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STEP is a spherical tokamak prototype power plant that is being designed to demonstrate net electric power. The design phase involves the exploitation of plasma models to optimise fusion performance subject to satisfying various physics and engineering constraints. A modelling workflow, including integrated core plasma modelling, MHD stability analysis, SOL and pedestal modelling, coil set and free boundary equilibrium solvers, and whole plant design, has been developed to specify the design parameters and to develop viable scenarios. The integrated core plasma model JETTO is used to develop individual flat-top operating points that satisfy imposed criteria for fusion power performance within operational constraints. Key plasma parameters such as normalised beta, Greenwald density fraction, auxiliary power and radiated power have been scanned to scope the operational space and to derive a collection of candidate non-inductive flat-top points. The assumed auxiliary heating and current drive is either from electron cyclotron systems only or a combination of electron cyclotron and electron Bernstein waves. At present stages of transport modelling, there is a large uncertainty in overall confinement for relevant parameter regimes. For each of the two auxiliary heating and current drive systems scenarios, two candidate flat-top points have been developed based on different confinement assumptions, totalling to four operating points. A lower confinement assumption generally suggests operating points in high-density, high auxiliary power regimes, whereas higher confinement would allow access to a broader parameter regime in density and power while maintaining target fusion power performance., Comment: 44 pages, 15 figures. Submitted to Nucl. Fusion (IOP)

The interactions of charged particles with carbon nanotubes may excite electromagnetic modes in the electron gas produced in the cylindrical graphene shell constituting the nanotube wall. This wake effect has recently been proposed as a potential novel method of short-wavelength high-gradient particle acceleration. In this work, the excitation of these wakefields is studied by means of the linearized hydrodynamic model. In this model, the electronic excitations on the nanotube surface are described treating the electron gas as a 2D plasma with additional contributions to the fluid momentum equation from specific solid-state properties of the gas. General expressions are derived for the excited longitudinal and transverse wakefields. Numerical results are obtained for a charged particle moving within a carbon nanotube, paraxially to its axis, showing how the wakefield is affected by parameters such as the particle velocity and its radial position, the nanotube radius, and a friction factor, which can be used as a phenomenological parameter to describe effects from the ionic lattice. Assuming a particle driver propagating on axis at a given velocity, optimal parameters were obtained to maximize the longitudinal wakefield amplitude.

Charged particle acceleration using solid-state nanostructures has attracted attention in recent years as a method of achieving ultra-high-gradient acceleration in the TV/m domain. More concretely, metallic hollow nanostructures could be suitable for particle acceleration through the excitation of wakefields by a laser or a high-intensity charged particle beam in a high-density solid-state plasma. For instance, due to their special channelling properties as well as optoelectronic and thermo-mechanical properties, carbon nanotubes could be an excellent medium for this purpose. This article investigates the feasibility of generating ultra-high gradient acceleration using carbon nanotube arrays, modelled as solid-state plasmas in conventional particle-in-cell simulations performed in a two-dimensional axisymmetric quasi}-3D geometry. The generation of beam-driven plasma wakefields depending on different parameters of the solid structure is discussed in detail. Furthermore, by adopting an effective plasma-density approach, existing analytical expressions, originally derived for homogeneous plasmas, can be used to describe wakefields driven in periodic non-uniform plasmas., Comment: 15 pages, 13 figures

High-brightness beams generated by particle sources based on advanced accelerator concepts have the potential to become an essential part of future accelerator technology. High-gradient accelerators can generate and rapidly accelerate particle beams to relativistic energies while minimizing irreversible detrimental effects to the beam brightness that occur at low beam energies. Due to the high accelerating gradients, these novel accelerators are also significantly more compact than conventional technology. The beam parameters of these particle sources are largely determined by the injection and subsequent acceleration processes. While there has been significant progress crucial parameters that are required for a future collider or more near-term applications, including X-ray free-electron lasers (XFELs), such as a sufficiently small energy spread and small emittance for bunches with a high charge and at high pulse repetition rate. Major research and development efforts are required to realize these approaches for a front-end injector for a future collider in order to address these limitations. In particular, this includes methods to control and manipulate the phase-space and spin degrees-of-freedom of ultrashort LWFA electron bunches with high accuracy, methods that increase the laser-to-electron beam efficiency and increased repetition rate. This also includes the development of high-resolution diagnostics, such as full 6D phase-space measurements, beam polarimetry and high-fidelity simulation tools. A further increase in beam luminosity can be achieve through emittance damping. For future colliders, the damping rings might be replaced by a substantially more compact plasma-based approach. Here, plasma wigglers are used to achieve similar damping performance but over a two orders of magnitude reduced length., Comment: contribution to Snowmass 2021

