  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. The Larmor precession frequency for a time varying magnetic
field, instead of conventionally followed static magnetic field is derived for
the first time. With the dispersion relation in Ion Resonance depending on its
frequency of gyration, an AC 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
analytically. Principally noting the objectives of Synchrotron in varying the
magnetic field and its frequency to generate high energy particles, the present
theory addresses the same. Its applications can be explored in Space Propulsion
Systems, Magnetic Confinement Fusion, Magnetic Resonance Imaging (MRI) and
sub-harmonic heating and cooling. Using this theory one can aptly generate RF
Power using device specific designed resonant antennas coupling it with with
Plasma.
