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. nonrelativistic) continuum mechanics are formulated in terms of Newtonian concepts and require the Euclidean structure of Galilean spacetime. Such ideas are incompatible with the fundamental postulates of General Relativity and can only appear in a nonrelativistic reduction of a relativistic theory. Cosserat rod theories afford an economical description of nonrelativistic 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 spacebased 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.
VortexInduced Vibration
After completing my PhD in 2000 I worked on the effective simulation of vortexinduced 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 discretevortex methods and has also been used to model light windrain induced vibrations of cablestayed 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 rayoptics 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 spacecurve on 3dimensional Euclidean space. Any such spacecurve is specified on Euclidean space, up to rigid motions, by its Frenet curvature and torsion. The Frenet torsion is a measure of the nonplanarity of the spacecurve 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 LenseThirring effect, using ringlasers.
Highfield plasmas and radiation reaction
Recent developments in highenergy laser science have seen a surge of interest in the collective behaviour of highdensity 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 highenergy laser science have ensured that it is no longer the case. Our recent work has focussed on the development of manybody theories of radiating charged matter, which we are using to explore the nonlinear 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, 1415, p. 10311035 5 p.
Research output: Contribution to journal › Journal article
Aspects of electromagnetic radiation reaction in strong fields
Burton, D. & Noble, A. 03/2014 In : Contemporary Physics. 55, 2, p. 110121 12 p.
Research output: Contribution to journal › Journal 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 journal › Journal 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 journal › Journal 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 journal › Journal article
BornInfeld axiondilaton electrodynamics and electromagnetic confinement
Burton, D. A., Dereli, T. & Tucker, R. 20/09/2011 In : Physics Letters B. 703, 4, p. 530535 6 p.
Research output: Contribution to journal › Journal article
Exploring BornInfeld 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 journal › 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
Research output: Contribution to journal › Journal article
Longitudinal wavebreaking 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 journal › Journal article
Spinning particles in scalartensor gravity.
Burton, D. A., Tucker, R. W. & Wang, CH. 28/04/2008 In : Physics Letters A. 372, 18, p. 31413144 4 p.
Research output: Contribution to journal › 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. 909931 23 p.
Research output: Contribution to journal › 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, 12, p. 89117 29 p.
Research output: Contribution to journal › Journal article
David Burton's Publications
2015
Nonperturbative aspects of particle acceleration in nonlinear electrodynamics
Burton, D., Flood, S. & Wen, H. 17/04/2015 In : Journal of Mathematical Physics. 56, 11 p.042901
Research output: Contribution to journal › Journal article
Strong fields and slow light
Flood, S. & Burton, D. 03/2015 CLF Annual Report 20132014. Oxford: Central Laser Facility, 45
Research output: Contribution in Book/Report/Proceedings › Chapter
2014
On the entropy of radiation reaction
Burton, D. & Noble, A. 7/03/2014 In : Physics Letters A. 378, 1415, p. 10311035 5 p.
Research output: Contribution to journal › Journal article
Aspects of electromagnetic radiation reaction in strong fields
Burton, D. & Noble, A. 03/2014 In : Contemporary Physics. 55, 2, p. 110121 12 p.
Research output: Contribution to journal › Journal article
Recent developments in LorentzAbrahamDirac fluid theory
Burton, D. 2014 Central Laser Facility Annual Report 20122013. 4 p.
Research output: Contribution in Book/Report/Proceedings › Chapter
2013
The radiative selfforce 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 LaserGenerated 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/Proceedings › 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.043101
Research output: Contribution to journal › Journal article
A new equation of state for waterbagdistributed plasma
Burton, D. 2013 Central Laser Facility Annual Report 20112012. Wyborn, B. (ed.). Didcot: Central Laser Facility, p. 26 1 p.
Research output: Contribution in Book/Report/Proceedings › Chapter
2012
Highfield electrodynamics in plasmas
Burton, D. & Wen, H. 2012 Central Laser Facility Annual Report 20102011. Wyborn, B. (ed.). Central Laser Facility, 4 p.
Research output: Contribution in Book/Report/Proceedings › Other 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 journal › Journal article
2011
BornInfeld axiondilaton electrodynamics and electromagnetic confinement
Burton, D. A., Dereli, T. & Tucker, R. 20/09/2011 In : Physics Letters B. 703, 4, p. 530535 6 p.
Research output: Contribution to journal › Journal article
