A map for systems with resonant trappings and scatterings

Abstract

Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the phase space in such systems are resonant scatterings and trappings. For systems with weak diffusive scatterings the transport properties can be described with the Chirikov standard map, and the map parameters control the transition between stochastic and regular dynamics. In this paper we put forward the map for resonant systems with strong scatterings that result in non-diffusive drift in the phase space, and trappings that produce fast jumps in the phase space. We demonstrate that this map describes the transition between stochastic and regular dynamics and find the critical parameter values for this transition.

11 pages, 2 figures

References in corpus (1)

• Kinetic equation for nonlinear wave-particle interaction: solution properties and asymptotic dynamics

Cited by in corpus (4)

• Long-term dynamics driven by resonant wave-particle interactions: from Hamiltonian resonance theory to phase space mapping
• Mapping for nonlinear electron interaction with whistler-mode waves
• On application of stochastic differential equations for simulation of nonlinear wave-particle resonant interactions
• On a transitional regime of electron resonant interaction with whistler-mode waves in inhomogeneous space plasma