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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 stage 13 . 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 stage 20 means that our results are an important step towards the development of future high-energy particle accelerators 21 , 22 . Electron acceleration to very high energies is achieved in a single step by injecting electrons into a ‘wake’ of charge created in a 10-metre-long plasma by speeding long proton bunches.

To develop plasma wakefield acceleration into a compact and affordable replacement for conventional accelerators, beams of charged particles must be accelerated at high efficiency in a high electric field; here this is demonstrated for a bunch of charged electrons ‘surfing’ on a previously excited plasma wave. A particle accelerator for the future Particle colliders that operate at the high-energy frontier using electric fields generated by radio waves are approaching the limits of feasibility in terms of size and cost, but there are other acceleration techniques that could make less expensive and more compact devices. The plasma wakefield accelerator, in which an electron bunch is accelerated by making it 'surf' on a plasma wave excited by another electron bunch, promises an energy gain in the gigaelectron-volt regime over just a few centimetres — an energy gain that requires hundreds of metres using traditional accelerators. Previously, this technique had only been used to accelerate a very small number of electrons at a time. Now, researchers working at FACET, the Facility for Advanced Accelerator Experimental Tests at SLAC National Accelerator Laboratory, USA, have achieved acceleration of about half a billion electrons at once with an unprecedented efficiency for a plasma accelerator. This achievement could be a milestone in the development of affordable and compact accelerators for applications ranging from high energy physics to medical and industrial applications. High-efficiency acceleration of charged particle beams at high gradients of energy gain per unit length is necessary to achieve an affordable and compact high-energy collider. The plasma wakefield accelerator is one concept 1 , 2 , 3 being developed for this purpose. In plasma wakefield acceleration, a charge-density wake with high accelerating fields is driven by the passage of an ultra-relativistic bunch of charged particles (the drive bunch) through a plasma 4 , 5 , 6 . If a second bunch of relativistic electrons (the trailing bunch) with sufficient charge follows in the wake of the drive bunch at an appropriate distance, it can be efficiently accelerated to high energy. Previous experiments using just a single 42-gigaelectronvolt drive bunch have accelerated electrons with a continuous energy spectrum and a maximum energy of up to 85 gigaelectronvolts from the tail of the same bunch in less than a metre of plasma 7 . However, the total charge of these accelerated electrons was insufficient to extract a substantial amount of energy from the wake. Here we report high-efficiency acceleration of a discrete trailing bunch of electrons that contains sufficient charge to extract a substantial amount of energy from the high-gradient, nonlinear plasma wakefield accelerator. Specifically, we show the acceleration of about 74 picocoulombs of charge contained in the core of the trailing bunch in an accelerating gradient of about 4.4 gigavolts per metre. These core particles gain about 1.6 gigaelectronvolts of energy per particle, with a final energy spread as low as 0.7 per cent (2.0 per cent on average), and an energy-transfer efficiency from the wake to the bunch that can exceed 30 per cent (17.7 per cent on average). This acceleration of a distinct bunch of electrons containing a substantial charge and having a small energy spread with both a high accelerating gradient and a high energy-transfer efficiency represents a milestone in the development of plasma wakefield acceleration into a compact and affordable accelerator technology.

Ab initio simulations of the propagation in a plasma of a soon to be available relativistic electron-positron beam or fireball beam provide an effective mean for the study of microphysics relevant to astrophysical scenarios. We show that the current filamentation instability associated with some of these scenarios reaches saturation after only 10 cm of propagation in a typical laboratory plasma with a density ∼1017 cm−3. The different regimes of the instability, from the purely transverse to the mixed mode filamentation, can be accessed by varying the background plasma density. The instability generates large local plasma gradients, intense transverse magnetic fields, and enhanced emission of radiation. We suggest that these effects may be observed experimentally for the first time.

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.

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 describe an external electron injection scheme for the AWAKE experiment. We use scattering in two foils, that are necessary as vacuum window and laser beam dump, to decrease the betatron function of the incoming electron beam for injection and matching into plasma wakefields driven by a self-modulated proton bunch. We show that, for a total aluminum foil thickness of ~ 280 μm, multiple Coulomb scattering increases the beam emittance by a factor of ~ 10 and decreases the betatron function by a factor of ~ 3. The plasma in the accelerator is created by a ionizing laser pulse, counter-propagating with respect to the electron beam. This allows for the electron bunch to enter the plasma through an \"infinitely\" sharp vapor-plasma boundary, away from the foils.

Ab initio simulations of the propagation in a plasma of a soon to be available relativistic electron–positron beam or fireball beam provide an effective mean for the study of microphysics relevant to astrophysical scenarios. We show that the current filamentation instability associated with some of these scenarios reaches saturation after only 10 cm of propagation in a typical laboratory plasma with a density ∼1017 cm−3. The different regimes of the instability, from the purely transverse to the mixed mode filamentation, can be accessed by varying the background plasma density. The instability generates large local plasma gradients, intense transverse magnetic fields, and enhanced emission of radiation. We suggest that these effects may be observed experimentally for the first time.

The Advanced Wakefield Experiment (AWAKE) at CERN is the first plasma wakefield accelerator experiment to use a proton bunch as driver. The long bunch undergoes seeded self-modulation (SSM) in a 10 m-long plasma. SSM transforms the bunch into a train of short micro-bunches that resonantly drive high-amplitude wakefields. We use optical transition radiation (OTR) and a streak camera to obtain time-resolved images of the bunch transverse charge density distribution in a given plane. In this paper we present a method to obtain 3D images of the bunch by scanning the OTR across the entrance slit of the streak camera. Reconstruction of the 3D distribution is possible because with seeding self-modulation is reproducible. The 3D images allow for checking the axi-symmetry of SSM and for detecting the possible presence of the non-axi-symmetric hosing instability (HI).

The Advanced Wakefield Experiment (AWAKE) develops the first plasma wakefield accelerator with a high-energy proton bunch as driver. The 400 GeV bunch from CERN Super Proton Synchrotron (SPS) propagates through a 10 m long rubidium plasma, ionized by a 4TW laser pulse co-propagating with the proton bunch. The relativistic ionization front seeds a self-modulation process. The seeded self-modulation transforms the bunch into a train of micro-bunches resonantly driving wakefields. We measure the density modulation of the bunch, in time, with a streak camera with picosecond resolution. The observed effect corresponds to alternating focusing and defocusing fields. We present a procedure recovering the charge of the bunch from the experimental streak camera images containing the charge density. These studies are important to determine the charge per micro-bunch along the modulated proton bunch and to understand the wakefields driven by the modulated bunch.

The AWAKE experiment at CERN recently demonstrated the world's first acceleration of electrons in a proton-driven plasma wakefield accelerator. Such accelerators show great promise for a new generation of linear e-p colliders using 1-10 GV/m accelerating fields. Efficiently driving a wakefield requires 100-fold self-modulation of the 12cm Super Proton Synchrotron (SPS) proton bunch using a plasma-driven process which must be carefully controlled to saturation. Previous works have modelled this process assuming azimuthal symmetry of the transverse spatial and momentum profiles. In this work, 3D particle-in-cell (PIC) simulations with the code QuickPIC are used to model the self-modulation of non-round bunches. We find that asymmetry in the initial seed wakefield leads to the formation of highly asymmetric microbunches which evolve incoherently along the symmetry axes of the initial bunch profile. However, the resonantly-driven accelerating wakefield is highly stable to both focused and astigmatic non-round bunches.