Accelerator Physics

Accelerator Physics

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Research Activity

Along with our colleagues in the Lancaster University's Engineering Department, the members of the Lancaster accelerator physics group are part of the Cockcroft Institute of Accelerator Science and Technology based at the Daresbury Science and Innovation Campus near Warrington, Cheshire.

Particle accelerators are potent tools that lie at the heart of research into particle physics but also play significant roles in fields such as medicine. Wherever a beam of high-energy particles or light can be of use, particle accelerators offer a solution.

There are always demands for particle beams with higher energies and higher intensities, but there are limitations to what can be achieved using the accelerators of today. Some of these limitations are practical ones determined by cost and size, whereas others are fundamental and relate to unanswered questions about how charged particles interact with electromagnetic fields. We use our expertise in particle physics and mathematical physics to address these limitations. You can find out more about our plasma interactions research on our plasma physics research pages.

On the experimental side of our work, we investigate a range of topics such as how we can use beams of polarised particles to help probe mysteries in particle physics. On the theoretical side, we develop new effective classical and quantum theories for analysing matter in extreme conditions, with implications for cosmic particle acceleration as well as for experiments in the laboratory.

Key Research

  • The development and design of high-flux sources of positrons and gamma-rays for future high-energy colliders and other applications. For example, developing the positron source for the International Linear Collider
  • Simulating the dynamics and interactions of polarised particle beams in experiments such as Fermilab muon g-2
  • Leading the CASCADE collaboration in its search for weakly-interacting sub-eV particles such as axions using radio-frequency cavities
  • Investigating wave propagation in spatially dispersive media and photonic structures
  • Exploring radiation reaction in ultra-intense laser-plasmas as members of the ALPHA-X collaboration

PhD Opportunities


  • Super-macro-particles to improve in Particle-in-cell codes


    Dr Jonathan Gratus (Lancaster University)
    Dr Hywel Owen (Manchester University)


    A studentship is available from Oct 2020 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 ( for more information.

  • Muon g-2 experiment


    Dr Ian Bailey


    The Fermilab muon g-2 experiment is attempting to measure the anomalous magnetic moment of the muon: a quantity which is sensitive to the existence of ‘new physics’. The magnetic moment will be determined by measuring the energies and directions of electrons coming from the decay of a beam of muons orbiting inside a storage ring. In this project, you will learn skills in accelerator beam dynamics as part of the Cockcroft Institute of Accelerator Science and Technology. You will apply these skills to enhance simulations of the g-2 muon spin dynamics and help analyse the experimental data as part of the g-2 collaboration.

  • Search for the axion


    Dr Ian Bailey
    Professor Yuri Pashkin
    Dr Edward Laird


    In recent years, there has been a growing interest in the 'hidden sector' and non-traditional dark matter candidates such as axions and dark photons. If either of these hypothetical particles exists, they can be detected through their interaction with strong magnetic fields. This interaction should lead to the generation of photons whose frequency is related to the mass of the hypothetical particles. This calls for the development of sensing techniques that are capable to detect extremely weak electromagnetic signals in a wide frequency range.

    There are growing efforts around the UK to undertake a nationwide project aimed at the detection of axions and dark photons using various methods. Superconducting quantum circuits offer the possibility to build amplifiers with extremely low noise temperature covering a wide frequency range.

    In this project, you would have opportunities to develop superconducting detector technologies and/or develop computer simulations to optimise the sensitivity of future resonant detectors of axions and dark photons. This project will be undertaken in collaboration with the University of Sheffield and the Cockroft Institute. You may also have the opportunity to work on either the ADMX experiment in the US or planned experiments in the UK. In the latter case, you will use nanofabrication and cryogenic facilities of the Lancaster Quantum Technology Centre.

  • Laser Driven Relativistic Particle Acceleration


    Professor Steven Jamison


    We seek a PhD candidate to undertake experimental research on laser-driven relativistic particle beam acceleration. The research will be carried out at STFC Daresbury National Laboratory, in an exciting and collaborative project involving students and staff from Lancaster University, University of Manchester and STFC Daresbury National Laboratory.

    Relativistic particle acceleration driven by ultrafast optical lasers holds potential to revolutionise high energy particle accelerators. In the application of ultrafast electron diffraction, laser-driven acceleration offers control of particle beams on the femtosecond (10-15s) time scale. Also, the high-field strengths available in ultrafast lasers may enable orders of magnitude reduction in size and cost of kilometre-scale accelerators of x-ray-free-electron lasers and high-energy particle physics.

