Simulation of Ions Axial and Planar Motion in an Ultra-Cold Penning Trap with a Rotating Wall Potential*

Ultra-cold ions trapped in a rotating-wall Penning trap form a two-dimensional crystal with approximately triangular symmetry. A rotating wall torque balances the cooling laser torque, allowing ions to be cooled to very low temperatures. The spectrum of normal modes can easily be measured from the motion of the ions both in the directions parallel and perpendicular to external magnetic field. Spectral analysis shows many discrete peaks thereby identifying the vibrational modes and associated energies. Assuming thermal equilibrium, all modes would share the same energy or temperature.  We use the “Cold-Atom” code to directly simulate the N-body classical system and study the ion dynamics, temperature of the normal modes and possible non-equilibrium excitation.