Dr Jonathan Gratus

Lecturer

Research Interests

I am investigating the mathematics for modeling of charged particles and electromagnetic fields in particle accelerators. These may be conventional vacuum accelerators, for example as in the LHC at CERN or the new type of laser driven plasma wakefield accelerators. Here a powerful laser pulse enters a plasma and creates a bunch of high energy electrons.(See here)I am interested in Coherent Synchrotron Radiation (CSR), Beam plasma interaction, Ultra-relativistic approximations, the Maxwell-Vlasov equations and the Klimontovich distribution.I am also investigating the nature of the stress-energy-momentum tensor associated with the electromagnetic field in a medium.

A pictorial introduction to differential geometry, leading to Maxwell's equations as three pictures
Gratus, J. 21/09/2017 In: arxiv.org.
Journal article

Subwavelength mode profile customisation using functional materials
Gratus, J., Kinsler, P., Letizia, R., Boyd, T. 6/09/2017 In: Journal of Physics Communications. 1, 2, 8 p.
Journal article

Electromagnetic mode profile shaping in waveguides
Gratus, J., Kinsler, P., Letizia, R., Boyd, T. 3/01/2017 In: Applied Physics A. 123, 6 p.
Journal article

On spacetime transformation optics: temporal and spatial dispersion
Gratus, J., Kinsler, P., McCall, M.W., Thompson, R.T. 12/2016 In: New Journal of Physics. 18, 19 p.
Journal article

Dispersion in space-time transformation optics
Kinsler, P., Gratus, J., McCall, M., Thompson, R. 14/08/2016 In: Electromagnetic Theory (EMTS), 2016 URSI International Symposium on. IEEE p. 356-358. 3 p. ISBN: 9781509025039. Electronic ISBN: 9781509025022.
Conference contribution

Electromagnetic mode profile shaping in waveguides
Boyd, T., Kinsler, P., Gratus, J., Letizia, R. 14/08/2016 In: Electromagnetic Theory (EMTS), 2016 URSI International Symposium on. IEEE p. 725-727. 3 p. ISBN: 9781509025039. Electronic ISBN: 9781509025022.
Conference contribution

Customised mode profiles using functional materials
Gratus, J., Kinsler, P., Letizia, R., Boyd, T. 14/07/2016 In: arxiv.org.
Journal article

On the self-force in Bopp-Podolsky electrodynamics
Gratus, J., Perlick, V., Tucker, R.W. 7/10/2015 In: Journal of Physics A: Mathematical and Theoretical. 48, 43, 28 p.
Journal article

Spatially dispersive inhomogeneous dielectric wire media with periodic structure
Gratus, J., McCormack, M., Letizia, R. 30/07/2015 In: Proceedings of PIERS 2015 in Prague, July 6-9, 2015. Cambridge, Mass. : The Electromagnetics Academy p. 675-680. 6 p.
Paper

Spatially dispersive inhomogeneous electromagnetic media with periodic structure
Gratus, J., McCormack, M. 30/01/2015 In: Journal of Optics. 17, 2, 10 p.
Journal article

Reconstruction of lattice parameters and beam momentum distribution from turn-by-turn beam position monitor readings in circular accelerators
Gratus, J., Edmonds, C., Hock, K., Machida, S., Muratori, B., Torromé, R.G., wolski, A. 2/05/2014 In: Physical Review Special Topics: Accelerators and Beams. 17, 5, 9 p.
Journal article

Inhomogeneous spatially dispersive electromagnetic media
Gratus, J., McCormack, M. 3/09/2013 In: Progress In Electromagnetics Research Symposium Proceedings, Stockholm, Sweden, Aug. 12-15, 2013. p. 1007-1012. 6 p.
Paper

Colombeau algebra: a pedagogical introduction
Gratus, J. 1/08/2013 In: arxiv.org.
Journal article

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

Conservation laws and stress–energy–momentum tensors for systems with background fields
Gratus, J., Tucker, R., Obukhov, Y. 10/2012 In: Annals of Physics. 327, 10, p. 2560-2590. 31 p.
Journal article

Symplectic integrator for s-dependent static magnetic fields based on mixed-variable generating functions
Wolski, A., Gratus, J., Tucker, R. 04/2012 In: Journal of Instrumentation. 7, 4, p. -. 20 p.
Journal article

