Research Summary
I am interested in applying mathematical techniques to physical systems in interesting ways. Some examples of my research interests are:
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Chern-Simons Vortices
Chern-Simons vortices are examples of topological solitons - that is smooth, localised lumps of energy that are stable (under perturbation and decay) due to their topological nature. I am currently studying the dynamics of these vortices using numerical methods in Python and MATLAB.
[More detail to follow].
[More detail to follow].
Animations showing the separation of two Chern-Simons vortices for a given value of the Chern-Simons parameter. The left figure shows the magnetic field (red:high, blue:low) and the right shows the electric field (vector plot).
PhD Thesis - Exploring the Edges of Electromagnetism using Extreme Fields
My PhD thesis was undertaken from 2010-2014 at Lancaster university, thanks to funding provided by the EPSRC.
My research during my thesis considered aspects of nonlinear electromagnetism and the effects of spin under the influence of extreme fields - that is electromagnetic (EM) fields of especially high field strength or field gradient. In terms of nonlinear electromagnetism, my research focused on unique properties of Born-Infeld theory with regards to the propagation of electromagnetic radiation through regions of background EM fields. Prior to my studies, it was already known that light waves propagating in regions of EM fields travel at speed slower than the speed of light in vacuum according to Born-Infeld electrodynamics - my research sought to ascertain whether this property was unique to Born-Infeld theory or if other possible theories demonstrated this effect. I found that this depended on the direction of the background EM field relative to the plane wave, but Born-Infeld theory was the only field known to have a solution with the configuration shown in the figures to the right. Hence it is advisable to ensure any slow light experiment has a magnetic field component parallel to the wave's own magnetic field (similarly for electric fields). |
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I also investigated plasma waves as a possible way to distinguish between nonlinear theories of electromagnetism - in particular I wanted to find out if the energy gained by an electron in a plasma wave depended on the theory. While I did find the energy of an electron in a plasma wave in a particularly elegant form, the dependence on the theory of electromagnetism was unclear - further numerical work would be required to clarify this.
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Finally I considered the effects of the coupling of the electromagnetic field and the spin of a relativistic spinning particle. I presented a new derivation of the relativistic equations of motion for such a particle (the relativistic Stern-Gerlach and TBMT equations) via de Rham currents.
By analysing these equations in the context of a plasma wave (with extremely high field gradients) a new trajectory was found - transverse to the wave motion "surfing" along the plasma wave- a trajectory that exists only for particle with non-zero spin and in a background field with non-zero gradient. |
Though this trajectory was found to be linearly unstable, it is possible that this trajectory could negatively impact efforts to create neat electron bunches in laser-plasma wakefield accelerators.
Publications
S. P. Flood & D. A. Burton, Testing vacuum electrodynamics using "slow light" experiments, EPL, 100 60005
(arXiv pre-print link)
We investigated properties of Born-Infeld-like theories in the context of slow light experiments, concluding that a more optimal configuration of experiment should be employed in order to investigate Born-Infeld theory.
(arXiv pre-print link)
We investigated properties of Born-Infeld-like theories in the context of slow light experiments, concluding that a more optimal configuration of experiment should be employed in order to investigate Born-Infeld theory.
S. P. Flood & D. A. Burton Strong fields and slow light
A discussion of Born-Infeld-like theories and the slow-light effect for the Central Laser facility's annual report.
A discussion of Born-Infeld-like theories and the slow-light effect for the Central Laser facility's annual report.
D. A. Burton, S. P. Flood & H. Wen, Non-perturbative aspects of particle acceleration in non-linear electrodynamics
(arXiv pre-print link)
We investigated particle acceleration in the context of nonlinear electrodynamics; in particular, we deduced the energy gain of an electron in a maximum amplitude plasma wave is independent of the theory of electromagnetism.
(arXiv pre-print link)
We investigated particle acceleration in the context of nonlinear electrodynamics; in particular, we deduced the energy gain of an electron in a maximum amplitude plasma wave is independent of the theory of electromagnetism.
S. P. Flood & D. A. Burton, Stern-Gerlach surfing in laser wakefield accelerators,
(arXiv pre-print link)
We found a surfing solution to the the equations of motion of a classical particle with spin in the electric field produced by a plasma wave and analysed the stability of this solution. A new derivation of the equations of motion is also presented.
(arXiv pre-print link)
We found a surfing solution to the the equations of motion of a classical particle with spin in the electric field produced by a plasma wave and analysed the stability of this solution. A new derivation of the equations of motion is also presented.
Conferences Attended
GR20/Amaldi 10 - Conference on Gravitational Waves
University of Warsaw, 7th - 13th July 2013 [ATTENDED DG WORKSHOP] Barcelona Postgrad Encounters in Theoretical Physics University of Barcelona, 17th-19th October 2012 [PRESENTATION] 515 WE-Heraeus-Seminar - Algebro-geometric Methods in Fundamental Physics Physikzentrum Bad Honnef (Germany), 3 – 7 September 2012 |
475. WE-Heraeus-Seminar - Problems and Developments of Classical Electrodynamics Physikzentrum Bad Honnef (Germany), 20th – 25th March 2011 [POSTER PRESENTED] Laser-Plasma Interactions and Applications University of Strathclyde, 14th - 26th August 2011 [POSTER PRESENTED] |
Cockcroft Institute Postgraduate Conference Cockcroft Institute, Daresbury, 5th October 2011 [PRESENTATION] Awarded runner-up prize High Power Laser Christmas meeting 2010 RAL, Abingdon, 15th-17th December [POSTER PRESENTED] |