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement., Comment: 13 pages, 11 figures

We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($\ge(4.1\pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$\pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated., Comment: Letter and Supplemental Material, 6 figures, 8 pages

In 2017, AWAKE demonstrated the seeded self-modulation (SSM) of a 400 GeV proton beam from the Super Proton Synchrotron (SPS) at CERN. The angular distribution of the protons deflected due to SSM is a quantitative measure of the process, which agrees with simulations by the two-dimensional (axisymmetric) particle-in-cell code LCODE. Agreement is achieved for beam populations between $10^{11}$ and $3 \times 10^{11}$ particles, various plasma density gradients ($-20 \div 20\%$) and two plasma densities ($2\times 10^{14} \text{cm}^{-3}$ and $7 \times 10^{14} \text{cm}^{-3}$). The agreement is reached only in the case of a wide enough simulation box (at least five plasma wavelengths)., Comment: 8 pages, 9 figures, 1 table

By means of hollow plasma, multiple proton bunches work well in driving nonlinear plasma wakefields and accelerate electrons to energy frontier with preserved beam quality. However, the acceleration of positrons is different because the accelerating structure is strongly charge dependent. There is a discrepancy between keeping a small normalized emittance and a small energy spread. This results from the conflict that the plasma electrons used to provide focusing to the multiple proton bunches dilute the positron bunch. By loading an extra electron bunch to repel the plasma electrons and meanwhile reducing the plasma density slightly to shift the accelerating phase with a conducive slope to the positron bunch, the positron bunch can be accelerate to 400 GeV (40% of the driver energy) with an energy spread as low as 1% and well preserved normalized emittance. The successful generation of high quality and high energy positrons paves the way to the future energy frontier lepton colliders., Comment: 14 pages, 5 figures

We give direct experimental evidence for the observation of the full transverse self-modulation of a relativistic proton bunch propagating through a dense plasma. The bunch exits the plasma with a density modulation resulting from radial wakefield effects with a period reciprocal to the plasma frequency. We show that the modulation is seeded by using an intense laser pulse co-propagating with the proton bunch which creates a relativistic ionization front within the bunch. We show by varying the plasma density over one order of magnitude that the modulation period scales with the expected dependence on the plasma density., Comment: 4 figures, AWAKE collaboration paper, Submitted to PRL

High energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. In order to increase the energy or reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration, in which the electrons in a plasma are excited, leading to strong electric fields, is one such promising novel acceleration technique. Pioneering experiments have shown that an intense laser pulse or electron bunch traversing a plasma, drives electric fields of 10s GV/m and above. These values are well beyond those achieved in conventional RF accelerators which are limited to ~0.1 GV/m. A limitation of laser pulses and electron bunches is their low stored energy, which motivates the use of multiple stages to reach very high energies. The use of proton bunches is compelling, as they have the potential to drive wakefields and accelerate electrons to high energy in a single accelerating stage. The long proton bunches currently available can be used, as they undergo self-modulation, a particle-plasma interaction which longitudinally splits the bunch into a series of high density microbunches, which then act resonantly to create large wakefields. The AWAKE experiment at CERN uses intense bunches of protons, each of energy 400 GeV, with a total bunch energy of 19 kJ, to drive a wakefield in a 10 m long plasma. Bunches of electrons are injected into the wakefield formed by the proton microbunches. This paper presents measurements of electrons accelerated up to 2 GeV at AWAKE. This constitutes the first demonstration of proton-driven plasma wakefield acceleration. The potential for this scheme to produce very high energy electron bunches in a single accelerating stage means that the results shown here are a significant step towards the development of future high energy particle accelerators., Comment: 7 pages, 4 figures. Updated acknowledgements and one reference