Stephen N. Lyle: Self-force and inertia: old light on new ideas: Springer Lecture Notes in Physics, Vol. 796, 2011, 396 p., €74.85, ISBN: 978-3-642-04784-8
Gratus, J. 2012 General Relativity and Gravitation 2 p.
Book/Film/Article review

The origin of the Schott term in the electromagnetic self force of a classical point charge
Ferris, M.R., Gratus, J. 09/2011 In: Journal of Mathematical Physics. 52, 9, p. -. 9 p.
Journal article

Covariant constitutive relations and relativistic inhomogeneous plasmas
Gratus, J., Tucker, R. 04/2011 In: Journal of Mathematical Physics. 52, 4, 26 p.
Journal article

Covariant electromagnetic constitutive theory for dispersive continua
Goto, S., Gratus, J., Hale, A., Tucker, R., Walton, T. 2011 In: Elasticity and anelasticity. Moscow : Moscow University Press p. 264-271. 8 p.
Paper

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

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

Covariant constitutive relations, landau damping and non-stationary inhomogeneous plasmas
Gratus, J., Tucker, R. 2010 In: Progress In Electromagnetics Research M. 13, p. 145-156. 11 p.
Journal article

New perspectives on the relevance of gravitation for the covariant description of electromagnetically polarizable media
Dereli, T., Gratus, J., Tucker, R.W. 25/05/2007 In: Journal of Physics -London- a Mathematical and General. 40, 21, p. 5695-5715. 21 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

The covariant description of electromagnetically polarizable media
Dereli, T., Gratus, J., Tucker, R.W. 29/01/2007 In: Physics Letters A. 361, 3, p. 190-193. 4 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

A spatial view of information
Gratus, J., Porter, T. 12/11/2006 In: Theoretical Computer Science. 365, 3, p. 206-215. 10 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

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

A noncommutative geometric analysis of a sphere-torus topology change
Gratus, J. 02/2004 In: Journal of Geometry and Physics. 49, 2, p. 156-175. 20 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

An improved method of gravicraft propulsion.
Gratus, J., Tucker, R. 08/2003 In: Acta Astronautica. 53, 3, p. 161-172. 12 p.
Journal article

The dynamics of Cosserat nets
Gratus, J., Tucker, R.W. 2003 In: Journal of Applied Mathematics. 2003, 4, p. 187-226. 40 p.
Journal article

Nets of one dimensional Cosserat continua
Gratus, J., 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

A quantum geometric description of a q-brane with intrinsic spin
Gratus, J., Tucker, R.W. 06/2000 In: Nuclear Physics B - Proceedings Supplements. 88, 1-3, p. 349-354. 6 p.
Journal article

'Wick rotations': The noncommutative hyperboloids and other surfaces of rotations
Gratus, J. 01/1999 In: Letters in Mathematical Physics. 47, 2, p. 97-109. 13 p.
Journal article

Noncommutative differential geometry, and the matrix representations of generalised algebras
Gratus, J. 05/1998 In: Journal of Geometry and Physics. 25, 3-4, p. 227-244. 18 p.
Journal article

A natural basis for spinor and vector fields on the noncommutative sphere
Gratus, J. 04/1998 In: Journal of Mathematical Physics. 39, 4, p. 2306-2324. 19 p.
Journal article

A natural basis of states for the noncommutative sphere and its Moyal bracket
Gratus, J. 08/1997 In: Journal of Mathematical Physics. 38, 8, p. 4283-4300. 18 p.
Journal article

Classical and quantum implications of the causality structure of two-dimensional space-times with degenerate metrics
Gratus, J., Tucker, R. 1996 In: Journal of Mathematical Physics. 37, 12, p. 6018-6032. 14 p.
Journal article

Topology change and the propagation of massless fields
GRATUS, J., Tucker, R. 07/1995 In: Journal of Mathematical Physics. 36, 7, p. 3353-3376. 24 p.
Journal article

Quantum-mechanics on graphs
GRATUS, J., Lambert, C., Robinson, S., Tucker, R. 21/10/1994 In: Journal of Physics -London- a Mathematical and General. 27, 20, p. 6881-6892. 12 p.
Journal article