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Dr David Burton

Dr David Burton

Lecturer

C505 Physics Building
Lancaster University
Bailrigg
Lancaster
United Kingdom
LA1 4YB

+44 (0)1524 592843

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.

Selected Publications

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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

A kinetic model of radiating electrons

Noble, A., Gratus, J., Burton, D. & Jaroszynski, D. 2013 In : Journal of Mathematical Physics. 54, 4, 8 p.043101

Research output: Contribution to journalJournal article

Testing vacuum electrodynamics using "slow light" experiments

Flood, S. P. & Burton, D. A. 2012 In : EPL. 100, 4 p.60005

Research output: Contribution to journalJournal article

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.095501

Research output: Contribution to journalJournal article

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

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal 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

Research output: Contribution to journalJournal 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.075502

Research output: Contribution to journalJournal article

Spinning particles in scalar-tensor gravity.

Burton, D. A., Tucker, R. W. & Wang, C-H. 28/04/2008 In : Physics Letters A. 372, 18, p. 3141-3144 4 p.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

David Burton's Publications

2014

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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

Recent developments in Lorentz-Abraham-Dirac fluid theory

Burton, D. 2014 Central Laser Facility Annual Report 2012-2013. 4 p.

Research output: Contribution in Book/Report/ProceedingsChapter

2013

The radiative self-force and charged fluids

Burton, D., Carr, A., Gratus, J. & Noble, A. 9/05/2013 Laser Acceleration of Electrons, Protons, and Ions II; and Medical Applications of Laser-Generated Beams of Particles II; and Harnessing Relativistic Plasma Waves III. Esarey, E., Schroeder, C. B., Leemans, W. P., Ledingham, K. W. D. & Jaroszyski, D. A. (eds.). SPIE, Vol. 8779

Research output: Contribution in Book/Report/ProceedingsPaper

A kinetic model of radiating electrons

Noble, A., Gratus, J., Burton, D. & Jaroszynski, D. 2013 In : Journal of Mathematical Physics. 54, 4, 8 p.043101

Research output: Contribution to journalJournal article

A new equation of state for waterbag-distributed plasma

Burton, D. 2013 Central Laser Facility Annual Report 2011-2012. Wyborn, B. (ed.). Didcot: Central Laser Facility, p. 26 1 p.

Research output: Contribution in Book/Report/ProceedingsChapter

2012

High-field electrodynamics in plasmas

Burton, D. & Wen, H. 2012 Central Laser Facility Annual Report 2010-2011. Wyborn, B. (ed.). Central Laser Facility, 4 p.

Research output: Contribution in Book/Report/ProceedingsOther chapter contribution

Testing vacuum electrodynamics using "slow light" experiments

Flood, S. P. & Burton, D. A. 2012 In : EPL. 100, 4 p.60005

Research output: Contribution to journalJournal article

2011

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.

Research output: Contribution to journalJournal article

Non-linear electrostatic waves in Born-Infeld plasmas

Burton, D. A. & Wen, H. 5/07/2011 AIP Conference Proceedings: XIX International Fall Workshop on Geometry and Physics. Herdeiro, C. & Picken, R. (eds.). American Institute of Physics, Vol. 1360, p. 87-92 6 p.

Research output: Contribution in Book/Report/ProceedingsConference contribution

Linear and non-linear waves in Born-Infeld plasma

Burton, D. A. & Wen, H. 2/06/2011 Proceedings of SPIE: Harnessing Relativistic Plasma Waves as Novel Radiation Sources from Terahertz to X-Rays and Beyond II. Jaroszynski, D. (ed.). Vol. 8075, p. 80750B

Research output: Contribution in Book/Report/ProceedingsConference contribution

F. de Felice, D. Bini Classical measurements on curved space-times

Burton, D. A. 06/2011 In : The Observatory .

Research output: Contribution to journalBook/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

Research output: Contribution to journalJournal 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

Research output: Contribution to journalJournal article

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.095501

Research output: Contribution to journalJournal article

Kinetic theory of radiation reaction

Noble, A., Jaroszynski, D., Gratus, J. & Burton, D. 2011 Central Laser Facility Annual Report 2010-2011. Central Laser Facility, 2 p.

