Trajectory-Simulation of a Charged Particle Beam on Trochoidal Orbit
Bratati Choudhury, Santanu Paul, Malay Kanti Dey
The trochoidal motion of a charged particle beam in a sector magnet, having a higher magnetic field region separated by a straight boundary from a lower magnetic field region, has been analyzed by simulating the desired magnetic field for trochoidal motion and charged particle trajectories. The trajectories have been simulated by numerically solving the equations of motion of charged particles in the magnetic field. A set of normalized equations of motion are formulated and numerically solved to obtain the reference trajectory, as well as a set of paraxial trajectories. The results show that the gradient of magnetic field near the boundary line of high-field and low-field region appears as an alternating gradient field as far as the trochoidal orbit is concerned. In trochoidal orbit the charged particle beam passes the boundary in opposite directions alternatively and hence the alternating field-gradient provides strong focusing in the vertical direction, apart from the focusing in the horizontal direction present in conventional sector magnets. Using these properties of trochoidal orbits effectively a compact dispersive system with inherent strong vertical focusing can be devised without any separate focusing elements.
Bratati Choudhury, Santanu Paul, Malay Kanti Dey. Trajectory-Simulation of a Charged Particle Beam on Trochoidal Orbit. International Journal of Multidisciplinary Research and Development, Volume 3, Issue 2, 2016, Pages 24-28