This introductory article is a synopsis of the status and prospects of particle-beam-driven plasma wakefield acceleration (PWFA). Conceptual and experimental breakthroughs obtained over the last years have initiated a rapid growth of the research field, and increased maturity of underlying technology allows an increasing number of research groups to engage in experimental R&D. We briefly describe the fundamental mechanisms of PWFA, from which its chief attractions arise. Most importantly, this is the capability of extremely rapid acceleration of electrons and positrons at gradients many orders of magnitude larger than in conventional accelerators. This allows the size of accelerator units to be shrunk from the kilometre to metre scale, and possibly the quality of accelerated electron beam output to be improved by orders of magnitude. In turn, such compact and high-quality accelerators are potentially transformative for applications across natural, material and life sciences. This overview provides contextual background for the manuscripts of this issue, resulting from a Theo Murphy meeting held in the summer of 2018. This article is part of the Theo Murphy meeting issue 'Directions in particle beam-driven plasma wakefield acceleration'.

We briefly summarize the work and discussions that occurred during the Working Group 8 sessions of the EAAC 2017, dedicated to advanced and novel accelerators for high energy physics applications.

The transverse dynamics of a 28.5 GeV electron beam propagating in a 1.4 m long, 0-2 x 10^14 cm^-3 plasma are studied experimentally in the underdense or blow-out regime. The transverse component of the wake field excited by the short electron bunch focuses the bunch, which experiences multiple betatron oscillations as the plasma density is increased. The spot size variations are observed using optical transition radiation and Cherenkov radiation. In this regime, the behavoir of the spot size as a function of the plasma density is well described by a simple beam envelope model. Dynamic changes of the beam envelope are observed by time resolving the Cherenkov light.

It is widely accepted that the next lepton collider beyond a Higgs factory would require center-of-mass energy of the order of up to 15 TeV. Since, given reasonable space and cost restrictions, conventional accelerator technology reaches its limits near this energy, high-gradient advanced acceleration concepts are attractive. Advanced and novel accelerators (ANAs) are leading candidates due to their ability to produce acceleration gradients on the order of 1-100 GV/m, leading to compact acceleration facilities. However, intermediate energy facilities (IEF) are required to test the critical technology elements on the way towards multi-TeV-class collliders. Here a science case for a 20-100 GeV center-of-mass energy ANA-based lepton collider that can be a candidate for an intermediate energy facility is presented. The IEF can provide numerous opportunities for high energy physics studies including precision Quantum Chromodynamics and Beyond the Standard Model physics measurements, investigation of charged particle interactions with extreme electromagnetic fields, and exploring muon and proton beam acceleration. Possible applications of this collider include the studies of γγ and electron beam-fixed target/beamdump collider designs. Thus, the goal of the proposed IEF is to both carry out particle physics measurements in the 20-100 GeV ranges as well as to serve as an ANA demonstrator facility.

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'.

High-energy particle accelerators have been crucial in providing a deeper understanding of fundamental particles and the forces that govern their interactions. To increase the energy of the particles or to reduce the size of the accelerator, new acceleration schemes need to be developed. Plasma wakefield acceleration^1-5, in which the electrons in a plasma are excited, leading to strong electric fields (so called 'wakefields'), is one such promising acceleration technique. Experiments have shown that an intense laser pulse^6-9 or electron bunch^10,11 traversing a plasma can drive electric fields of tens of gigavolts per metre and above-well beyond those achieved in conventional radio-frequency accelerators (about 0.1 gigavolt per metre). However, the low stored energy of laser pulses and electron bunches means that multiple acceleration stages are needed to reach very high particle energies^5,12. The use of proton bunches is compelling because they have the potential to drive wakefields and to accelerate electrons to high energy in a single acceleration stage¹³. Long, thin proton bunches can be used because they undergo a process called self-modulation^14-16, a particle-plasma interaction that splits the bunch longitudinally into a series of high-density microbunches, which then act resonantly to create large wakefields. The Advanced Wakefield (AWAKE) experiment at CERN^17-19 uses high-intensity proton bunches-in which each proton has an energy of 400 gigaelectronvolts, resulting in a total bunch energy of 19 kilojoules-to drive a wakefield in a ten-metre-long plasma. Electron bunches are then injected into this wakefield. Here we present measurements of electrons accelerated up to two gigaelectronvolts at the AWAKE experiment, in a demonstration of proton-driven plasma wakefield acceleration. Measurements were conducted under various plasma conditions and the acceleration was found to be consistent and reliable. The potential for this scheme to produce very high-energy electron bunches in a single accelerating stage²⁰ means that our results are an important step towards the development of future high-energy particle accelerators^21,22.