Detection of Collective Beam Modes in the Paul Trap Simulator Experiment

Experiments have been performed to excite and detect collective transverse symmetric and quadrupole modes $(m= 0,2)$ in the Paul Trap Simulator Experiment (PTSX). PTSX is a compact laboratory Paul trap that simulates a long, thin charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient transport system by putting the physicist in the frame-of-reference of the beam. The transverse dynamics of particles in both systems are described by the same sets of equations -- including nonlinear space-charge effects. The frequency spectrum of collective mode oscillations depends on the details of the distribution function, the focusing field strength, the self-field intensity parameter, and geometric effects such as the proximity of the conducting wall. These oscillations typically involve various combinations of the frequencies $\hat \omega_q$, $\hat \omega_p$, and $(\hat \omega_q^2 - \hat \omega_p^2/2)^{1/2}$ (where $\hat\omega_q$ is the average transverse focusing frequency and $\hat\omega_p$ is the plasma frequency) modified by geometric effects $(r_p/r_w)$. Initial experiments focus on identifying collective modes whose signature will serve as a robust diagnostic for key properties of the beam, such as line density and transverse emittance. The experimental results are compared with the output of particle-in-cell simulations performed using the WARP code.