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Zonal flow generation through four wave interaction in reduced models of fusion plasma turbulence
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Gallagher, Stephen J. (2013) Zonal flow generation through four wave interaction in reduced models of fusion plasma turbulence. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2704458~S1
Abstract
In tokamaks, turbulence is a key contributor to cross field transport. However,
it is also responsible for the spontaneous generation of large scale structures
such as zonal
ows. These are of relevance to fusion plasmas as they can create transport
barriers which aid plasma confinement. The interaction between drift waves
and zonal
ows can be investigated using reduced models such as the Hasegawa-
Mima and Hasegawa-Wakatani equations.
A four-wave truncated model is developed for the Extended-Hasegawa-Mima
(EHM) equation. This produces a set of four ordinary differential equations (ODEs)
that are used to investigate the modulational instability (MI), a mechanism by which
drift waves can produce a zonal
ow. These equations are linearised to produce a
dispersion relation for the MI which is used to produce a set of maps of the linear
growth rate of the MI. These show how additional modes become unstable as the
gyroradius is increased. The truncated model and dispersion relation are then compared
to measurements taken from simulations of the full EHM partial differential
equation (PDE) which has been seeded with an appropriate initial condition. Good
agreement is found when the pump wave has no component in the direction of the
density gradient.
A similar truncated model is derived for the Extended-Hasegawa-Wakatani
(EHW) equations. As the EHW system has separate equations for density and
potential this leads to a set of eight ODEs. The linearisation technique used for the
EHM system cannot be applied here. Instead, approximations based on the built in
EHW instability are made to calculate a linear growth rate for the zonal
ow using
the ODEs describing it. These analytical predictions are then compared to a full
PDE simulation of the system, which is initialised using random noise. It is found
that for particular sets of waves the ODEs provide a good prediction of the linear
growth rate.
A driving term is added to the EHM equation to reproduce the effect of
the built in instability of the EHW equations. This causes a drift wave spectrum to
grow when full EHW PDE simulations are seeded with random noise. The four-wave
ODE model is updated to include this driving. The ODE model again produces good
predictions for the growth rate of the zonal
flow.
Item Type: | Thesis (PhD) |
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Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
Library of Congress Subject Headings (LCSH): | Plasma turbulence, Plasma dynamics -- Mathematics, Differential equations, Plasma stability, Differential equations, Partial |
Official Date: | August 2013 |
Institution: | University of Warwick |
Theses Department: | Department of Physics |
Thesis Type: | PhD |
Publication Status: | Unpublished |
Supervisor(s)/Advisor: | Hnat, Bogdan |
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) |
Extent: | xvi, 170 leaves : illustrations, charts. |
Language: | eng |
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