Confinement in time dependent traps

Time dependent confining fields have been widely used for high precision spectroscopy measurements during the last decades. In addition, there has been a renewed interest in the field of particle confinement in trapping fields for low power fusion devices, dusty plasmas and advanced chemical processing. The authors study the confinement of charged particles by time dependent, linear and nonlinear, fields with arbitrary pulse shape. They assumed that the trapped particles are perturbed by collisions with a background gas or any other source of momentum fluctuations. The basic parameters of the confinement are determined using asymptotic expansions based on singular perturbation techniques. Parametric instabilities, which result in the loss of confinement, are identified for different field strengths and pulse shapes