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The charged particles moving through a carbon nanotube (CNT) may be used to excite electromagnetic modes in the electron gas produced in the cylindrical graphene shell that makes up a nanotube wall. This effect has recently been proposed as a potential novel method of short-wavelength-high-gradient particle acceleration. In this contribution, the existing theory based on a linearized hydrodynamic model for a localized point-charge propagating in a single wall nanotube (SWNT) is reviewed. In this model, the electron gas is treated as a plasma with additional contributions to the fluid momentum equation from specific solid-state properties of the gas. The governing set of differential equations is formed by the continuity and momentum equations for the involved species. These equations are then coupled by Maxwell’s equations. The differential equation system is solved applying a modified Fourier-Bessel transform. An analysis has been realized to determine the plasma modes able to excite a longitudinal electrical wakefield component in the SWNT to accelerate test charges. Numerical results are obtained showing the influence of the damping factor, the velocity of the driver, the nanotube radius, and the particle position on the excited wakefields. A discussion is presented on the suitability and possible limitations of using this method for modelling CNT-based particle acceleration.

Simulations of proton-driven plasma wakefield accelerators have demonstrated substantially higher accelerating gradients compared to conventional accelerators and the viability of accelerating electrons to the energy frontier in a single plasma stage. However, due to the strong intrinsic transverse fields varying both radially and in time, the witness beam quality is still far from suitable for practical application in future colliders. Here we demonstrate the efficient acceleration of electrons in proton-driven wakefields in a hollow plasma channel. In this regime, the witness bunch is positioned in the region with a strong accelerating field, free from plasma electrons and ions. We show that the electron beam carrying the charge of about 10% of 1 TeV proton driver charge can be accelerated to 0.6 TeV with a preserved normalized emittance in a single channel of 700 m. This high-quality and high-charge beam may pave the way for the development of future plasma-based energy frontier colliders.

A long, narrow, relativistic charged particle bunch propagating in plasma is subject to the self -modulation (SM) instability. We show that SM of a proton bunch can be seeded by the wakefields driven by a preceding electron bunch. SM timing reproducibility and control are at the level of a small fraction of the modulation period. With this seeding method, we independently control the amplitude of the seed wakefields with the charge of the electron bunch and the growth rate of SM with the charge of the proton bunch. Seeding leads to larger growth of the wakefields than in the instability case.

Plasma wakefield acceleration is a promising technology to reduce the size of particle accelerators. The use of high energy protons to drive wakefields in plasma has been demonstrated during Run 1 of the AWAKE programme at CERN. Protons of energy 400 GeV drove wakefields that accelerated electrons to 2 GeV in under 10 m of plasma. The AWAKE collaboration is now embarking on Run 2 with the main aims to demonstrate stable accelerating gradients of 0.5–1 GV/m, preserve emittance of the electron bunches during acceleration and develop plasma sources scalable to 100s of metres and beyond. By the end of Run 2, the AWAKE scheme should be able to provide electron beams for particle physics experiments and several possible experiments have already been evaluated. This article summarises the programme of AWAKE Run 2 and how it will be achieved as well as the possible application of the AWAKE scheme to novel particle physics experiments.

In this article, we briefly summarize the experiments performed during the first run of the Advanced Wakefield Experiment, AWAKE, at CERN (European Organization for Nuclear Research). The final goal of AWAKE Run 1 (2013–2018) was to demonstrate that 10–20 MeV electrons can be accelerated to GeV energies in a plasma wakefield driven by a highly relativistic self-modulated proton bunch. We describe the experiment, outline the measurement concept and present first results. Last, we outline our plans for the future. This article is part of the Theo Murphy meeting issue ‘Directions in particle beam-driven plasma wakefield acceleration’.

We study experimentally the longitudinal and transverse wakefields driven by a highly relativistic proton bunch during self-modulation in plasma. We show that the wakefields’ growth and amplitude increase with increasing seed amplitude as well as with the proton bunch charge in the plasma. We study transverse wakefields using the maximum radius of the proton bunch distribution measured on a screen downstream from the plasma. We study longitudinal wakefields by externally injecting electrons and measuring their final energy. Measurements agree with trends predicted by theory and numerical simulations and validate our understanding of the development of self-modulation. Experiments were performed in the context of the Advanced Wakefield Experiment (AWAKE).

In this article, we briefly summarize the experiments performed during the first run of the Advanced Wakefield Experiment, AWAKE, at CERN (European Organization for Nuclear Research). The final goal of AWAKE Run 1 (2013–2018) was to demonstrate that 10–20 MeV electrons can be accelerated to GeV energies in a plasma wakefield driven by a highly relativistic self-modulated proton bunch. We describe the experiment, outline the measurement concept and present first results. Last, we outline our plans for the future. This article is part of the Theo Murphy meeting issue ‘Directions in particle beam-driven plasma wakefield acceleration’.

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 [F. Braunmller, T. Nechaeva et al. (AWAKE Collaboration), Phys. Rev. Lett. 125, 264801 (2020)]: 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.