Dr David Burton

Lecturer

Research Interests

I am a member of the Mathematical Physics Group and have a number of interests all of which involve the application of modern differential geometry to spacetime physics and Newtonian field theories.

Relativistic continuum mechanics

Many of the laws of classical (i.e. non-relativistic) continuum mechanics are formulated in terms of Newtonian concepts and require the Euclidean structure of Galilean space-time. Such ideas are incompatible with the fundamental postulates of General Relativity and can only appear in a non-relativistic reduction of a relativistic theory. Cosserat rod theories afford an economical description of non-relativistic slender media but are formulated in terms of balance laws using Euclidean structures. My PhD research concentrated on the interaction of slender elastic media and the gravitational field, in both Newtonian and General Relativistic contexts, and I developed a General Relativistic theory of Cosserat rods. The aim was to investigate novel methods of gravitational wave detection and I showed that space-based schemes with the mathematical concept of strings and rods at their core are both useful and highly desirable. In recent years, I revisited relativistic continuum mechanics and worked on a theory of relativistic anelasticity describing the material evolution of defects and growth compatible with General Relativity.

Vortex-Induced Vibration

After completing my PhD in 2000 I worked on the effective simulation of vortex-induced vibrations of marine risers in collaboration with Orcina Ltd. A realistic, predictive and computationally efficient mathematical model of a fluid interacting with one or more solid bodies is both desirable, from an engineering perspective, and challenging for the physicist to construct. The sort of physical situations I examined consisted of a slender solid body immersed in a fluid with finite inflow speed and possessed a Reynolds number of the order of 100,000. The fluid sector of the calculations employed discrete-vortex methods and has also been used to model light wind-rain induced vibrations of cable-stayed bridges.

Twisted modes and gravitomagnetic fields

This work involves the geometrical modelling of electromagnetic modes in closed tubular cavities, e.g. a toroidal cavity, on background spacetimes. We call such cavities "wavetubes" because they possess propagating modes (waves). The aim was to understand how the wavetube and spacetime geometry alters the behaviour of the contained electromagnetic field. Most analyses in this field tend to rely on geometrical ray-optics arguments and completely neglect the vectorial nature of the electromagnetic field. Using the covariant Maxwell equations for accelerating media we showed how the spacetime and wavetube geometries influence the mode spectrum. The shape of the wavetube is specified by a closed space-curve on 3-dimensional Euclidean space. Any such space-curve is specified on Euclidean space, up to rigid motions, by its Frenet curvature and torsion. The Frenet torsion is a measure of the non-planarity of the space-curve and we showed how its mean value contributes to the mode spectrum. This work is of relevance to those who intend to measure gravitomagnetic phenomena, such as the Lense-Thirring effect, using ring-lasers.

High-field plasmas and radiation reaction

Recent developments in high-energy laser science have seen a surge of interest in the collective behaviour of high-density charged relativistic matter. However, the dynamical behaviour of relativistic charged matter reacting to its own electromagnetic field has been a source of intense debate ever since the problem was first tackled by Dirac in the 1930s. Until recently, this area was of purely theoretical interest but contemporary developments in high-energy laser science have ensured that it is no longer the case. Our recent work has focussed on the development of many-body theories of radiating charged matter, which we are using to explore the non-linear collective behaviour of intense radiating matter and probe parameter regimes in which the radiation reaction of plasmas and beams is significant.

This work is supported by the Cockcroft Institute.

Stern-Gerlach surfing in laser wakefield accelerators
Flood, S., Burton, D. 25/09/2015 In: Physics Letters A. 379, 36, p. 1966-1974. 9 p.
Journal article

Non-perturbative aspects of particle acceleration in non-linear electrodynamics
Burton, D., Flood, S., Wen, H. 17/04/2015 In: Journal of Mathematical Physics. 56, 11 p.
Journal article

Strong fields and slow light
Flood, S., Burton, D. 03/2015 In: CLF Annual Report 2013-2014. Oxford : Central Laser Facility
Chapter

On the entropy of radiation reaction
Burton, D., Noble, A. 7/03/2014 In: Physics Letters A. 378, 14-15, p. 1031-1035. 5 p.
Journal article

Aspects of electromagnetic radiation reaction in strong fields
Burton, D., Noble, A. 03/2014 In: Contemporary Physics. 55, 2, p. 110-121. 12 p.
Journal article

Recent developments in Lorentz-Abraham-Dirac fluid theory
Burton, D. 2014 In: Central Laser Facility Annual Report 2012-2013. 4 p. ISBN: 9780957440203.
Chapter

The radiative self-force and charged fluids
Burton, D., Carr, A., Gratus, J., Noble, A. 9/05/2013 In: Laser Acceleration of Electrons, Protons, and Ions II; and Medical Applications of Laser-Generated Beams of Particles II; and Harnessing Relativistic Plasma Waves III. SPIE
Paper

