Rapid geometrical chaotization in slow-fast Hamiltonian systems

In this Rapid Communication we demonstrate effects of a new mechanism of adiabaticity destruction in Hamiltonian systems with a separatrix in the phase space. In contrast to the slow diffusive-like destruction typical for many systems, this new mechanism is responsible for very fast chaotization in a large phase volume. To investigate this mechanism we consider a Hamiltonian system with two degrees of freedom and with a separatrix in the phase plane of fast variables. The fast chaotization is due to an asymmetry of the separatrix and corresponding geometrical jumps of an adiabatic invariant. This system describes the motion of charged particles in a inhomogeneous electromagnetic field with a specific configuration. We show that geometrical jumps of the adiabatic invariant result in a very fast chaotization of particle motion.