Seeded Self-modulation (SSM) has been demonstrated to transform a long proton bunch into many equidistant micro-bunches (e.g., the AWAKE case), which then resonantly excite strong wakefields. However, the wakefields in a uniform plasma suffer from a quick amplitude drop after reaching the peak. This is caused by a significant decrease of the wake phase velocity during self-modulation. A large number of protons slip out of focusing and decelerating regions and get lost, and thus cannot contribute to the wakefield growth. Previously suggested solutions incorporate a sharp or a linear plasma longitudinal density increase which can compensate the backward phase shift and therefore enhance the wakefields. In this paper, we propose a new plasma density profile, which can further boost the wakefield amplitude by 30%. More importantly, almost 24% of protons initially located along one plasma period survive in a micro-bunch after modulation. The underlying physics is discussed., Comment: 5 pages, 4 figures

Hollow plasma has been introduced into the proton-driven plasma wakefield accelerators to overcome the issue of beam quality degradation caused by the nonlinear transverse wakefields varying in radius and time in uniform plasma. It has been demonstrated in simulations that the electrons can be accelerated to energy frontier with well-preserved beam quality in a long hollow plasma channel. However, this scheme imposes tight requirements on the beam-channel alignment. Otherwise asymmetric transverse wakefields along the axis are induced, which could distort the driving bunch and deteriorate the witness beam quality. In this paper, by means of the 2D cartesian particle-in-cell simulations, we examine the potentially detrimental effects induced by the driving beam-channel offset and initial driver tilt, and then propose and assess the solutions to these driver inaccuracy issues., Comment: 4 pages, 4 figures

Solid-state based wakefield acceleration of charged particles was previously proposed to obtain extremely high gradients on the order of 1-10 TeV/m. In recent years the possibility of using either metallic or carbon nanotube structures is attracting new attention. The use of carbon nanotubes would allow us to accelerate and channel particles overcoming many of the limitations of using natural crystals, e.g. channeling aperture restrictions and thermal-mechanical robustness issues. In this paper, we propose a potential proof of concept experiment using carbon nanotube arrays, assuming the beam parameters and conditions of accelerator facilities already available, such as CLEAR at CERN and CLARA at Daresbury. The acceleration performance of carbon nanotube arrays is investigated by using a 2D Particle-In-Cell (PIC) model based on a multi-hollow plasma. Optimum experimental beam parameters and system layout are discussed., Comment: 4 pages, 6 figures; Proceedings of the 9th International Particle Accelerator Conference, IPAC18

Plasma-based accelerators have achieved tremendous progress in the past few decades, thanks to the advances of high power lasers and the availability of high-energy and relativistic particle beams. However, the electrons (or positrons) accelerated in the plasma wakefields are subject to radiation losses, which generally suppress the final energy gains of the beams. In this paper, radiation reaction in plasma-based high-energy accelerators is investigated using test particle approach. Energy-frontier TeV colliders based on a multiple stage laser-driven plasma wakefield accelerator and a single-staged proton-driven plasma wakefield accelerator are studied in detail. The results show that the higher axial and transverse field gradients seen by an off-axis injected witness beam result in a stronger damping force on the accelerated particles. Proton-driven plasma wakefield accelerated electrons are shown to lose less energy compared to those accelerated in a multi-staged laser-driven plasma wakefield accelerator.

Terahertz frequency wakefields can be excited by ultra-short relativistic electron bunches travelling through dielectric lined waveguide (DLW) structures. These wakefields can either accelerate a witness bunch with high gradient, or modulate the energy of the driving bunch. In this paper, we study a passive dechirper based on the DLW to compensate the correlated energy spread of the bunches accelerated by the laser plasma wakefield accelerator (LWFA). A rectangular waveguide structure was employed taking advantage of its continuously tunable gap during operation. The assumed 200 MeV driving bunch had a Gaussian distribution with a bunch length of 3.0 {\mu}m, a relative correlated energy spread of 1%, and a total charge of 10 pC. Both of the CST Wakefield Solver and PIC Solver were used to simulate and optimize such a dechirper. Effect of the time-dependent self-wake on the driving bunch was analyzed in terms of the energy modulation and the transverse phase space.