Nonlinear electrostatic waves in BornInfeld 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. 8792 6 p.
Research output: Contribution in Book/Report/Proceedings › Conference contribution
Linear and nonlinear waves in BornInfeld plasma
Burton, D. A. & Wen, H. 2/06/2011 Proceedings of SPIE: Harnessing Relativistic Plasma Waves as Novel Radiation Sources from Terahertz to XRays and Beyond II. Jaroszynski, D. (ed.). Vol. 8075, p. 80750B
Research output: Contribution in Book/Report/Proceedings › Conference contribution
F. de Felice, D. Bini Classical measurements on curved spacetimes
Burton, D. A. 06/2011 In : The Observatory .
Research output: Contribution to journal › 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
Research output: Contribution to journal › 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
Research output: Contribution to journal › Journal article
Exploring BornInfeld 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 journal › Journal article
Kinetic theory of radiation reaction
Noble, A., Jaroszynski, D., Gratus, J. & Burton, D. 2011 Central Laser Facility Annual Report 20102011. Central Laser Facility, 2 p.
Research output: Contribution in Book/Report/Proceedings › 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 Laser acceleration of electrons, protons, and ions and medical applications of lasergenerated secondary sources of radiation and particles. Leemans, W. P., Esarey, E., Hooker, S. M., Ledingham, K. W. D., Spohr, K. & McKenna, P. (eds.). BELLINGHAM: SPIEINT SOC OPTICAL ENGINEERING, p.  6 p.
Research output: Contribution in Book/Report/Proceedings › Conference contribution
New perspectives on the electrodynamics of intense laserplasmas.
Burton, D. A. & Tucker, R. W. 2011 In : Central Laser Facility Annual Report 200910. p. 13 2 p.
Research output: Contribution to journal › Journal 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. 217222 6 p.
Research output: Contribution to journal › Journal article
Longitudinal wavebreaking 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 journal › Journal 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 journal › Journal 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. 8798 12 p. (Advances in Mechanics and Mathematics)
Research output: Contribution in Book/Report/Proceedings › Chapter
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. 252257 6 p. (AIP Conference Proceedings)
Research output: Contribution in Book/Report/Proceedings › 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. 113 13 p.
Research output: Contribution to journal › Journal article
Challenges in controlling matter and light.
Burton, D. A. & Tucker, R. W. 2009 In : Central Laser Facility Annual Report 200809. p. 102105 4 p.
Research output: Contribution to journal › Journal article
2008
Spinning particles in scalartensor gravity.
Burton, D. A., Tucker, R. W. & Wang, CH. 28/04/2008 In : Physics Letters A. 372, 18, p. 31413144 4 p.
Research output: Contribution to journal › Journal article
Electrostatic wavebreaking in thermal plasmas
Burton, D. A. & Noble, A. 2008 Central Laser Facility Annual Report 20072008. Didcot: Central Laser Facility, p. 110113 3 p.
Research output: Contribution in Book/Report/Proceedings › Chapter (peerreviewed)
Impedance of ultrarelativistic charged distributions in tapering geometries
Burton, D. A., Tucker, R. W. & Christie, D. C. 2008 Proceedings of EPAC08, Genoa, Italy. p. 15891591 3 p.
Research output: Contribution in Book/Report/Proceedings › Paper
2007
Nicholas M. J. Woodhouse: General Relativity.
Burton, D. A. 11/2007 In : General Relativity and Gravitation. 39, 11, p. 19671968 2 p.
Research output: Contribution to journal › Journal article
Asymptotic Analysis for Ultrarelativistic Charge.
Burton, D. A., Gratus, J. & Tucker, R. W. 03/2007 In : Annals of Physics. 322, 3, p. 599630 32 p.
Research output: Contribution to journal › 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. 811829 19 p.
Research output: Contribution to journal › Journal article
Dynamical model of Cosserat nanotubes.
Burton, D. A. & Gould, T. 2007 In : Journal of Physics: Conference Series. 62, p. 2333 11 p.
Research output: Contribution to journal › Journal 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 journal › Journal article
Asymptotic analysis of ultrarelativistic charge
Burton, D. A., Gratus, J. & Tucker, R. W. 2006 In : Proceedings of the 10th European Particle Accelerator Conference (EPA06).
Research output: Contribution to journal › Journal article
Relativistic anelasticity
Epstein, M., Burton, D. A. & Tucker, R. W. 2006 In : Classical and Quantum Gravity. 23, p. 35453571 27 p.
Research output: Contribution to journal › 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. 155169 15 p.
Research output: Contribution to journal › Journal 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. 15551574 20 p.
Research output: Contribution to journal › 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. 909931 23 p.
Research output: Contribution to journal › 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, 12, p. 89117 29 p.
Research output: Contribution to journal › Journal article
2004
Hydrodynamic forces on two moving discs.
Burton, D. A., Gratus, J. & Tucker, R. W. 2004 In : Theoretical and Applied Mechanics. 31, 2, p. 153187 35 p.
