The energy frontier of particle physics is several trillion electron volts, but colliders capable of reaching this regime (such as the Large Hadron Collider and the International Linear Collider) are costly and time-consuming to build; it is therefore important to explore new methods of accelerating particles to high energies. Plasma-based accelerators are particularly attractive because they are capable of producing accelerating fields that are orders of magnitude larger than those used in conventional colliders. In these accelerators, a drive beam (either laser or particle) produces a plasma wave (wakefield) that accelerates charged particles. The ultimate utility of plasma accelerators will depend on sustaining ultrahigh accelerating fields over a substantial length to achieve a significant energy gain. Here we show that an energy gain of more than 42 GeV is achieved in a plasma wakefield accelerator of 85 cm length, driven by a 42 GeV electron beam at the Stanford Linear Accelerator Center (SLAC). The results are in excellent agreement with the predictions of three-dimensional particle-in-cell simulations. Most of the beam electrons lose energy to the plasma wave, but some electrons in the back of the same beam pulse are accelerated with a field of approximately 52 GV m(-1). This effectively doubles their energy, producing the energy gain of the 3-km-long SLAC accelerator in less than a metre for a small fraction of the electrons in the injected bunch. This is an important step towards demonstrating the viability of plasma accelerators for high-energy physics 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 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. 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. 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.

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, 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 or electron bunch 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. 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. Long, thin proton bunches can be used because they undergo a process called self-modulation, 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 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 means that our results are an important step towards the development of future high-energy particle accelerators.

We demonstrate that trains of subpicosecond electron microbunches, with subpicosecond spacing, can be produced by placing a mask in a region of the beam line where the beam transverse size is dominated by the correlated energy spread. We show that the number, length, and spacing of the microbunches can be controlled through the parameters of the beam and the mask. Such microbunch trains can be further compressed and accelerated and have applications to free electron lasers and plasma wakefield accelerators.