I'm not a SImetrix user, so YMMV.
You'd expect ringing if there was a significant capacitance somewhere in the circuit. Take a careful look at your 'ideal' diode model.
However the decay and the varying period don't look right for 'real life' ringing, so I would suspect some sort of simulation artefact. Try simplifying the sim by removing (shorting) R1, and try reducing the maximum timestep.