Bennett radius is reduced and is on the order of a Debye length. Through use of this fluid modeling, an essential connection between temperature, fractional charge neutralization, and the relativistic dilatation factor is found. The case of a rotating cool electron column is also analyzed through this fluid model. A rigid rotor solution is found only when the rest frame pressure is isotropic, which is in agreement with Newcomb’s [Phys. Fluids 29, 1854 (1986)] earlier result. When the rest frame pressure is anisotropic a particular sheared rotor solution is found. The use of this warm fluid modeling is intended to demonstrate a delicate interplay between the steady flow profiles possible and the thermodynamic properties of a relativistic beam.