INTENSE NONNEUTRAL BEAM-PROPAGATION IN A PERIODIC SOLENOIDAL FIELD USING A MACROSCOPIC FLUID MODEL WITH ZERO THERMAL EMITTANCE

A macroscopic fluid model is developed to describe the nonlinear dynam ics and collective processes in an intense high-current beam propagati ng in the z-direction through a periodic focusing solenoidal field B-z (z + S) = B-z(z), where S is the axial periodicity length. The analysi s assumes that space-charge effects dominate the effects of thermal be am emittance, Kr-b(2) much greater than epsilon(th)(2), and is based o n the macroscopic moment-Maxwell equations, truncated by neglecting th e pressure tensor and higher-order moments. Here, K = 2N(b)Z(i)(2)e(2) /<(gamma)over cap>(3)(b)m beta(b)(2)c(2) is the self-field perveance, N-b is the number of particles per unit axial length, and r(b) is the characteristic beam radius. Assuming a thin beam with r(b) much less t han S, azimuthally symmetric beam equilibria with partial derivative/p artial derivative t = 0 = partial derivative/partial derivative theta are investigated, allowing for an axial modulation of the beam density n(b)(r,z) and macroscopic flow velocity V-rb(r,z)(e) over cap(r) + V- theta b(r,z)(e) over cap(theta) + V-zb(r,z)(e) over cap(z) by the peri odic focusing field. To illustrate the considerable flexibility of the macroscopic formalism, assuming (nearly) uniform axial flow velocity V-b over the beam cross section, beam equilibrium properties are calcu lated for two examples: (a) uniform radial density profile over the in terval 0 less than or equal to r < r(b)(z), and (b) an infinitesimally thin annular beam centered at r = r(b)(z). The analysis generally all ows for the azimuthal flow velocity V-theta b(r,z) to differ from the Larmor frequency, and the model is used to calculate the (leading-orde r) correction delta V-zb(r,z) to the axial flow velocity for the step- function density profile in case (a) above. (C) 1997 American Institut e of Physics.