A kinetic model of radiating electrons
Noble, A., Gratus, J., Burton, D., Jaroszynski, D. 2013 In: Journal of Mathematical Physics. 54, 4, 8 p.
Journal article

A new equation of state for waterbag-distributed plasma
Burton, D. 2013 In: Central Laser Facility Annual Report 2011-2012. Didcot : Central Laser Facility p. 26. 1 p. ISBN: 9780955661693.
Chapter

High-field electrodynamics in plasmas
Burton, D., Wen, H. 2012
Other chapter contribution

Testing vacuum electrodynamics using "slow light" experiments
Flood, S.P., Burton, D.A. 2012 In: EPL. 100, 4 p.
Journal article

Born-Infeld axion-dilaton electrodynamics and electromagnetic confinement
Burton, D.A., Dereli, T., Tucker, R. 20/09/2011 In: Physics Letters B. 703, 4, p. 530-535. 6 p.
Journal article

Non-linear electrostatic waves in Born-Infeld plasmas
Burton, D.A., Wen, H. 5/07/2011 In: AIP Conference Proceedings. American Institute of Physics p. 87-92. 6 p. ISBN: 978-0-7354-0918-7 .
Conference contribution

Linear and non-linear waves in Born-Infeld plasma
Burton, D.A., Wen, H. 2/06/2011 In: Proceedings of SPIE. p. 80750B. ISBN: 9780819486653.
Conference contribution

F. de Felice, D. Bini Classical measurements on curved space-times
Burton, D.A. 06/2011 In: The Observatory .
Book/Film/Article review

A linear collision operator for relativistic plasmas.
Noble, A., Burton, D.A. 14/03/2011 In: Journal of Physics -London- a Mathematical and General. 44, 14, p. 145502.
Journal article

Wake potentials and impedances of charged beams in gradually tapering structures
Burton, D.A., Christie, D.C., Smith, J.D.A., Tucker, R.W. 4/03/2011 In: Journal of Mathematical Physics. 52, 3, p. 032902. 30 p.
Journal article

Axions, dilatons and non-linear vacuum electrodynamics
Tucker, R., Burton, D., Dereli, T. 03/2011
Conference paper

Exploring Born-Infeld electrodynamics using plasmas.
Burton, D.A., Trines, R.M.G.M., Walton, T., Wen, H. 10/02/2011 In: Journal of Physics -London- a Mathematical and General. 44, 9, 11 p.
Journal article

Kinetic theory of radiation reaction
Noble, A., Jaroszynski, D., Gratus, J., Burton, D. 2011 In: Central Laser Facility Annual Report 2010-2011. Central Laser Facility 2 p.
Chapter

Kinetic treatment of radiation reaction effects
Noble, A., Gratus, J., Burton, D., Ersfeld, B., Islam, M.R., Kravets, Y., Raj, G., Jaroszynski, D. 2011 In: Laser acceleration of electrons, protons, and ions and medical applications of laser-generated secondary sources of radiation and particles. BELLINGHAM : SPIE-INT SOC OPTICAL ENGINEERING p. -. 6 p. ISBN: 978-0-81948-669-1.
Conference contribution

New perspectives on the electrodynamics of intense laser-plasmas.
Burton, D.A., Tucker, R.W. 2011 In: Central Laser Facility Annual Report 2009-10. p. 13. 2 p.
Journal article

Mathematical physics activities at the Cockcroft Institute.
Burton, D.A., Gratus, J., Perlick, V., Tucker, R.W., Christie, D.C., Goto, S., Hale, A., Noble, A., Walton, C., Canovan, C.E.S., Ferris, M., Gallego Torrome, R., Smith, J.D.A., Wen, H. 04/2010 In: ICFA Beam Dynamics Newsletter. 51, p. 217-222. 6 p.
Journal article

Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmas
Burton, D.A., Noble, A. 19/02/2010 In: Journal of Physics -London- a Mathematical and General. 43, 7, 19 p.
Journal article

B. Schutz : a first course in general relativity, 2nd Edn. (book review)
Burton, D.A. 02/2010 In: The Observatory .
Journal article

Practical applications of simple Cosserat methods
Burton, D.A., Tucker, R.W. 2010 In: Mechanics of generalized continua. Springer p. 87-98. 12 p. ISBN: 9781441956941.
Chapter

Geometry of thermal plasma oscillations.
Burton, D.A., Noble, A. 22/01/2009 In: ADVANCED ACCELERATOR CONCEPTS: Proceedings of the Thirteenth Advanced Accelerator Concepts Workshop. p. 252-257. 6 p. ISBN: 978-0-7354-0617-9.
Chapter

Discontinuous distributions in thermal plasmas.
Burton, D.A., Noble, A., Wen, H. 01/2009 In: Il Nuovo Cimento C - Colloquia on Physics. 32, 1, p. 1-13. 13 p.
Journal article

