The effect of quasi-accelerator modes on diffusion

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Abstract

We examine the diffusion in action of a generic Hamiltonian mapping over a range of actions for which the local standard mapping approximation exhibits stable accelerator modes. For the generic mapping the corresponding orbits are not completely stable, but the orbits may appear to be stable over many mappings periods. We examine the effect of these “quasi-accelerator mode” orbits on the diffusion. We find the most important physical effect in enhancing the diffusion to be the growth and decay of the locally stable mode (island) area, which leads to trapping and detrapping of phase space within the mode. An analytic theory is developed to incorporate this effect into a Fokker-Planck description of the diffusion. The solution for the distribution function, generated by a constant flux across the mode, is calculated and compared to numerical results. Provided a reasonable approximation to the locally stable island area is used in the theory, good agreement between theoretical and numerical results is obtained in a parameter range for which the effect of the mode is significant.

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