Change of the adiabatic invariant due to separatrix crossing

Details Change of the adiabatic invariant due to separatrix crossing Change of the adiabatic invariant due to separatrix crossing

May 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvl..56.2117t&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 56, May 19, 1986, p. 2117-2120. Research supported by the University of Colorado,

Physics

52

Adiabatic Conditions, Charged Particles, Degrees Of Freedom, Electrostatic Waves, Hamiltonian Functions, Oscillators, Canonical Forms, Truncation Errors

Scientific paper

When a parameter in the Hamiltonian of a one-degree-of-freedom oscillator is slowly varied at rate epsilon, an adiabatic invariant exists which is conserved to all orders in epsilon, except on phase-space orbits which cross a separatrix. In the present work, the change in the adiabatic invariant due to a separatrix crossing is given to order epsilon for a wide class of Hamiltonian systems. This result is applied to the special case of a charged particle moving under the influence of an electrostatic wave with slowly varying amplitude and frequency.

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