Accelerator Physics
Group Members
Loading People
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 highenergy 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 highflux sources of positrons and gammarays for future highenergy 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 g2
 Leading the CASCADE collaboration in its search for weaklyinteracting subeV particles such as axions using radiofrequency cavities
 Investigating wave propagation in spatially dispersive media and photonic structures
 Exploring radiation reaction in ultraintense laserplasmas as members of the ALPHAX collaboration
PhD Opportunities
Accordion

Supermacroparticles to improve in Particleincell codes
Supervisor
Dr Jonathan Gratus (Lancaster University)
Dr Hywel Owen (Manchester University)Description
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. Particleincell (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 (j.gratus@lancaster.ac.uk) for more information.

Muon g2 experiment
Supervisor
Dr Ian Bailey
Description
The Fermilab muon g2 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 g2 muon spin dynamics and help analyse the experimental data as part of the g2 collaboration.

Search for the axion
Supervisors
Dr Ian Bailey
Professor Yuri Pashkin
Dr Edward LairdDescription
In recent years, there has been a growing interest in the 'hidden sector' and nontraditional 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
Supervisor
Professor Steven Jamison
Description
We seek a PhD candidate to undertake experimental research on laserdriven 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, laserdriven acceleration offers control of particle beams on the femtosecond (10^{15}s) time scale. Also, the highfield strengths available in ultrafast lasers may enable orders of magnitude reduction in size and cost of kilometrescale accelerators of xrayfreeelectron lasers and highenergy particle physics.
The successful candidate will join a research team developing novel acceleration concepts using ultrafast lasers, and working towards several proofofconcept demonstrations of laser acceleration of relativistic beams. They will carry out work in the optimisation of multiMV/m optical and infrared sources, in highfield nonlinear optics, in mmscale accelerating structures, and in developing systems for the experimental demonstration of acceleration of relativistic beams. Through their research with highpower laser and electronbeam 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 postdoctoral 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 s.jamison@lancaster.ac.uk for further information. For general information about PhD studies in Physics at Lancaster please contact our postgraduate admissions staff at pypgadmiss@lancaster.ac.uk. You can apply directly at http://www.lancaster.ac.uk/physics/study/phd/ 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
Supervisor
Dr Elisabetta Boella
Description
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 socalled energetics problem (e.g., how the energy released during the explosive event is converted into highspeed flows, heat and energetic particles) and plans to advance our knowledge on this topic through massively parallel fully kinetic simulations.
Simulations based on the ParticleInCell 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 ultraintense lasers.
The successful candidate will join a vibrant team developing a cuttingedge 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, lasermatter interaction, highenergydensityphysics, numerical techniques, and highperformancecomputing.
Interested candidates should contact Dr Elisabetta Boella (e.boella@lancaster.ac.uk) 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
Supervisors
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 laserdriven particle accelerators. Our research, which involves a combination of femtosecond laser nonlinear optics and submm structures for electromagneticelectron 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 experimentallyfocused studentship will investigate the interaction of intense THz electromagnetic pulses (generated by nonlinear optics and ultrafast lasers) with 100keV and >50 MeV electron beams.
 The theory/simulationfocussed 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 postdoctoral 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.

Supermacroparticles to improve in PIC codes
Supervisor
Dr Jonathan Gratus
Description
PIC codes are used extensively in both conventional beam dynamics and laserplasma interactions. Macroparticles 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 macroparticle is \smeared" or \diluted" over the nearest cell points.
We propose an improved method of modelling the macroparticles. Current PIC codes only record the position and velocity of each macroparticle. By contrast, our new method will record higher moments. These new supermacroparticles (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 macroparticles. The potential advantages, however, may be huge, equivalent to replacing tens or hundreds of macroparticles 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 fullscale 3dimensional implementation, lowerdimensional 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 spacecharge into SMPs. Radiation reaction is difficult to model for standard macroparticles as the only information is position an velocity. However, since SMP have information about higher moments one can model spacecharge 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 macroparticles 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.
References
[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 ParticleinCell simulation with an arbitrary formfactor", Computer Physics Communications, Volume 135, Issue 2, 144 (2001)
[3] J.L. Vay, C.G.R. Geddes, E. CormierMichel, 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 timedependent wire media
Supervisor
Dr Jonathan Gratus
Description
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 spacetime symmetry it is reasonably straightforward to convert the concept of spatial dispersive inhomogeneous media into time and frequencydependent media. Thus one can relatively quickly arrive at the timedependent permittivity one will need to shape an electron bunch. The challenge for the numerical simulation of this model is the challenge of implementing directly timedependent 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 peerreviewed 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, timedependent 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 timedependent 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.
References
[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. 24782494.
[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.
Supervisors
Dr Jonathan Gratus (Lancaster) and Prof. Rebecca Seviour (Huddersfield)
Description
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 timedomain 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 (j.gratus@lancaster.ac.uk) for more information.

Highquality electrons and highbrightness xrays from wakefield acceleration
Supervisor
Dr Elisabetta Boella
Description
Laser wakefield accelerators (LWFA) are able to sustain accelerating gradients orders of magnitude larger than radiofrequency 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 xray 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 highquality beams and highbrightness radiation from LWFA are major challenges in the field.
Within this PhD project, we intend to tackle these major challenges. Leveraging highfidelity numerical simulations, we aim at improving the electron beam and xray 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 ultraintense lasers and working towards several proofofconcept demonstrations of laserdriven 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, lasermatter interaction, highenergydensityphysics, numerical techniques, and highperformancecomputing. 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 (e.boella@lancaster.ac.uk) 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 twoyear 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 twoyear cycle covers topics such as:
 Hamiltonian beam dynamics
 Freeelectron 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 transferableskills training courses through the university.