General formulas for adiabatic invariants in nearly periodic Hamiltonian systems. (17th December 2020)

• Record Type: Journal Article
• Authors: Burby, J. W.; Squire, J.
• Is Part Of: Journal of plasma physics. Volume 86:Number 6(2020)
• Publication Date: 2020-12-17
• Subjects: plasma dynamics, -- plasma nonlinear phenomena; Plasma (Ionized gases) -- Periodicals; 530.4405
• DOI: 10.1017/S002237782000080X
• Languages: English
• ISSNs: 0022-3778

Abstract

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 non-unique near-identity coordinate transformation, even though the adiabatic invariant itself is a uniquely defined scalar. A less well-known 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 charged-particle dynamics in a strong magnetic field and magnetic field-line dynamics when the field lines are nearly closed.