Conservation principles for plasmas and relativistic electron beams

Many useful conservation theorems are derived for relativistic electron beams and anisotropic plasmas. All these theorems are valid for confined-flow and irrotational-flow devices, and cold, collisionless plasmas. All the theorems are derived in a similar way, and a generalization of this method, using linear operators, is given. Among the power theorems discussed are: Tonks' theorem, the instantaneous and sinusoidal small-signal theorems, the energy theorem, a large-disturbance theorem, the Manley-Rowe formulas, an ac power theorem, and a cross-correlation theorem. Contributions to power and energy from surface waves are included. Allowing for relativistic flow and writing all equations in the laboratory frame does not significantly complicate the theorems, and in fact clarifies them somewhat. Many simple applications are discussed, although not in detail. Among these are: small-signal energy, power, and passivity; energy velocity in electron beam and plasma wave-guides; and a conservation theorem for multiple electron beams and electron beam-plasma interactions.