Research output: Contribution in Book/Report/ProceedingsChapter

Kinetic treatment of radiation reaction effects

Noble, A., Gratus, J., Burton, D., Ersfeld, B., Islam, M. R., Kravets, Y., Raj, G. & Jaroszynski, D. 2011 Laser acceleration of electrons, protons, and ions and medical applications of laser-generated secondary sources of radiation and particles. Leemans, W. P., Esarey, E., Hooker, S. M., Ledingham, K. W. D., Spohr, K. & McKenna, P. (eds.). BELLINGHAM: SPIE-INT SOC OPTICAL ENGINEERING, p. - 6 p.

Research output: Contribution in Book/Report/ProceedingsConference 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.

Research output: Contribution to journalJournal article

2010

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.

Research output: Contribution to journalJournal 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.075502

Research output: Contribution to journalJournal article

B. Schutz : a first course in general relativity, 2nd Edn. (book review)

Burton, D. A. 02/2010 In : The Observatory .

Research output: Contribution to journalJournal article

Practical applications of simple Cosserat methods.

Burton, D. A. & Tucker, R. W. 2010 Mechanics of generalized continua : one hundred years after the Cosserats. Maugin, G. A. & Metrikine, A. V. (eds.). 21 ed. Springer, p. 87-98 12 p. (Advances in Mechanics and Mathematics)

Research output: Contribution in Book/Report/ProceedingsChapter

2009

Geometry of thermal plasma oscillations.

Burton, D. A. & Noble, A. 22/01/2009 ADVANCED ACCELERATOR CONCEPTS: Proceedings of the Thirteenth Advanced Accelerator Concepts Workshop. 1086 ed. Vol. 1086, p. 252-257 6 p. (AIP Conference Proceedings)

Research output: Contribution in Book/Report/ProceedingsChapter

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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

2008

Spinning particles in scalar-tensor gravity.

Burton, D. A., Tucker, R. W. & Wang, C-H. 28/04/2008 In : Physics Letters A. 372, 18, p. 3141-3144 4 p.

Research output: Contribution to journalJournal article

Electrostatic wave-breaking in thermal plasmas

Burton, D. A. & Noble, A. 2008 Central Laser Facility Annual Report 2007-2008. Didcot: Central Laser Facility, p. 110-113 3 p.

Research output: Contribution in Book/Report/ProceedingsChapter (peer-reviewed)

Impedance of ultra-relativistic charged distributions in tapering geometries

Burton, D. A., Tucker, R. W. & Christie, D. C. 2008 Proceedings of EPAC08, Genoa, Italy. p. 1589-1591 3 p.

Research output: Contribution in Book/Report/ProceedingsPaper

2007

Nicholas M. J. Woodhouse: General Relativity.

Burton, D. A. 11/2007 In : General Relativity and Gravitation. 39, 11, p. 1967-1968 2 p.

Research output: Contribution to journalJournal article

Asymptotic Analysis for Ultra-relativistic Charge.

Burton, D. A., Gratus, J. & Tucker, R. W. 03/2007 In : Annals of Physics. 322, 3, p. 599-630 32 p.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

Dynamical model of Cosserat nanotubes.

Burton, D. A. & Gould, T. 2007 In : Journal of Physics: Conference Series. 62, p. 23-33 11 p.

Research output: Contribution to journalJournal article

2006

A Cosserat rod model with microstructure.

Gould, T. & Burton, D. A. 2006 In : New Journal of Physics. 8, 137, 17 p.

Research output: Contribution to journalJournal 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).

Research output: Contribution to journalJournal article

Relativistic anelasticity

Epstein, M., Burton, D. A. & Tucker, R. W. 2006 In : Classical and Quantum Gravity. 23, p. 3545-3571 27 p.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

2005

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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal 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.

Research output: Contribution to journalJournal article

2004

Hydrodynamic forces on two moving discs.

Burton, D. A., Gratus, J. & Tucker, R. W. 2004 In : Theoretical & Applied Mechanics. 31, 2, p. 153-187 35 p.

Research output: Contribution to journalJournal article

2003

A primer on exterior differential calculus

Burton, D. A. 2003 In : Theoretical & Applied Mechanics. 30, p. 85-162 78 p.

