# General formulas for adiabatic invariants in nearly periodic Hamiltonian systems

@article{Burby2020GeneralFF, title={General formulas for adiabatic invariants in nearly periodic Hamiltonian systems}, author={Joshua William Burby and Jonathan Squire}, journal={Journal of Plasma Physics}, year={2020}, volume={86} }

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…

## 8 Citations

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- 2021

M. Kruskal showed that each continuous-time nearly-periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. When the nearlyperiodic system is also Hamiltonian,…

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M. Kruskal showed that each nearly-periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of…

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. A continuous-time dynamical system with parameter ε is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as ε approaches 0. Nearly-periodic maps are…

### Approximate symmetries of guiding-centre motion

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In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric,…

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- 2021

The fundament of the classical guiding center theory is gyro-phase averaging, which cannot be well deﬁned over a non-trivial magnetic ﬁeld topology. The local gyro-phase coordinate frame hides the…

### pl as mp h ] 1 8 O ct 2 02 0 Approximate symmetries of guiding-centre motion

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Quasisymmetry builds a third invariant for charged-particle motion besides energy and magnetic moment. We address quasisymmetry at the level of approximate symmetries of first-order guiding-centre…

### Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion

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In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions…

### Minimizing Separatrix Crossings through Isoprominence

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A simple property of magnetic ﬁelds that minimizes bouncing to passing type transitions of guiding center orbits is deﬁned and discussed. This property, called isoprominence, is explored through the…

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