    The successful candidate will join a research team developing novel acceleration concepts using ultrafast lasers, and working towards several proof-of-concept demonstrations of laser acceleration of relativistic beams. They will carry out work in the optimisation of multi-MV/m optical and infrared sources, in high-field non-linear optics, in mm-scale accelerating structures, and in developing systems for the experimental demonstration of acceleration of relativistic beams. Through their research with high-power laser and electron-beam facilities, they will develop skills in ultrafast laser science, in relativistic particle beams physics, and the theory and modelling of ultrafast optics and particle dynamics.

    The applicant will be expected to have a first or upper second class degree in physics, medical physics, electrical engineering or other appropriate qualification. A full graduate programme of training and development is provided by the Cockcroft Institute. The student will register at the Lancaster University, supervised by the THz acceleration project lead, Professor Steven Jamison.

    The student will join a vibrant group of students and post-doctoral researchers already making significant progress in this area. The studentship will also work closely with scientists and Engineers at STFC Daresbury Laboratory National Laboratory. There will also be opportunities for travel and collaboration with scientific institutes and universities outside the U.K.

    The Physics Department is a holder of an Athena SWAN Silver award and JUNO Championship status and is strongly committed to fostering diversity within its community as a source of excellence, cultural enrichment, and social strength. We welcome those who would contribute to the further diversification of our department.

    Interested candidates should contact Professor Steven Jamison for further information. For general information about PhD studies in Physics at Lancaster please contact our postgraduate admissions staff at You can apply directly at stating the title of the project and the name of the supervisor in your application.

    Closing Date

    Applications will be accepted until the post is filled.

  • The energetics of magnetic reconnection: from astrophysics to laboratory plasmas


    Dr Elisabetta Boella


    Magnetic reconnection is a fundamental process occurring in magnetized plasmas. It consists of a sudden and rapid change of the magnetic field topology accompanied by the release of magnetic energy [1]. Magnetic reconnection events are pervasive in space, astrophysical and laboratory plasmas.

    Extensive theoretical, numerical, experimental, and observational works have contributed to clarifying many aspects of the dynamics of magnetic reconnection during the last two decades. Nevertheless, several open challenges still prevent a deeper comprehension of the process. This PhD project focuses on the so-called energetics problem (e.g., how the energy released during the explosive event is converted into high-speed flows, heat and energetic particles) and plans to advance our knowledge on this topic through massively parallel fully kinetic simulations.

    Simulations based on the Particle-In-Cell technique will address both astrophysical and laboratory scenarios. The fast progress in laser technology offers an amazing opportunity to explore magnetic reconnection in the laboratory with properly scaled experiments. Indeed, reproducing astrophysical processes in the laboratory under controlled conditions is a promising path to gain physical insights that would be otherwise inaccessible. Numerical simulations play a critical role as they allow for identifying the proper configurations where magnetic reconnection can be explored using ultra-intense lasers.

    The successful candidate will join a vibrant team developing a cutting-edge research program on plasma kinetic simulations. They are expected to interact with colleagues at Lancaster University and the Cockcroft Institute (STFC Daresbury Laboratory National Laboratory, Warrington) working on complementary subjects. There will be the possibility to collaborate with researchers based in scientific institutes and universities in and outside the U.K.

    Through the development of this project, the student will acquire skills and expertise in plasma physics, laser-matter interaction, high-energy-density-physics, numerical techniques, and high-performance-computing.

    Interested candidates should contact Dr Elisabetta Boella ( for further information.

    [1] E. G. Zweibel and M. Yamada, Annu. Rev. Astron. Astr. 47, 291 (2009).

  • Ultrafast laser driven acceleration of relativistic electron beams


    Professor Steven Jamison - Lancaster University

    Associated project supervisors: Dr D Graham / Prof R Appleby - University of Manchester, Department of Physics

    Lancaster University, together with collaborators at University of Manchester and the Cockcroft Institute for particle accelerator science, have developed internationally leading approaches to laser-driven particle accelerators. Our research, which involves a combination of femtosecond laser non-linear optics and sub-mm structures for electromagnetic-electron beam interactions, featured as the cover article in Nature Photonics in December 2020†.

    Opportunities are now available for talented physicists to join our research programme as a PhD student, in either experimentally focused or theory/simulation focused projects.

    • The experimentally-focused studentship will investigate the interaction of intense THz electromagnetic pulses (generated by non-linear optics and ultrafast lasers) with 100keV and >50 MeV electron beams.
    • The theory/simulation-focussed studentship will investigate the mechanisms of energy depletion and back reaction on the electromagnetic field during extremely high gradient (GV/m) and ultrafast (few femtosecond) conditions.

    The student will join a vibrant team of PhD students and post-doctoral researchers from Lancaster University and University of Manchester. The research team have extensive laser and electron beam experimental facilities at STFC Daresbury National Laboratory, Lancaster and Manchester universities, and access to relativistic beam test accelerators at the National Laboratory.

