Dr Jonathan GratusSenior Lecturer
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.
I have recently written up "A pictorial introduction to differential geometry,leading to Maxwell’s equations as three pictures." This will be useful for all students of general relativity and differential geometry. It can be found here.
PhD Supervision Interests
Super-macro-particles to improve in Particle-in-cell codes. Supervisor: Dr. Jonathan Gratus (Lancaster University), co-supervisor Dr. Hywel Owen (Manchester University). Project Description: A studentship is available from Oct 2019 on the development of the theory, computer coding and testing of an exciting new idea for improving the numerical simulation of charged particles. Particle-in-cell (PIC) codes are essential for the numerical simulation of charged particles in both conventional accelerators and plasmas. They are used extensively for understanding of the physics and design of future machines. A typical code may have to track tens of billions of particles and may need to run on high performance computer clusters. We are investigating a revolutionary new method which promises to dramatically reduce the computation needed for simulations. This method increases the dynamical information of each particle while reducing the total number of particles. To aid in this task we need an enthusiastic PhD student to incorporate the new dynamical equations into existing PIC codes and compare the results with standard simulations. For the student of a more theoretical consideration there is the opportunity to develop the theory using powerful tools of differential geometry and general relativity. The applicant will be expected to have a first or upper second class degree in mathematics, physics, computer science, engineering or other appropriate qualification. A full graduate programme of training and development is provided by the Cockcroft Institute. Potential applicants are encouraged to contact Dr. Jonathan Gratus (firstname.lastname@example.org) for more information. The first round of interview will take place in November-December 2019 Anticipated Start Date: October 2020 for 3.5 Years =========================================== Title: Shaping the electric field in artificial EM materials. Supervisors: Dr. Jonathan Gratus (Lancaster) and Prof. Rebecca Seviour (Huddersfield) An opportunity has arisen to undertake a PhD at one of the UKs top universities in the area of engineered spatially dispersive materials. A class of materials that are artificial created, like metamaterials, where the materials constitutive parameters depend, spatially, on the wavevector. The successful applicant will join an established national collaboration of theoreticians and experimental physicists and engineers working in the area of engineered spatially dispersive materials. The student will build upon recent work by the collaboration using established numerical tools to further develop our understanding of the properties of these interesting materials, and enable their physical realisation. Engineering spatial dispersion can offer many advantages to current RF technologies. Using spatially dispersive media may enable the EM field profile of a propagating wave to have an engineered field profile, engineered to present peak EM fields at the aperture of antennas. This may enable a fundamental shift in MIMO technologies, i.e. optimising waveform profiles for exploitation. Project Programme of work: Building upon previous work the student will start by using the commercial numerical EM 3D solvers HFSS, CST and Comsol. (1) the student will investigate the effects of disorder on the predicted longitudinal modes in shaped wire array media. The simulations will focus on a 4x4 array of wires, with varying degrees of variation of wire position and wire radius. Variations will be chosen from a uniform random distribution, representing variations in coordinate position of the wire and radius, starting with 1%, 2%, 5% and 10%. For each of these sets of variations at least 100 disorder ensembles will be modelled. The effects of the disorder on longitudinal mode and electric field profile will be analysed, look at the extrema and average responses. The effect of disorder only on position and radius will be studied both separately and jointly. (2) The student will start to model a physical realisable spatially dispersive wire array media capable of supporting longitudinal EM waves, using time-domain simulations. a. Time domain simulations of wire array media loaded in an oversized waveguide. Looking at longitudinal electric field patterns, optimising the field structure, modelling the wire media with physically realisable materials and with maximal variations from (1) that still enable the realisation of longitudinal electric modes, optimised for 1GHz. b. Model 1GHz longitudinal electric field wave propagation in standard waveguide. c. Design and model a coupling/matching section that will couple the longitudinal electric field wave propagation in (b) to the oversized wire media loaded in oversized waveguide of (a). d. Parallel work: look to engineer a wire array media, between two antennas, that by design the electric field profile has a peak amplitude at the points of contact with the antennas. A full graduate programme of training and development is provided by the Cockcroft Institute. Potential applicants are encouraged to contact Dr. Jonathan Gratus (email@example.com) for more information. Anticipated Start Date: October 2020 for 3.5 Years