The present analysis considers an intense non-neutral ion beam with characteristic axial velocity V b b b c and directed kinetic energy ͑g b 2 1͒m b c 2 propagating in the z direction through an applied focusing field which produces a transverse focusing force F foc 2g b m b v 2 bb ͑xê x 1 yê y ͒ on a beam ion (smooth focusing approximation). For a thermal equilibrium distribution function F b ͑H 0 Ќ ͒ const 3 exp͑2H 0 Ќ ͞T b ͒, it is shown that the normalized radial density profile pr 2 b n 0

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... ͑r͒͞N b , plotted as a function of r͞r b , depends on a single dimensionless parameter, which is a measure of the normalized beam intensity. Here, N b ϵ R dx dy n 0 b ͑r͒ is the number of beam ions per unit axial length and r 2 b ϵ N 21 b R dx dy r 2 n 0 b ͑r͒ is the mean-square beam radius. "Universal" profiles for the beam density are presented for a wide range of system parameters. The present results are readily extended to the case of a cylindrical non-neutral plasma column confined by a uniform axial magnetic field B 0êz . PACS numbers: 29.27.Bd, A detailed understanding of the influence of spacecharge effects on the equilibrium and stability properties of intense charged particle beams is increasingly important for applications of high-intensity accelerators and transport systems to basic scientific research, heavy ion fusion, spallation neutron sources, waste transmutation, and tritium production [1-6]. In the beam frame, such intense non-neutral beams [1-13] share many properties in common with laboratory-confined non-neutral plasmas [1,14-19], including thermal equilibrium properties, with density profile shape that exhibits a sensitive nonlinear dependence on space-charge intensity [1, 2, [11] [12] [13] [14] [15] [16] [17] [18] [19] . For the case of a thermal equilibrium distribution function F b ͑H 0 Ќ ͒, standard analyses [1,2,11-13] of the nonlinear Vlasov-Maxwell equation for an intense cylindrical beam typically characterize the equilibrium density profile terms of two parameters corresponding to the (transverse) temperature T b and onaxis densityn b , or scaled versions thereof. Here, r is the radial distance from the beam axis. Indeed, in the earliest [14] and more recent [1,11,15] theoretical analyses of the thermal equilibrium properties of space-charge-dominated beams by Davidson et al., and in thermal equilibrium analyses [2,13] by Reiser et al., the studies have typically investigated equilibrium properties of appropriately normalized quantities as a function of the (dimensionless) onaxis beam intensity v 2 pb ͞v 2 bb 4pn b Z 2 b e 2 ͞g b m b v 2 bb (proportional ton b ) and the characteristic on-axis Debye length l Db ͑T b g 2 b ͞4pn b Z 2 b e 2 ͒ 1͞2 (proportional to T 1͞2 b ͞n 1͞2 b ͒, treatingn b and T b as independent parameters. The purpose of the present article is to show that the normalized radial profile for pr 2 b n 0 b ͑r͒͞N b , plotted versus r͞r b , can be characterized in terms of a single dimensionless parameter d b defined by d b N b Z 2 b e 2 ͞2g 2 b T b . Here, N b R dx dy n 0 b ͑r͒ is the number of beam ions per unit axial length, g b is the relativistic mass factor, and r 2 b N 21 b R dx dy r 2 n 0 b ͑r͒ is the mean-square beam radius. The fact that the profiles for pr 2 b n 0 b ͑r͒͞N b versus r͞r b are "universal" for specified values of d b is a very powerful result. For example, a detailed measurement of the radial density profile n 0 b ͑r͒ in thermal equilibrium permits a direct determination of N b and r 2 b , and an inference (through a "best-fit" determination of d b ) of the temperature T b . The use of detailed measurements of the thermal equilibrium density profile n 0 b ͑r͒ to infer the transverse temperature T b through a best-fit analysis has been employed in recent experimental studies of laboratoryconfined non-neutral plasmas by Chao et al. [19]. In the present paper, following a discussion of the assumptions and theoretical model, the nonlinear Vlasov-Maxwell equations are investigated analytically and numerically for the case of a thermal equilibrium beam, and universal profiles for pr 2 b n 0 b ͑r͒͞N b are plotted versus r͞r b . The results are then extended, by analogy, to the case of a rotating, non-neutral plasma column confined by a uniform axial magnetic field B 0êz [1, [14] [15] [16] [17] [18] [19] . The present analysis considers an intense non-neutral ion beam with characteristic radius r b and axial momentum is the relativistic mass factor, Z b e and m b are the ion charge and rest mass, respectively, and the applied transverse focusing force on a beam ion is modeled (in the smooth focusing approximation) by F foc 2g b m b v 2 bb ͑xê x 1 yê y ͒, where ͑x, y͒ is the transverse displacement from the beam axis and v bb const is the focusing frequency. In addition, for present purposes, the particle motion in the beam frame is assumed to be nonrelativistic, and we consider the class of intense non-neutral beam equilibrium solutions ͑≠͞≠t 0͒ to the nonlinear Vlasov-Maxwell equations 1098-4402͞99͞2(11)͞114401(6)$15.00