31 July 2016 to 5 August 2016
Gaylord Hotel and Conference Center
US/Eastern timezone

Pushing Particles in Extreme Fields

3 Aug 2016, 10:50
20m
Baltimore 2 (Gaylord Hotel)

Baltimore 2

Gaylord Hotel

Oral Working Group 2 WG2

Speaker

Dr. Daniel Gordon (Naval Research Laboratory)

Abstract

There is increasing awareness that conventional particle tracking algorithms require impractical time steps in extreme fields. However, there seems to be some confusion about the source of this problem, and no general approach to overcome it. We argue that the source of the errors is directly attributable to the operator splitting scheme that is typically employed, most notably in the Boris algorithm. A new approach is offered that solves the problem.

Summary

There is increasing awareness that conventional particle tracking algorithms require impractical time steps in extreme fields. However, there seems to be some confusion about the source of this problem, and no general approach to overcome it. We argue that the source of the errors is directly attributable to the operator splitting scheme that is typically employed, most notably in the Boris algorithm. In particular, even if the electric field impulse and magnetic field rotation are computed exactly, a large error remains. The problem can be analyzed for the case of constant, but arbitrarily polarized and independent, electric and magnetic fields. The error can be expressed in terms of exponentials of nested commutators of the generators of boosts and rotations. To lowest order in the field, the Boris scheme causes the error to vanish, but to third order in the field there is an error that has to be controlled by decreasing the time step. In an extreme field the necessary time step is often impractically short. The scheme introduced in this paper overcomes this problem completely by avoiding operator splitting altogether, while retaining the property of the Boris scheme that magnetic fields cannot change the particle energy. In fact, the scheme respects Lorentz invariance to machine precision.

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Primary author

Dr. Daniel Gordon (Naval Research Laboratory)

Co-authors

Dr. Bahman Hafizi (Naval Research Laboratory) Dr. John Palastro (Naval Research Laboratory)

Presentation Materials

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