Resonant interaction of fast particles with Alfvén waves in spherical tokamaks
Author(s)
Lilley, Matthew Keith
Type
Thesis
Abstract
The Spherical Tokamak (ST) concept has become one of the main avenues in magnetic
nuclear fusion research since STs successfully demonstrated plasma operation
at [Beta] = 2P[mu]0=B2~1. Next step ST machines aiming at achieving burning plasma
conditions in high [Beta] plasmas are being planned, such as the Spherical Tokamak
Power Plant (STPP) and the Component Testing Facility (CTF). Instabilities of
fast particle-driven Alfven eigenmodes are often observed in present-day STs. Such
instabilities, driven by fusion-born alpha particles as well as by fast ions produced
with auxiliary heating schemes, in the next step STs may pose a major problem as
these instabilities may affect confinement and losses of the fast ions.
A theory of compressional Alfven eigenmodes (CAE) with frequencies above the
deuterium cyclotron frequency,[omega] > [omega]cD, is developed for plasma parameters of a
STPP, and modes in the ion-ion hybrid frequency range, [omega]cT < [omega] < [omega]cD, are also
investigated in order to assess the potential of diagnosing the deuterium-tritium
(D-T) ratio. For the 1-D character of a STPP equilibrium with [Beta]~1 , a `hollow
cylinder' toroidal plasma model is employed for studying CAEs with arbitrary values
of the parallel wave-vector k[||] = k[.]B/|B|. The existence of weakly-damped CAEs,
free of mode conversion, is shown to be associated with the `well' in the magnetic
field profile, B = B (R), that can exist at the magnetic axis.
A significant part of this thesis focusses on the experimentally observed effects
of resonant wave-particle interaction between Alfven waves and fast particles in the
Mega Amp Spherical Tokamak (MAST) device at the Culham Laboratory, UK, and
in the LArge Plasma Device (LAPD) in the University of California, Los-Angeles,
USA. New robust experimental scenarios for exciting CAEs in the MAST spherical tokamak are developed, and interpretation of the observed CAEs in the frequency
range [omega]cD/3 < [omega] < [omega]cD is given in the context of the 1-D ST model and the Doppler
shifted cyclotron resonance. The e ciency of the Doppler resonance between co
and counter directed fast ions and left and right hand polarised Alfven waves is
further assessed experimentally on the LAPD device, with probe ions injected in
the presence of Alfv en waves launched by an external antenna.
The developed theory of CAEs is then applied to a calculation of the linear kinetic
drive of CAEs in the MAST experiments. A model representation of the fast ion
distribution function, produced by neutral beam injection (NBI), is used by fitting
to the TRANSP Monte-Carlo NBI modelling results. The main free energy sources
associated with temperature anisotropy and bump-on-tail are estimated analytically,
and the CAE stability boundary is qualitatively assessed.
In order to explain the experimentally observed difference between steady-state
and pulsating Alfvenic modes, the non-linear theory of fast particle driven modes
near marginal stability is extended to include dynamical friction (drag). For the
bump-on-tail problem, the drag is shown to always give an explosive amplitude
evolution in contrast to diffusion in velocity space in the vicinity of the wave-particle
resonance. This is then extended to the case of experimentally observed NBI-driven
toroidal Alfven eigenmodes (TAEs) in the MAST machine. The experimentally
observed differences between TAEs driven by fast ions produced with ion cyclotron
resonance heating (ICRH) and NBI are then interpreted. The problem of drag
dominated collisions for modes excited by fusion-born alpha particles in burning
plasmas such as a STPP and ITER is underlined.
nuclear fusion research since STs successfully demonstrated plasma operation
at [Beta] = 2P[mu]0=B2~1. Next step ST machines aiming at achieving burning plasma
conditions in high [Beta] plasmas are being planned, such as the Spherical Tokamak
Power Plant (STPP) and the Component Testing Facility (CTF). Instabilities of
fast particle-driven Alfven eigenmodes are often observed in present-day STs. Such
instabilities, driven by fusion-born alpha particles as well as by fast ions produced
with auxiliary heating schemes, in the next step STs may pose a major problem as
these instabilities may affect confinement and losses of the fast ions.
A theory of compressional Alfven eigenmodes (CAE) with frequencies above the
deuterium cyclotron frequency,[omega] > [omega]cD, is developed for plasma parameters of a
STPP, and modes in the ion-ion hybrid frequency range, [omega]cT < [omega] < [omega]cD, are also
investigated in order to assess the potential of diagnosing the deuterium-tritium
(D-T) ratio. For the 1-D character of a STPP equilibrium with [Beta]~1 , a `hollow
cylinder' toroidal plasma model is employed for studying CAEs with arbitrary values
of the parallel wave-vector k[||] = k[.]B/|B|. The existence of weakly-damped CAEs,
free of mode conversion, is shown to be associated with the `well' in the magnetic
field profile, B = B (R), that can exist at the magnetic axis.
A significant part of this thesis focusses on the experimentally observed effects
of resonant wave-particle interaction between Alfven waves and fast particles in the
Mega Amp Spherical Tokamak (MAST) device at the Culham Laboratory, UK, and
in the LArge Plasma Device (LAPD) in the University of California, Los-Angeles,
USA. New robust experimental scenarios for exciting CAEs in the MAST spherical tokamak are developed, and interpretation of the observed CAEs in the frequency
range [omega]cD/3 < [omega] < [omega]cD is given in the context of the 1-D ST model and the Doppler
shifted cyclotron resonance. The e ciency of the Doppler resonance between co
and counter directed fast ions and left and right hand polarised Alfven waves is
further assessed experimentally on the LAPD device, with probe ions injected in
the presence of Alfv en waves launched by an external antenna.
The developed theory of CAEs is then applied to a calculation of the linear kinetic
drive of CAEs in the MAST experiments. A model representation of the fast ion
distribution function, produced by neutral beam injection (NBI), is used by fitting
to the TRANSP Monte-Carlo NBI modelling results. The main free energy sources
associated with temperature anisotropy and bump-on-tail are estimated analytically,
and the CAE stability boundary is qualitatively assessed.
In order to explain the experimentally observed difference between steady-state
and pulsating Alfvenic modes, the non-linear theory of fast particle driven modes
near marginal stability is extended to include dynamical friction (drag). For the
bump-on-tail problem, the drag is shown to always give an explosive amplitude
evolution in contrast to diffusion in velocity space in the vicinity of the wave-particle
resonance. This is then extended to the case of experimentally observed NBI-driven
toroidal Alfven eigenmodes (TAEs) in the MAST machine. The experimentally
observed differences between TAEs driven by fast ions produced with ion cyclotron
resonance heating (ICRH) and NBI are then interpreted. The problem of drag
dominated collisions for modes excited by fusion-born alpha particles in burning
plasmas such as a STPP and ITER is underlined.
Date Issued
2009-02
Date Awarded
2009-06
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Coppins, Michael
Creator
Lilley, Matthew Keith
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)