Resonant trapping of charged particles in oscillating electric and magnetic fields

Abstract

The classical motion of a charged particle in oscillating magnetic and electric fields is investigated. Introducing a rotating coordinate system greatly simplifies the equations of motion and allows a formal analogy to the problem of three coupled oscillators with anisotropic damping. The solutions are calculated analytically, as a linear combination of the normal modes of oscillation There are two resonance frequencies, one at We=qBo/m, the cyclotron frequency, and the other at Wl= qBo/2m, the Larmor frequency. It is shown that when the resonance condition W=We is achieved, that is, the frequency of the oscillating field equals the cyclotron frequency of the particle, the particle is confined to a region of space of volume given approximately by 8v3o/3WeW21. Here Vo, is the modulus of the initial velocity of the particle and W1=qB1/m is the frequency of the particle about B1, the magnitude of the oscillating field. The orbit of the particle is shown to be a closed curve in the rotating system, or a closed surface in the laboratory system. On the other hand, when W=Wl, the particle drifts away, exponentially. The results suggest a resonant method for charged particle confinement and resonant isotope separation. We simulate the motion for the isotopes 235,238U, triply ionized, and show that they can be resonantly separated. The charge-to-mass ratios in this case differ by less than 1%. [1] V.L.B de Jesus, A.P. Guimarães and I.S. Oliveira, J.Phys.B, to be published. See also "Further Remarks on the Quantum Dynamics of a Charged Particle in an Oscillating Magnetic Field" from the same authors, in this conference.