Abstract: The motion of a neutral particle with magnetic moment,μ antiparallel to the field of an Ioffe trap is studied are obtained. With interaction between the magnetic moment of the particle and the magnetic field, classical motion equations of neutral particles in an Ioffe trap are abtained. With limited conditions we derive concise form of the motion equations using a perturbative method. They are Mathieu equations. With proper parameters the Mathieu equations are solved with traditional WKBJ method. As an attempt, we study periodic solutions, i.e., Floquet solutions of the Mathieu equation. It is necessary that parameters (λ and q) in the Mathieu equation satisfy special relations. With appropriate Ioffe trap parameters and initial condition of the particle, we present several periodic solutions.

Key words: Ioffe trap, Mathieu equation, WKBJ method, Floquet solution