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<b>Intense Nonneutral Beam Propagation in a Periodic Solenoidal Field using a Macroscopic Fluid Model with Zero Thermal Emittance </b>
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Authors:   Ronald C. Davidson, Peter Stoltz, and Chiping Chen

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A macroscopic fluid model is developed to describe the nonlinear dynamics and collective processes in an intense high-current beam propagating in the z-direction through a periodic focusing solenoidal field. The analysis assumes that space-charge effects dominate the effects of thermal beam emittance and is based on the macroscopic moment-Maxwell equations, truncated by neglecting the pressure tensor and higher-order moments. Assuming a thin beam with the characteristic beam radius r<sub>b</sub> less than the axial periodicity length, azimuthally symmetric beam equilibria with delta/delta t = 0 = delta/delta theta are investigated, allowing for an axial modulation of the beam density and macroscopic flow velocity by the periodic focusing field. To illustrate the considerable flexibility of the macroscopic formalism, assuming (nearly) uniform axial flow velocity V<sub>b</sub> over the beam cross section, beam equilibrium properties are calculated for two examples: (a) uniform radial density profile over the interval 0 is less than or equal to r less than r<sub>b</sub>(z), and (b) an infinitesimally thin annular beam centered at r = r<sub>b</sub>(z). The analysis generally allows for the azimuthal flow velocity to differ from the Larmor frequency, and the model is used to calculate the (leading-order) correction to the axial flow velocity for the step-function density profile in case (a) above.

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<b>Note:</b> Some of the more technical terms have been left out of the above abstract as the present version of html does not support mathematical symbols and greek notation.

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<b>For a copy of this report:</b> Contact Ronald C. Davidson, Princeton Plasma Physics Laboratory, Princeton University, P.O. Box 451, Princeton, NJ 08543 or e-mail caphilli@pppl.gov.