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Title: Characterisation of fully nonlinear Berk-Breizman phenomenonology
Author: Vann, R. G. L.
ISNI:       0000 0001 2445 0928
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2002
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The Berk-Breizman augmentation of the Vlasov-Maxwell system (henceforth the VM(BB) system) is widely used to model nonlinear resonant excitation and damping of wave fields by energetic particles in magnetic fusion plasmas. A code, based on the Piecewise Parabolic Method, is used to integrate the fully nonlinear Berk-Breizman system of equations across the whole parameter space. The present work provides, for the first time, numerical solutions to the fully nonlinear set of model equations. By considering the time evolution of the electric field energy, we show that the system behaviour can be classified into four types, namely damped, steady state, periodic and chaotic. Each type of behaviour occurs in well-defined regions of parameter space. We present a diagram in parameter space that shows how the model's behaviour changes as key parameters are varied. Moreover we demonstrate, by consideration of diagrams in (x; v) phase space, that the underlying process generic to the parameter values is the competition between the (re)formation of the spatially uniform equilibrium distribution and the formation of a phase space hole. The development of the aforementioned code is a major component of this project. A common problem with direct Vlasov solvers is ensuring that the distribution function remains positive. A related problem is to guarantee that the numerical scheme does not introduce false oscillations in velocity space. We use a variety of schemes to assess the importance of these issues and to determine an optimal strategy for Eulerian split approaches to Vlasov solvers. From these tests we conclude that maintaining positivity is less important than correctly dissipating the fine-scale structure which arises naturally in the solution to many Vlasov problems. Furthermore we show that there are distinct advantages to using high order schemes, i.e. third order rather than second. A natural choice which satisfies all of these requirements is the Piecewise Parabolic Method (PPM) This time splitting scheme is capable of solving many Vlasov-type systems. In this thesis we generate, systematically test, and demonstrate the high performance of an algorithm designed specifically for solving the VM(BB) system.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council ; United Kingdom Atomic Energy Authority
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC Physics