Tokamak Axisymmetric Stability : Vertical Displacements and their Consequences
Author(s)
Windridge, Melanie Jane
Type
Thesis
Abstract
Vertical Displacement Events (VDEs) are a major concern for future tokamak
operation since their consequences—halo currents and the associated j × B forces
on the vacuum vessel—have the potential to be very damaging when scaled up
to ITER-size devices. VDEs become more likely for elongated plasmas, which are
inherently vertically unstable and most tokamaks, including ITER, will operate
with elongated plasmas to take advantage of the higher [Beta], and therefore higher
efficiency. Plasma stability to vertical displacement and halo current mitigation
are therefore critical areas of study for future tokamak devices.
The extreme geometry of Spherical Tokamaks (STs) makes them interesting machines
on which to investigate stability and halo current behaviour, and none more
so than the Mega Amp`ere Spherical Tokamak (MAST), which has a unique open
vacuum vessel design. This thesis combines simple analytic exploration, theoretical
modelling, and experimental work and analysis on the MAST tokamak.
The vertical stability of the plasma is studied in MAST with a view to determining
whether the non-linearity in the vertical feedback controller is increased in
STs compared to conventional tokamaks. It is thought that the higher curvature
of the vertical field index in STs will play a role, along with the deterioration in
efficacy of the vertical feedback with progressing excursion from equilibrium. The
open design of the MAST vessel brings an extra dimension to the problem, with
the passive stabilisation being provided by internal coil casings. Contrary to the
design of many other tokamaks, where a toroidal shell with coils outside is used,
the MAST vessel is cylindrical with poloidal field coils hanging on the inside. The
origin of non-linearity in the plasma response is explored by way of a simple heuristic
analytic model of an up-down symmetric plasma. Simulations are made using
the non-linear equilibrium evolution code DINA-CH to model plasma discharges
subject to a sinusoidal perturbation. Both MAST and a hypothetical conventional
aspect ratio tokamak are investigated. The responses of the plasma are subjected
to harmonic analysis to determine the non-linearity in the systems and enhanced
non-linearity is found in MAST. Experiments undertaken specifically to explore
this effect in the MAST tokamak are also detailed. These non-linear effects in
plasma control require consideration by controller designers.
Having examined plasma stability in MAST, one of the primary consequences
of VDEs—halo currents—are explored in detail. Forced VDE experiments are
described and the data analysed to give a picture of where in the MAST vessel
halo currents flow. A new method is developed for use with the DINA code to
calculate the halo currents flowing in the different passive conductors, based on
summing over flux surfaces. Further investigation is made into the stability of
the MAST plasma at high displacements from equilibrium, and it is found that
MAST has a region of extreme instability, where both the feedback and the passive
stabilisation are insufficient to hold the plasma and thus the plasma acceleration
is very rapid.
The mechanisms for generating halo currents are considered in detail and an
analytic circuit-equation model is used to demonstrate the consistency of our understanding
and to investigate the relative strength of the main drivers in MAST.
operation since their consequences—halo currents and the associated j × B forces
on the vacuum vessel—have the potential to be very damaging when scaled up
to ITER-size devices. VDEs become more likely for elongated plasmas, which are
inherently vertically unstable and most tokamaks, including ITER, will operate
with elongated plasmas to take advantage of the higher [Beta], and therefore higher
efficiency. Plasma stability to vertical displacement and halo current mitigation
are therefore critical areas of study for future tokamak devices.
The extreme geometry of Spherical Tokamaks (STs) makes them interesting machines
on which to investigate stability and halo current behaviour, and none more
so than the Mega Amp`ere Spherical Tokamak (MAST), which has a unique open
vacuum vessel design. This thesis combines simple analytic exploration, theoretical
modelling, and experimental work and analysis on the MAST tokamak.
The vertical stability of the plasma is studied in MAST with a view to determining
whether the non-linearity in the vertical feedback controller is increased in
STs compared to conventional tokamaks. It is thought that the higher curvature
of the vertical field index in STs will play a role, along with the deterioration in
efficacy of the vertical feedback with progressing excursion from equilibrium. The
open design of the MAST vessel brings an extra dimension to the problem, with
the passive stabilisation being provided by internal coil casings. Contrary to the
design of many other tokamaks, where a toroidal shell with coils outside is used,
the MAST vessel is cylindrical with poloidal field coils hanging on the inside. The
origin of non-linearity in the plasma response is explored by way of a simple heuristic
analytic model of an up-down symmetric plasma. Simulations are made using
the non-linear equilibrium evolution code DINA-CH to model plasma discharges
subject to a sinusoidal perturbation. Both MAST and a hypothetical conventional
aspect ratio tokamak are investigated. The responses of the plasma are subjected
to harmonic analysis to determine the non-linearity in the systems and enhanced
non-linearity is found in MAST. Experiments undertaken specifically to explore
this effect in the MAST tokamak are also detailed. These non-linear effects in
plasma control require consideration by controller designers.
Having examined plasma stability in MAST, one of the primary consequences
of VDEs—halo currents—are explored in detail. Forced VDE experiments are
described and the data analysed to give a picture of where in the MAST vessel
halo currents flow. A new method is developed for use with the DINA code to
calculate the halo currents flowing in the different passive conductors, based on
summing over flux surfaces. Further investigation is made into the stability of
the MAST plasma at high displacements from equilibrium, and it is found that
MAST has a region of extreme instability, where both the feedback and the passive
stabilisation are insufficient to hold the plasma and thus the plasma acceleration
is very rapid.
The mechanisms for generating halo currents are considered in detail and an
analytic circuit-equation model is used to demonstrate the consistency of our understanding
and to investigate the relative strength of the main drivers in MAST.
Date Issued
2009-06
Date Awarded
2009-10
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Coppins, Michael
Creator
Windridge, Melanie Jane
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)