Classical charged particle resonance in induction field

Starting from first principles, the space charge manipulation of charged particles in an induction field in free space based on an unique magnetic field strength and its oscillation frequency relationship is demonstrated numerically and theoretically. With the dispersion relation in ion resonance depending on its frequency of gyration, an alternating current driven electromagnet based particle resonance has been proposed circumventing the use of superconducting permanent magnets. Complete resonance achieved under the proposed conditions results in a sustained, fixed-frequency particle trajectory that is independent of its speed or drift. Such oscillation is visualized in a D-shaped resonant assembly. The amplitude and the wavelength calculations for the trajectory are demonstrated, and the applicability of this unique magnetic field strength and its sinusoidal varying frequency relation in plasma instability is explored.