  • Super-macro-particles to improve in PIC codes


    Dr Jonathan Gratus


    PIC codes are used extensively in both conventional beam dynamics and laser-plasma interactions. Macro-particles are essential given the large number of particles one wishes to simulate. To calculate the input for Maxwell's equations, the charge and current of each macro-particle is \smeared" or \diluted" over the nearest cell points.

    We propose an improved method of modelling the macro-particles. Current PIC codes only record the position and velocity of each macro-particle. By contrast, our new method will record higher moments. These new super-macro-particles (SMPs) will then have to be smeared over a large number of cells, the higher moments being used to reconstruct the phase space distribution of charge. This method will increase the sophistication of the algorithm, albeit at a small cost compared to the usual method of simply increasing the number of macro-particles. The potential advantages, however, may be huge, equivalent to replacing tens or hundreds of macro-particles with a handful of these new SMPs. Indeed, if enough moments are chosen, an entire bunch of particles could be represented by a single SMP.

    There are two key steps for the successful implementation of this algorithm. The rest is to calculate the correct dynamical equations for the moments. The second is the reconstruction of the phase space distribution for each SMP. Using powerful techniques of differential geometry, JG has already shown that the equations of motion for the quadrupole moment have unexpected features. [1]

    By October 2019 a general analytic formula for both the dynamics of the SMPs and the reconstruction of the distribution will have been calculated and we are looking for a PhD student to help implement this algorithm. As a prelude to full-scale 3-dimensional implementation, lower-dimensional codes could be run and benchmarked against existing codes.

    The SMP approach will be excellent at calculating CSR wakes where the distance between the centres is large. There is also the possibility of incorporating space-charge into SMPs. Radiation reaction is difficult to model for standard macro-particles as the only information is position an velocity. However, since SMP have information about higher moments one can model space-charge by altering the equation for the second and higher moments.

    Currently, we wish to develop the algorithm and demonstrate proof of principle. However, it is hoped the code could be applied to several existing projects, in particular, FELs where the CSR is so important.

    As far as is known to the proposers (after searching) no similar approach has been considered. Although several people, starting with Esirkepov [2] and including Vay et al [3] do consider smearing the macro-particles over several cells with a chosen shape.

    Program of PhD: We will search for a student with an interest in programming. In the first year, as well as the CI lectures, the student will learn the necessary differential geometry and theory of distributions to understand the nature of the algorithm. They will also improve their coding skills maybe leading to writing a simple 1d PIC code. She or he will then implement a 1d SMP can compare the result. In years two and three the student will familiarise themselves with an existing 3d PIC code and implement the SMP.


    [1] Gratus, J., Banaszek, T. \The correct and unusual coordinate transformation rules for electromagnetic quadrupoles" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. Volume 474, 2213 (2018)

    [2] \T.Zh. Esirkepov, Exact charge conservation scheme for Particle-in-Cell simulation with an arbitrary form-factor", Computer Physics Communications, Volume 135, Issue 2, 144 (2001)

    [3] J.-L. Vay, C.G.R. Geddes, E. Cormier-Michel, D.P. Grote, \Numerical methods for instability mitigation in the modelling of laser wakefield accelerators in a Lorentz- boosted frame," Journal of Computational Physics, Volume 230, Issue 15, 5908 (2011)

  • Bunch profile shaping using time-dependent wire media


    Dr Jonathan Gratus


    Background: The successful collaboration of Jonathan Gratus, Rosa Letizia, Paul Kinsler, Taylor Boyd and Rebecca Seviour [1, 2, 3], has shown that the electric field profile in a waveguide or cavity can be shaped using a wire medium with varying wire radius. Using space-time symmetry it is reasonably straightforward to convert the concept of spatial dispersive inhomogeneous media into time and frequency-dependent media. Thus one can relatively quickly arrive at the time-dependent permittivity one will need to shape an electron bunch. The challenge for the numerical simulation of this model is the challenge of implementing directly time-dependent media.

    This project will support a $1.4million EPSRC proposal (Gratus, Letizia, Kinsler, Seviour (Huddersfield), McCall (Imperial)) which among other things will experimentally verify the existence of wave profile shaping in wire media.

    Taylor Boyd, who as a result of this project has 4 peer-reviewed journal articles will be submitting soon. The work is ideally suited for a PhD student.

    Program of PhD

    During the first year, as well as undergoing the Cockcroft postgraduate training, the student will learn about spatially and temporally dispersive, time-dependent and inhomogeneous media. Also, they would learn to run CST and run the profiles already develop successfully by our collaboration. He or she will then be able to develop the time-dependent proles necessary for bunch shaping. These theoretical results could be verified using a simple 1D EM solver. In year 2 the student will explore VSim together with the extension of open source code such as MEEP and MPB to go to 3D.


