General formulas for adiabatic invariants in nearly periodic Hamiltonian systems
Abstract
While it is well known that every nearly periodic Hamiltonian system possesses an adiabatic invariant, extant methods for computing terms in the adiabatic invariant series are inefficient. The most popular method involves the heavy intermediate calculation of a nonunique nearidentity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. A less wellknown method, developed by S. Omohundro, avoids calculating intermediate sequences of coordinate transformations but is also inefficient as it involves its own sequence of complex intermediate calculations. In order to improve the efficiency of future calculations of adiabatic invariants, we derive generally applicable, readily computable formulas for the first several terms in the adiabatic invariant series. To demonstrate the utility of these formulas, we apply them to chargedparticle dynamics in a strong magnetic field and magnetic fieldline dynamics when the field lines are nearly closed.
 Publication:

Journal of Plasma Physics
 Pub Date:
 December 2020
 DOI:
 10.1017/S002237782000080X
 arXiv:
 arXiv:2005.00634
 Bibcode:
 2020JPlPh..86f8301B
 Keywords:

 plasma dynamics;
 plasma nonlinear phenomena;
 Physics  Plasma Physics;
 Mathematical Physics
 EPrint:
 32 pages, submitted to JPP special issue on Hamiltonian systems in plasma physics