Research output: Contribution to journal › Journal article
2003
A primer on exterior differential calculus
Burton, D. A. 2003 In : Theoretical and Applied Mechanics. 30, p. 85162 78 p.
Research output: Contribution to journal › Journal article
2002
Geometry and dynamics of vortex sheets in 3 dimensions
Burton, D. A. & Tucker, R. 2002 In : Theoretical and Applied Mechanics. 29, p. 5575 21 p.
Research output: Contribution to journal › Journal article
Spin driven motion in intense spacetime wave geometries
Burton, D., Tucker, R. & Wang, C. 2002 In : Theoretical and Applied Mechanics. 2829, p. 7792 16 p.
Research output: Contribution to journal › Journal article
David Burton's Activities
2015
Space Charge 2015
Dr David Burton (Invited speaker), 25/03/2015
Activity: Conference participation › Participation in conference
A geometrical perspective on manybody theory and radiation reaction
Dr David Burton (Speaker), 6/03/2015
Activity: External academic engagement › Invited talk
2014
RTG Colloquium
Dr David Burton (Invited speaker), 3/12/2014
Activity: Conference participation › Participation in workshop, seminar, course
HighPower Lasers at the Forefront of Science and Technology
Dr David Burton (Invited speaker), 4/04/2014
Activity: Conference participation › Participation in conference
2013
Einstein's Relativity
Dr David Burton (Speaker), 22/11/2013
Activity: Public engagement and outreach › Schools engagement
Physics in Intense Fields
Dr David Burton (Speaker), 9/07/2013 → 11/07/2013
Activity: Conference participation › Participation in conference
Collective effects and the radiative selfforce
Dr David Burton (Invited speaker), 13/06/2013
Activity: Conference participation › Participation in workshop, seminar, course
SPIE Optics + Optoelectronics 2013
Dr David Burton (Invited speaker), 15/04/2013 → 18/04/2013
Activity: Conference participation › Participation in conference
2012
CLF Christmas Meeting 2012
Dr David Burton (Invited speaker), 17/12/2012 → 19/12/2012
Activity: Conference participation › Participation in conference
AGMP8 (Algebra, Geometry and Mathematical Physics)
Dr David Burton (Invited speaker), 12/09/2012 → 14/09/2012
Activity: Conference participation › Participation in conference
Featured article in the Highlights of 2011 brochure of Journal of Physics A: Mathematical and Theoretical
Dr David Burton (Recipient), 22/05/2012
Activity: Awards › Other distinction
Einstein's Relativity
Dr David Burton (Speaker), 23/03/2012
Activity: Public engagement and outreach › Schools engagement
2011
Advisory Panel to the Editorial Board of Journal of Physics A: Mathematical and Theoretical
Dr David Burton (Recipient), 22/12/2011 → …
Activity: Awards › Appointment
Featured article in the Highlights of 2010 brochure of Journal of Physics A: Mathematical and Theoretical
Dr David Burton (Recipient), 19/10/2011
Activity: Awards › Other distinction
Einstein's Relativity
Dr David Burton (Speaker), 5/07/2011
Activity: Public engagement and outreach › Schools engagement
Einstein's Relativity
Dr David Burton (Speaker), 14/06/2011
Activity: Public engagement and outreach › Schools engagement
SPIE Optics + Optoelectronics 2011
Dr David Burton (Invited speaker), 18/04/2011 → 21/04/2011
Activity: Conference participation › Participation in conference
Problems and Developments of Classical Electrodynamics
Dr David Burton (Invited speaker), 21/03/2011 → 25/03/2011
Activity: Conference participation › Participation in conference
Advisor for Richard Hammond's Engineering Connections
Dr David Burton (Advisor), 2011 → …
Activity: Public engagement and outreach › Media article or participation
2010
MOPNET 3 (Matrix and Operator Pencil Network)
Dr David Burton (Invited speaker), 20/03/2010 → 22/03/2010
Activity: Conference participation › Participation in conference
2009
Plasmas, Computation and Mathematics
Dr David Burton (Organiser), 18/07/2009 → 21/07/2009
Activity: Conference participation › Participation in conference
SPIE Optics + Optoelectronics 2009
Dr David Burton (Invited speaker), 20/04/2009 → 23/04/2009
Activity: Conference participation › Participation in conference
Einstein's Relativity
Dr David Burton (Speaker), 27/03/2009
Activity: Public engagement and outreach › Schools engagement
Secretary to the IOP Gravitational Physics Group
Dr David Burton (Member), 01/2009 → 12/2012
Activity: External academic engagement › Contribution 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), 10/10/2008 → 12/10/2008
Activity: Conference participation › Participation in conference
13th Advanced Accelerator Concepts Workshop
Dr David Burton (Speaker), 27/07/2008 → 2/08/2008
Activity: Conference participation › Participation in conference
Geometric analysis of wavebreaking in relativistic warm plasmas
Dr David Burton (Invited speaker), 18/04/2008
Activity: Conference participation › Participation in workshop, seminar, course
Current Students
Research students currently supervised by David Burton include:

Thomas BanaszekResearch Student

Cherry CanovanResearch Student+44 (0)1524 593282

Anthony CarrResearch Student+44 (0)1524 592222

Michael JenkinsResearch Student+44 (0)1524 592222

Matthew McCormackResearch Student+44 (0)1524 593282

Saleh QutubResearch Student

Ali TeimouriResearch Student

Nathan WoollettResearch Student+44 (0)1524 592222