AWAKE is a proton-driven plasma wakefield acceleration experiment. % We show that the experimental setup briefly described here is ready for systematic study of the seeded self-modulation of the 400\,GeV proton bunch in the 10\,m-long rubidium plasma with density adjustable from 1 to 10$\times10^{14}$\,cm$^{-3}$. % We show that the short laser pulse used for ionization of the rubidium vapor propagates all the way along the column, suggesting full ionization of the vapor. % We show that ionization occurs along the proton bunch, at the laser time and that the plasma that follows affects the proton bunch. %, Comment: Presented as an invited talk at the EPS=Plasma Physics Conference 2017

A plasma beam dump uses the collective oscillations of plasma electrons to absorb the kinetic energy of a particle beam. In this paper, a modified passive plasma beam dump scheme is proposed using either a gradient or stepped plasma profile to maintain a higher decelerating gradient compared to a uniform plasma. The improvement is a result of the plasma wavelength change preventing the re-acceleration of low energy particles. Particle-in-cell simulation results show that both stepped and gradient plasma profiles can achieve improved energy loss compared to a uniform plasma for an electron bunch of parameters routinely achieved in laser wakefield acceleration., Comment: 13 pages, 6 figures

The Advanced Proton Driven Plasma Wakefield Acceleration Experiment (AWAKE) aims at studying plasma wakefield generation and electron acceleration driven by proton bunches. It is a proof-of-principle R&D experiment at CERN and the world's first proton driven plasma wakefield acceleration experiment. The AWAKE experiment will be installed in the former CNGS facility and uses the 400 GeV/c proton beam bunches from the SPS. The first experiments will focus on the self-modulation instability of the long (rms ~12 cm) proton bunch in the plasma. These experiments are planned for the end of 2016. Later, in 2017/2018, low energy (~15 MeV) electrons will be externally injected to sample the wakefields and be accelerated beyond 1 GeV. The main goals of the experiment will be summarized. A summary of the AWAKE design and construction status will be presented., Comment: 7 pages, 7 figures, 2 tables

This report describes the conceptual steps in reaching the design of the AWAKE experiment currently under construction at CERN. We start with an introduction to plasma wakefield acceleration and the motivation for using proton drivers. We then describe the self-modulation instability --- a key to an early realization of the concept. This is then followed by the historical development of the experimental design, where the critical issues that arose and their solutions are described. We conclude with the design of the experiment as it is being realized at CERN and some words on the future outlook. A summary of the AWAKE design and construction status as presented in this conference is given in [1]., Comment: 15 pages, 24 figures, 1 table, 111 references, 121 author from 36 organizations

High quality electron beams, with high spatial and tempo- ral resolution, have an important use in electron diffraction experiments to probe and study the constituents of matter. A cold electron source is being developed based on elec- tron ionisation from an atom cloud trapped by using AC magneto-optical methods in the University of Manchester. The technique will produce bunches of electrons well suited for high precision and single shot electron diffraction. In this paper issues of modelling at low energies for this state of art electron source with very low energy spread are presented, with a focus on newly developed tools to model the scat- tering in the meshes used to support the extraction electric fields. The dependence on emittance growth on mesh wire thickness is studied., Comment: Presented in IPAC2015

Particle-in-cell simulations were performed by using PARMELA to characterise an electron injector with a booster linac for the AWAKE project in order to provide the baseline specifications required by the plasma wakefield experiments. Tolerances and errors were investigated. A 3 GHz travelling wave structure designed by using CST code. Particles were tracked by using the field maps acquired from these electromagnetic simulations. These results are pre- sented in comparison with the generic accelerating structure model within PARMELA., Comment: Presented in IPAC2015

PARS (Plasma Acceleration Research Station) is an electron beam driven plasma wakefield acceleration test stand proposed for VELA/CLARA facility in Daresbury Laboratory. In order to optimise various operational configurations, 2D numerical studies were performed by using VSIM for a range of parameters such as bunch length, radius, plasma density and positioning of the bunches with respect to each other for the two-beam acceleration scheme. In this paper, some of these numerical studies and considered measurement methods are presented., Comment: Presented in IPAC2015

The interaction of the witness beam with the surrounding plasma particles and wakefields was studied. The impli- cations of the elastic scattering process on beam emittance and, emittance evolution under the focusing and acceleration provided by plasma wakefields were discussed. Simulations results from GEANT4 are presented in this paper., Comment: Presented in IPAC2015