Research output: Contribution to journalJournal article

2002

Geometry and dynamics of vortex sheets in 3 dimensions

Burton, D. A. & Tucker, R. 2002 In : Theoretical & Applied Mechanics. 29, p. 55-75 21 p.

Research output: Contribution to journalJournal article

Spin driven motion in intense spacetime wave geometries

Burton, D., Tucker, R. & Wang, C. 2002 In : Theoretical & Applied Mechanics. 28-29, p. 77-92 16 p.

Research output: Contribution to journalJournal article

David Burton's Activities

2014

RTG Colloquium

Dr David Burton (Invited speaker), 3/12/2014

Activity: Conference participationParticipation in workshop, seminar, course

High-Power Lasers at the Forefront of Science and Technology

Dr David Burton (Invited speaker), 4/04/2014

Activity: Conference participationParticipation in conference

2013

Einstein's Relativity

Dr David Burton (Speaker), 22/11/2013

Activity: Public engagement and outreachSchools engagement

Physics in Intense Fields

Dr David Burton (Speaker), 9/07/201311/07/2013

Activity: Conference participationParticipation in conference

Collective effects and the radiative self-force

Dr David Burton (Invited speaker), 13/06/2013

Activity: Conference participationParticipation in workshop, seminar, course

SPIE Optics + Optoelectronics 2013

Dr David Burton (Invited speaker), 15/04/201318/04/2013

Activity: Conference participationParticipation in conference

2012

CLF Christmas Meeting 2012

Dr David Burton (Invited speaker), 17/12/201219/12/2012

Activity: Conference participationParticipation in conference

AGMP-8 (Algebra, Geometry and Mathematical Physics)

Dr David Burton (Invited speaker), 12/09/201214/09/2012

Activity: Conference participationParticipation in conference

Einstein's Relativity

Dr David Burton (Speaker), 23/03/2012

Activity: Public engagement and outreachSchools engagement

2011

Advisory Panel to the Editorial Board of Journal of Physics A: Mathematical and Theoretical

Dr David Burton (Recipient), 22/12/201131/12/2013

Activity: AwardsAppointment

Einstein's Relativity

Dr David Burton (Speaker), 5/07/2011

Activity: Public engagement and outreachSchools engagement

Einstein's Relativity

Dr David Burton (Speaker), 14/06/2011

Activity: Public engagement and outreachSchools engagement

SPIE Optics + Optoelectronics 2011

Dr David Burton (Invited speaker), 18/04/201121/04/2011

Activity: Conference participationParticipation in conference

Problems and Developments of Classical Electrodynamics

Dr David Burton (Invited speaker), 21/03/201125/03/2011

Activity: Conference participationParticipation in conference

Advisor for Richard Hammond's Engineering Connections

Dr David Burton (Advisor), 2011 → …

Activity: Public engagement and outreachMedia article or participation

2010

MOPNET 3 (Matrix and Operator Pencil Network)

Dr David Burton (Invited speaker), 20/03/201022/03/2010

Activity: Conference participationParticipation in conference

2009

Plasmas, Computation and Mathematics

Dr David Burton (Organiser), 18/07/200921/07/2009

Activity: Conference participationParticipation in conference

SPIE Optics + Optoelectronics 2009

Dr David Burton (Invited speaker), 20/04/200923/04/2009

Activity: Conference participationParticipation in conference

Einstein's Relativity

Dr David Burton (Speaker), 27/03/2009

Activity: Public engagement and outreachSchools engagement

Secretary to the IOP Gravitational Physics Group

Dr David Burton (Member), 01/200912/2012

Activity: External academic engagementContribution to the work of national or international committees and working groups

2008

8th International Seminar on Geometry, Continua and Microstructure

Dr David Burton (Invited speaker), 10/10/200812/10/2008

Activity: Conference participationParticipation in conference

13th Advanced Accelerator Concepts Workshop

Dr David Burton (Speaker), 27/07/20082/08/2008

Activity: Conference participationParticipation in conference

Geometric analysis of wave-breaking in relativistic warm plasmas

Dr David Burton (Invited speaker), 18/04/2008

Activity: Conference participationParticipation in workshop, seminar, course