INVITED: Slow manifold reduction for plasma science

@article{Burby2020INVITEDSM,
  title={INVITED: Slow manifold reduction for plasma science},
  author={Joshua William Burby and Taylor Klotz},
  journal={Commun. Nonlinear Sci. Numer. Simul.},
  year={2020},
  volume={89},
  pages={105289}
}
  • J. BurbyT. Klotz
  • Published 11 June 2020
  • Physics
  • Commun. Nonlinear Sci. Numer. Simul.
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11 Citations
Background Citations
6
Methods Citations
1

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11 Citations

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References

SHOWING 1-10 OF 101 REFERENCES

Initialization and the quasi-geostrophic slow manifold

Atmospheric dynamics span a range of time-scales. The projection of measured data to a slow manifold, ${\cal M}$, removes fast gravity waves from the initial state for numerical simulations of the…

Extending the zero-derivative principle for slow–fast dynamical systems

Slow–fast systems often possess slow manifolds, that is invariant or locally invariant sub-manifolds on which the dynamics evolves on the slow time scale. For systems with explicit timescale…

Guiding center dynamics as motion on a formal slow manifold in loop space

  • J. Burby
  • Physics
    Journal of Mathematical Physics
  • 2020
Since the late 1950's, the dynamics of a charged particle's ``guiding center" in a strong, inhomogeneous magnetic field have been understood in terms of near-identity coordinate transformations. The…

Constructive methods of invariant manifolds for kinetic problems

Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation

This paper demonstrates that with the knowledge only of a set of “slow” variables that can be used to parameterize the slow manifold, one can conveniently compute, using a legacy simulator, on a nearby manifold.

On the Nonexistence of a Slow Manifold

Abstract We identify the slow manifold of a primitive-equation system with the set of all solutions that are completely devoid of gravity-wave activity. We construct a five-variable model describing…

Variational nonlinear WKB in the Eulerian frame

Nonlinear WKB is a multiscale technique for studying locally-plane-wave solutions of nonlinear partial differential equations (PDE). Its application comprises two steps: (1) replacement of the…

Magnetohydrodynamic motion of a two-fluid plasma

The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled…

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

  • L. ChacónAdam Stanier
  • Computer Science
    J. Comput. Phys.
  • 2016

Hamiltonian structure of the guiding center plasma model

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades, and it plays a…
...