    [1] Taylor Boyd, Jonathan Gratus, Paul Kinsler, Rosa Letizia and Rebecca Seviour \Mode profile shaping in wire media: towards an experimental verification." Applied Sciences, Vol. 8, No. 8, 1276, 01.08.2018.

    [2] Taylor Boyd, Jonathan Gratus, Paul Kinsler and Rosa Letizia \Customizing longitudinal electric field profiles using spatial dispersion in dielectric wire arrays." Optics Express, Vol. 26, No. 3, 05.02.2018, p. 2478-2494.

    [3] Taylor Boyd, Jonathan Gratus, Paul Kinsler and Rosa Letizia \Subwavelength mode profile customisation using functional materials." Journal of Physics Communications, Vol. 1, No. 2, 025003, 06.09.2017.

  • Shaping the electric field in artificial EM materials.


    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 artificially 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 ( for more information.

  • High-quality electrons and high-brightness x-rays from wakefield acceleration


    Dr Elisabetta Boella


    Laser wakefield accelerators (LWFA) are able to sustain accelerating gradients orders of magnitude larger than radio-frequency accelerators. Therefore, they represent a possible compact and cheaper alternative to conventional acceleration methods [1]. They also constitute a potential novel light source [2]. Thus, they open up promising perspectives for future compact and affordable electron and x-ray light sources, hence enabling possible revolutionary advances in science, industry, medicine, and technology. However, at the current status, the electron beam quality and stability, as well as the radiation that they generate, do not meet yet the standard for applications. Achieving high-quality beams and high-brightness radiation from LWFA are major challenges in the field.

    Within this PhD project, we intend to tackle these major challenges. Leveraging high-fidelity numerical simulations, we aim at improving the electron beam and x-ray characteristics focusing on optimizing how electrons get trapped into the accelerating structure.

    The successful candidate will join a vibrant research team developing novel acceleration concepts using ultra-intense lasers and working towards several proof-of-concept demonstrations of laser-driven particle acceleration. They will interact with eminent theoretical and experimental physicists making significant progress in the field. Their theory and simulation effort will enable and support forefront experiments at the STFC Daresbury Laboratory National Laboratory (Warrington) and other national and international facilities.

    Through the development of this project, the student will acquire skills and expertise in plasma physics, laser-matter interaction, high-energy-density-physics, numerical techniques, and high-performance-computing. They will be registered at Lancaster University. They will also enrol in the graduate program at the Cockcroft Institute, part of STFC Daresbury Laboratory National Laboratory. Finally, they will have the opportunity to travel and collaborate with scientific institutes and universities in and outside the U.K.

    Interested candidates should contact Dr Elisabetta Boella ( for further information.

    [1] Tajima & Dawson, Phys. Rev. Lett. 43, 267 (1979); Esarey et al. Rev. Mod. Phys. 81, 1229 (2009).

    [2] Corde et al., Rev. Mod. Phys. 85, 1 (2013); Albert & Thomas, Plasma Phys. Contr. F. 58, 103001 (2016).

Postgraduate Training

All postgraduate students in the accelerator physics group are members of the Cockcroft Institute of Accelerator Science and Technology. The Cockcroft Institute runs a two-year postgraduate education programme in accelerator science and technology which is compulsory for its own PhD students and also available to students in other groups and at other universities. The lectures are recorded to be webcast and archived.

The lecture programme has an initial 3 months introductory period starting in October and runs once a week until December of each year. Lectures cover the basics of accelerator science and technology, including beam dynamics and magnet design.

The advanced portion of the lecture programme runs from January to September and on a two-year cycle covers topics such as:

  • Hamiltonian beam dynamics
  • Free-electron lasers
  • Radio frequency engineering
  • Laser plasma acceleration

All of our PhD students complete a number of assessments covering the Cockcroft Institute introductory course syllabus and are given the opportunity to carry out computational laboratory exercises including computational tools such as CST Microwave Studio, OPERA and MADX, to design RF cavities, magnets and particle beamlines respectively.

Depending on the nature of the PhD topic being covered, our students may also attend some of the graduate training offered by our colleagues in the Mathematical Physics group or Experimental Particle Physics groups.

Additional training opportunities

Further specialised training in accelerator physics may be offered through attendance at one or more of the CERN accelerator schools.

In addition to attending international conferences relevant to their degree, our students attend the annual accelerator PhD student conference at the Cockcroft Institute where they present their work and receive feedback on their presentation skills.

In common with all Lancaster postgraduate students, our students have access to a wide range of other general and transferable-skills training courses through the university.