The projects listed below can be tailored to Honours of PhD projects. Please contact Dr Matthew Hole at
matthew.hole@anu.edu.au for more details.
1. Multi-fluid plasma model of a neutral beam heated toroidal plasma
Supervisor: M. J. Hole Controlled magnetic confinement fusion offers the possibility of an inexhaustible supply of energy with zero greenhouse gas emissions. Over the past 50 years progress in achieving sustained confined fusion has advanced at an exponential rate, comparable to the continuous improvement in silicon technology for the information technology industry. Toroidal magnetic confinement devices have undergone several concept innovations, including the reverse field pinch, the Elmo bumpy torus,the steady-state helical winding stellerator, the addition of a magnetic field divertor, and most recently, the spherical tokamak. Forms of plasma heating have also evolved, ranging from Ohmic, various forms of wave heating (radio-frequency, ion and electron cyclotron, Alfven wave, lower hyrbid) to neutral beam heating. In modern tokamaks such as the Mega-Ampere Spherical Tokamak (MAST, U.K.) and the National Spherical Torus eXperiment (NSTX, U.S.) the fast ion energy contentresulting from neutral beam heating can exceed 40\% of the total kinetic energy. In this project, the fast ion population (arising from charge exchange with the neutral beam) will be modeled as a second species in a multi-fluid model. Fast particle distributions are provided by gyro-kinetic simulations from collaborators in the U.K. Comparison of the multi-component fluid model equilibrium to a standard toroidal equilibrium will be performed. Also included will be a radio-frequency heated fast-particle population with an analytic velocity distribution function, thereby providing scope to investigate the effect of energetic particles on the ANU H1 stellerator. The project requires strong analytical skills and a background in plasma theory. 2. Modeling Magnetic Fluctuations through Singular Value Decomposition
Supervisor: M. J. Hole
The frequency and wavelength of magnetic and electric fluctuations in plasma systems provide
diagnostic information both on the typeof mode activity present, and when folded with an eigenfunction analysis
of the mode, a constraint on the equilibrium. In a tokamak, toroidal and poloidal symmetry force a
quantization of the wavelength, and the number of wave periods is referred to as the mode number.
In the past, either a phase counting operation or principal component analysis of the time series has been
used to determine the mode number. Both these methods are not able to resolve different mode numbers
at the same frequency, or provide a measure of fit describing the accuracy of the solution. In this project,
a new technique, Singular Value Decomposition (SVD) in the Fourier domain, which resolves
modes degenerate in frequency and/or mode number, will be applied to wave activity in the
Mega-Ampere Spherical Tokamak (MAST). The problem involves taking existing equilibrium
and wave solutions for MAST, and modifying existing code to determine SVD fits to magnetic
fluctuation data from a poloidal array of magnetic pickup coils.
3. Interpretation of Energetic Particle Modes in MAST and H1
Supervisor: M. J. Hole
Each of the energetic particle distributions described in project 1. can modify the thermal population through collisions,
or drive a wide range of wave activity. For example, at sub ion-cyclotron frequencies $\omega\l
l\omega_{ci}$ the energetic ions can affectthe drive of ``sawteeth'', modes which cause periodic collapse
in the core pressure, and ``fishbones'' and shear-Alfvén Eigenmodes, modes that can lead to fluctuation
induced anamolous transport, and thereby reduce confinement. At frequencies $\omega$ comparable to
the ion cyclotron frequency $\omega_{ci}$, Compressional Alfvén Eigenmodes (CAE's) can be driven
by either fusion-born or beam-driven energetic ions that are in Doppler-shifted resonance with the mode.
In this project, one or more examples of high frequency mode activity, as measured by magnetic and
electrostatic probes will be studied in the fusion experiments MAST and/or H1. The mode numbers
and oscillation frequencies will be determined, the equilibrium refioned at the observation time, the
mode spectrum computed, and drive calculations/estimates performed. The project offers the student a
broad overview of the physics of energetic partilce modes in fusion plasmas, as well as providing an
opportunity for more detailed analysis.
4. Stability of the Mega-Ampere Spherical Tokamak
Supervisor: M. J. Hole
Toroidal magnetic confinement devices have undergone several concept innovations, including
the reverse field pinch, the Elmo bumpy torus, the steady-state helical winding stellerator, the
addition of a magnetic field divertor, and most recently, the Spherical Tokamak (ST).
The ST, a small aspect ratio tokamak (A=R/a=1.4) where a is the minor radius, and
$R$ the major radius) is the newest and one of the most promising routes to fusion power.
In these experiments the plasma resembles a cored-apple. The ST offers good confinement, a
higher stability threshold,and a lower toroidal field compared to the more costly conventional
design. Indeed, an early spherical tokamak, START, was able to achieve conditions in which
the toroidal beta $\beta_{t}$,the ratio of thermal to magnetic pressure exerted at the
plasma centre, reached a world record $\beta_{t}=40$\, more than three times that
in a conventional tokamak. Apart from offering high performance, ST's are also rich in
basic plasma physics phenomena, with complex field geometry and complicated particle orbits.
