Splitting methods for time integration of trajectories in combined electric and magnetic fields.

@article{Knapp2015SplittingMF,
  title={Splitting methods for time integration of trajectories in combined electric and magnetic fields.},
  author={Christian Knapp and Alexander Kendl and Antti Koskela and Alexander Ostermann},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={92 6},
  pages={
          063310
        }
}
  • C. Knapp, A. Kendl, A. Ostermann
  • Published 6 October 2015
  • Computer Science
  • Physical review. E, Statistical, nonlinear, and soft matter physics
The equations of motion of a single particle subject to an arbitrary electric and a static magnetic field form a Poisson system. We present a second-order time integration method which preserves well the Poisson structure and compare it to commonly used algorithms, such as the Boris scheme. All the methods are represented in a general framework of splitting methods. We use the so-called ϕ functions, which give efficient ways for both analyzing and implementing the algorithms. Numerical… 
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References

SHOWING 1-10 OF 18 REFERENCES
Classical Molecular Dynamics Simulation with the Velocity Verlet Algorithm at Strong External Magnetic Fields
We present a new method for incorporating arbitrarily strong static homogeneous external magnetic fields into molecular dynamics computer simulations. Conventional techniques dealing with magnetic…
Symplectic and energy-conserving algorithms for solving magnetic field trajectories.
  • S. Chin
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
This work shows that exponential-splitting algorithms of any order for solving particle trajectories in a general electric and magnetic field can be systematically derived by use of the angular momentum operator of quantum mechanics.
On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
TLDR
Free Lie algebra theory gives simple formulae for the number of determining equations for a method to have a particular order, and a new, more accurate way of applying the methods thus obtained to compositions of an arbitrary first-order integrator is described and tested.
Single particle motion in a Penning trap: description in the classical canonical formalism
This paper aims at the development of methods for the calculation of the characteristic frequencies of a Penning trap, taking into account deviations of the actual geometry from the ideal one,…
Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations
Exponential Taylor methods: Analysis and implementation
Numerical error in electron orbits with large Ω ce D t
An almost symmetric Strang splitting scheme for the construction of high order composition methods☆
Exponential integrators
TLDR
The main intention in this article is to present the mathematics behind these methods, and derive error bounds that are independent of stiffness or highest frequencies in the system.
Why is Boris algorithm so good
TLDR
It is shown that the Boris algorithm conserves phase space volume, even though it is not symplectic, making it an effective algorithm for the multi-scale dynamics of plasmas.
...
...