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The Hamiltonian Mechanics of Stochastic Acceleration

Description: We show how to nd the physical Langevin equation describing the trajectories of particles un- dergoing collisionless stochastic acceleration. These stochastic di erential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two ex… more
Date: July 17, 2013
Creator: Burby, J. W.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

Toroidal Precession as a Geometric Phase

Description: Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independe… more
Date: September 26, 2012
Creator: Burby, J. W. & Qin, H.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

VEST: Abstract Vector Calculus Simplification in Mathematica

Description: We present a new package, VEST (Vector Einstein Summation Tools), that performs abstract vector calculus computations in Mathematica. Through the use of index notation, VEST is able to reduce scalar and vector expressions of a very general type using a systematic canonicalization procedure. In addition, utilizing properties of the Levi-Civita symbol, the program can derive types of multi-term vector identities that are not recognized by canonicalization, subsequently applying these to simplify … more
Date: March 12, 2013
Creator: Squire, J.; Burby, J. & Qin, H.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

Automation of The Guiding Center Expansion

Description: We report on the use of the recently-developed Mathematica package VEST (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the transformation order-by-order. This procedure has several novel features. (1) It is designed to allow the user to easily explore the guiding center transformation's numerous nonunique forms or representations. (2) The procedure proceeds entirely in cartesian posit… more
Date: March 19, 2013
Creator: Burby, J. W.; Squire, J. & Qin, H.
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

AIP Conference Proceedings for the 19th Topical Conference on Radio Frequency Power in Plasmas

Description: An analytic model for single particle motion in the presence of a wave field and multiple cyclotron harmonics is developed and investigated. The model suggests that even in the absence of Doppler broadening, cyclotron harmonic layers have finite spatial extent. This allows for particles to interact with more than one harmonic layer simultaneously, provided the layers are tightly packed. The latter phenomenon is investigated in the context of the model using symplectic mapping techniques. Then t… more
Date: August 15, 2012
Creator: Burby, J. W.; Kramer, G. J.; Phillips, C. K. & Valeo, E. J.
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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