Challenges in controlling matter and light
Burton, D.A., Tucker, R.W. 2009 In: Central Laser Facility Annual Report 2008-09. p. 102-105. 4 p.
Journal article

Geometrical description of non-linear electrostatic oscillations in relativistic thermal plasmas.
Burton, D.A., Noble, A. 07/2008 In: arxiv.org.
Journal article

Spinning particles in scalar-tensor gravity
Burton, D.A., Tucker, R.W., Wang, C. 28/04/2008 In: Physics Letters A. 372, 18, p. 3141-3144. 4 p.
Journal article

Electrostatic wave-breaking in thermal plasmas
Burton, D.A., Noble, A. 2008 In: Central Laser Facility Annual Report 2007-2008. Didcot : Central Laser Facility p. 110-113. 3 p.
Chapter (peer-reviewed)

Impedance of ultra-relativistic charged distributions in tapering geometries
Burton, D.A., Tucker, R.W., Christie, D.C. 2008 In: Proceedings of EPAC08, Genoa, Italy. p. 1589-1591. 3 p.
Paper

Nicholas M. J. Woodhouse: General Relativity.
Burton, D.A. 11/2007 In: General Relativity and Gravitation. 39, 11, p. 1967-1968. 2 p.
Journal article

Asymptotic analysis of ultra-relativistic charge
Burton, D.A., Gratus, J., Tucker, R.W. 03/2007 In: Annals of Physics. 322, 3, p. 599-630. 32 p.
Journal article

Multiple currents in charged continua
Burton, D.A., Gratus, J., Tucker, R.W. 26/01/2007 In: Journal of Physics -London- a Mathematical and General. 40, 4, p. 811-829. 19 p.
Journal article

Dynamical model of Cosserat nanotubes.
Burton, D.A., Gould, T. 2007 In: Journal of Physics: Conference Series. 62, p. 23-33. 11 p.
Journal article

A Cosserat rod model with microstructure.
Gould, T., Burton, D.A. 2006 In: New Journal of Physics. 8, 137, 17 p.
Journal article

Asymptotic analysis of ultra-relativistic charge
Burton, D.A., Gratus, J., Tucker, R.W. 2006 In: Proceedings of the 10th European Particle Accelerator Conference (EPA06).
Journal article

Relativistic anelasticity
Epstein, M., Burton, D.A., Tucker, R.W. 2006 In: Classical and Quantum Gravity. 23, 10, p. 3545-3571. 27 p.
Journal article

The electrodynamics of charged continua.
Burton, D.A., Gratus, J., Tucker, R.W. 2006 In: Proceedings of workshop on global integrability of field theories applications. p. 155-169. 15 p.
Journal article

Geometry, Sagnac ring lasers and twisted EM modes
Tucker, R.W., Burton, D.A., Noble, A. 09/2005 In: General Relativity and Gravitation. 37, 9, p. 1555-1574. 20 p.
Journal article

Twisted electromagnetic modes and Sagnac ring lasers
Burton, D.A., Noble, A., Tucker, R.W., Wiltshire, D.L. 21/03/2005 In: Classical and Quantum Gravity. 22, 6, p. 909-931. 23 p.
Journal article

On the stability of stay cables under light wind and rain conditions
Burton, D.A., Cao, D., Wang, C., Tucker, R. 6/01/2005 In: Journal of Sound and Vibration. 279, 1-2, p. 89-117. 29 p.
Journal article

Hydrodynamic forces on two moving discs
Burton, D.A., Gratus, J., Tucker, R.W. 2004 In: Theoretical and Applied Mechanics. 31, 2, p. 153-187. 35 p.
Journal article

On the motion of matter in gravitational fields
Dereli, T., Tucker, R., Burton, D. 2004 In: Symmetries in gravity and field theory. Salamanca : Universidad de Salamanca ISBN: 9788478006397.
Chapter

A primer on exterior differential calculus
Burton, D.A. 2003 In: Theoretical and Applied Mechanics. 30, p. 85-162. 78 p.
Journal article

Geometry and dynamics of vortex sheets in 3 dimensions
Burton, D.A., Tucker, R. 2002 In: Theoretical and Applied Mechanics. 29, p. 55-75. 21 p.
Journal article

Spin driven motion in intense spacetime wave geometries
Burton, D., Tucker, R., Wang, C. 2002 In: Theoretical and Applied Mechanics. 28-29, p. 77-92. 16 p.
Journal article

Vortex-induced fluid forces on accelerating rigid boundaries in two dimensions
Burton, D., Hartley, D., Tucker, R. 2002 In: Proceedings of the fifth international seminar on geometry, continua and microstructures. Bucharest : Editura Academiei Române
Paper

On the control of matter with gravity
Wang, C., Burton, D., Gratus, J., Tucker, R. 07/2001
Conference paper