Multivariate Modeling of the Dynamics of Charged Particles

The trajectories of charged particles in a constant magnetic field are circles with radius dependent on the strength of this field. The presence of a travelling wave normal to this field perturbs these trajectories. When the interaction parameter exceeds a certain limit, the resultant motion becomes chaotic, dividing the phase space into stable regions, separated by stochastic boundaries. Under certain conditions, the particle can be accelerated to very high energies. Pictorial analysis provides the insight to the complexity of modes that are present and delineates the range of parameters best suited for efficient acceleration. Data generation is done using the Bulirsch-Stoer integrator that dramatically reduces processing demands. The analysis is made by building a 3D image using data slices. Subsequent planar cross sections as well as solid cutouts yield details about interconnection amongst various parameters in this interacting system.