In this project, the effect of conducting wall on the plasma stability of one of the world's
largest speherical tokamak experiments, the U.K. Mega Ampere Spherical Tokamak (MAST),
will be studied by numerical simulation. Existing numerical codes will be used to
generate equilibrium reconstructions, and an ideal MHD stability code will be used
to determine stability to the disruptive $n=1$ kink mode. The conducting boundary will
be approximated by a geometric ray tracing code. The project requires a strong physics background,
a sound understanding of electromagnetic theory, and good numeric skills. The project offers the student
involvement in a topical international research project.
5. Power law distributions from a system of driven Lorenz equations.
Supervisor : M.J. Hole
Lorenz equations were discovered by Ed Lorenz in 1963 as a very simplified model of
convection rolls in the upper atmosphere. These equations also appear in plasma turbulence,
magnetohydrodynamic shell models, and studies of lasers. In this project, a simple set of driven
cyclical Lorenz equations will be examined, which are capable of generating power law
distributions of energy. Existing code will be used to evolve the Lorenz equations, and the
behaviour of the system examined as a function of driving force. At weak drive the energy
oscillates sinusoidally. As the drive is increased the behaviour becomes progressively more
chaotic, and the distribution function for the total energy begins to exhibit power law behaviour.
The purpose of this project is to investigate the transition from linear to chaotic behaviour,
and time-permitting, determine the implications for plasma turbulence.
6. Stray capacitance of a multi-turn air cored inductor.
Supervisor : M. J. Hole
Electromagnetic oscillations of the plasma are detectable by magnetic pick up (or Mirnov) coils
that detect the oscillating magnetic field generated by the plasma. These diagnostics are
crucial for measuring both the very low frequency (< 1kHz) evolution of the equilibrium magnetic
field, and detecting oscillatory modes of the plasma. Recently, a new set of diagnostics have been
installed in the MAST plasma to detect high frequency (up to 5MHz) magnetic perturbations.
For this purpose, a new model has been developed to predict the stray capacitance of a two
layer air-cored inductor. In this project the analytic model will be extended to
three or more layers, test solenoids constructed, and the predictions of the first self-resonant
frequency compared to measurements using a vector network analyzer.
7. The polarization of multi-component wave populations
Supervisor : M.J. Hole.
Assoc. Supervisors (Univ. of Sydney): Iver H. Cairns, P. A. Robinson
Stochastic Growth Theory, pioneered by Prof. Robinson and Dr Cairns of the
University of Sydney, describes the distribution of electric field strengths of waves propagating
through an inhomogeneous plasma that has evolved to a dynamic state close to marginal stability.
SGT has had success in explaining the field distributions of a wide range of astrophysical and space objects,
including: pulsars, the Earths polar cap, magnetosheath and foreshock, type III solar radio bursts and thermal
noise in the solar wind. Recently,predictions for the distributions for the Stokes parameters, which
describe the polarization of light , have been developed for the superposition of multiple wave populations.
In this project it is envisaged that the distribution functions of polarity resolved pulsar and/or Auroral
Kilometric Radiation data will be computed, and compared with the new predictions. The project involves
the analysis and interpretation of data, together with an understanding of the physics of the source.
8. Stochastic Growth Theory in laboratory plasmas.
Supervisor: M. J. Hole
Assoc. Supervisors (Univ. of Sydney): Iver H. Cairns, P. A. Robinson
An improved understanding of fluctuations and turbulence, which can lead to turbulent radial transport
and therefore a loss of plasma confinement, is important for the realization of fusion as a power
supply. Traditional techniques for the analysis of fluctuations, such as perturbation
analysis, assume that the plasma is in steady state, and determine the linear wave response
of the plasma. Whilst successful for determining the microphysics response of a plasma in a
prescribed state, the technique provides little insight into determining the response of a plasma whose
properties are stochastically distributed about a dynamic equilibrium. This is particularly
important for instabilities whose wavelength is small compared to the system size. In this case,
local variation in plasma parameters can lead to a population of waves, whose
field strengths can be stochastically described by a probability distribution function (pdf).
The functional form of these pdfs reflects the varying degrees of interaction between the waves,
particles and background plasmas. The use of stochastic techniques is particularly important in the
description of small wavelength fluctuations in fusion plasmas, which are thought to be mostly
responsible for turbulent transport.
Over the last ten years a new theory has emerged to describe the distribution function of electric field strengths.
Stochastic Growth Theory (SGT), pioneered by Federation Fellow Prof. Robinson and Australian
Prof. Fellow Iver H. Cairns of the School of Physics (University of Sydney), describes the distribution
of electric field strengths of waves propagating through an inhomogeneous plasma that has evolved to a
dynamic state close to marginal stability. SGT has had success in explaining the field distributions of a
wide range of astrophysical and space phenomena, including: pulsars, the Earths polar cap, magnetosheath
and fore-shock,type III solar radio bursts and thermal noise in the solar wind.
In this project, SGT will be applied to measurements of electrostatic oscillations in fusion plasmas.
The purpose is to (a) determine whether SGT can be applied to laboratory plasmas, and (b) use
the measured pdf of the floating potential and ion saturation current to infer the properties of the plasma.
The project requires strong analytic and numeric skills, but offers the student a
project that bridges engineering, laboratory/fusion plasma physics, and basic plasma physics.