The Relativistic Heavy Ion Collider (RHIC) operation as the polarized proton collider presents unique challenges since both luminosity(L) and spin polarization(P) are important. With longitudinally polarized beams at the experiments, the figure of merit is LP{sup 4}. A lot of upgrades and modifications have been made since last polarized proton operation. A 9 MHz rf system is installed to improve longitudinal match at injection and to increase luminosity. The beam dump was upgraded to increase bunch intensity. A vertical survey of RHIC was performed before the run to get better magnet alignment. The orbit control is also improved this year. Additional efforts are put in to improve source polarization and AGS polarization transfer efficiency. To preserve polarization on the ramp, a new working point is chosen such that the vertical tune is near a third order resonance. The overview of the changes and the operation results are presented in this paper. Siberian snakes are essential tools to preserve polarization when accelerating polarized beams to higher energy. At the same time, the higher order resonances still can cause polarization loss. As seen in RHIC, the betatron tune has to be carefully set and maintained on the ramp and during the store …

The transverse Vlasov equilibrium distribution function of an unbunched ion beam propagating in a continuous focusing channel is specified by a function f{perpendicular} (H{perpendicular}), where H{perpendicular} is the single-particle Hamiltonian. In standard treatments of continuous focusing equilibria in Vlasov-Poisson electrostatic models, it is assumed that a stable beam equilibrium specified by monotonic f{perpendicular}(H{perpendicular}) with {partial_derivative}f{perpendicular}(H{perpendicular})/{partial_derivative}H{perpendicular} {le} 0 is axisymmetric (no variation in azimuthal angle, i.e., with {partial_derivative}/{partial_derivative}{theta} = 0). In this paper a simple, but rigorous, proof is presented that only axisymmetric equilibrium solutions are possible in Vlasov-Poisson models for any physical choice of f{perpendicular}(H{perpendicular}) with {partial_derivative}f{perpendicular}(H{perpendicular})/{partial_derivative}H{perpendicular} {le} 0 if the confining boundary of the system (the beam pipe) is axisymmetric or if the geometry is radially unbounded.