  Using a Direct Simulation Monte Carlo technique, we have studied the time
evolution of a cold atom cloud interacting with a time dependent radio
frequency (rf) dressed state potential. Exposure of a cloud of $^{87}Rb$ atoms,
trapped in a quadrupole magnetic trap, to a time dependent rf-field with
increasing amplitude and decreasing frequency, shows a variation in the number
of trapped atoms and the overall shape of the atom cloud. It is shown by
simulations that, initially at lower rf-field strength, the rf-field results in
ejection of atoms from the trap, leading to evaporative cooling of the atom
cloud. Later, at higher rf-field strength, the atoms undergo the non-adiabatic
Landau-Zener (LZ) transitions, which leads to their trapping in an rf-dressed
state potential of toroidal shape. The results of simulations explain the
experimentally observed results. The simulations can be useful to predict the
atom cloud dynamics and trapping geometries with other forms of the potential.
