Dynamic stability of the time-averaged orbiting potential trap: Exact classical analysis

We calculate exactly the modes of motion of the time-averaged orbiting pote ntial (TOP) trap with its four degrees of freedom, namely the three transla tions and the spin, taken into account. We find that, when gravity is negle cted, there are two parameters in the problem namely, the angular velocity of the rotating field and its strength. We present the stability diagram in these parameters. We find the mode frequencies calculated from the time-av eraged potential model used by the inventors of the TOP is an excellent app roximation to our exact results. However, for other parameters, this may no t be the case. (C) 1999 American Institute of Physics. [S0021-8979(99)08516 -3].