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It is shown by numerical simulations that, if a laser pulse from the eXawatt Center for Extreme Light Studies (Sarov) is used as a driver for a laser wakefield accelerator, an electron bunch with a charge of 50 pC can be accelerated to energy of 100 GeV with an energy spread of less than 1%. To this end, it is necessary to form a plasma channel 70 m long with a characteristic radius of 200 μm and a plasma density of 3 × 10 15 cm –3 on the axis. In a denser plasma, the acceleration rate is higher, but the acceleration length and the resulting energy are smaller. The accelerator parameters can be numerically optimized using a quasistatic model describing the laser pulse in terms of its envelope, which reduces the computation time by several orders of magnitude as compared to complete models.

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.

A laser pulse from one channel of the Russian eXawatt Center for Extreme Light Studies (XCELS) facility will make it possible to accelerate an electron bunch with a charge of 50 pC to an energy of GeV with an energy spread of 0.7%. This requires a plasma channel of length 70 m, radius , and plasma density on the axis of   . Numerical optimization of the acceleration process at such scales is computationally expensive, but can be efficiently performed using a quasistatic code by a two-step simulation method, which is described in the paper.

The quasistatic approximation (QSA) is an efficient method of simulating laser- and beam-driven plasma wakefield acceleration, but it becomes imprecise if some plasma particles make long longitudinal excursions in a strongly nonlinear wave, or if waves with non-zero group velocity are present in the plasma, or the plasma density gradients are sharp, or the beam shape changes rapidly. We present an extension to QSA that is free from its limitations and retains its main advantages of speed and reduced dimensionality. The new approach takes into account the exchange of information between adjacent plasma layers. We introduce the physical model, describe its numerical implementation, and compare the simulation results with available analytical solutions and other codes.

The channeling of laser pulses in waveguides filled with a rare plasma is one of promising techniques of laser wakefield acceleration. A solid-state capillary can precisely guide tightly focused pulses. Regardless of the material of the capillary, its walls behave like a plasma under the influence of a high-intensity laser pulse. Therefore, the waveguide modes in the capillaries have a universal structure, which depends only on the shape of the cross-section. Due to the large ratio of the capillary radius to the laser wavelength, the modes in circular capillaries differ from the classical TE and TM modes. The attenuation length for such modes is two orders of magnitude longer than that obtained from the classical formula, and the incident pulse of the proper radius can transfer up to 98% of its initial energy to the fundamental mode. However, finding eigenmodes in capillaries of arbitrary cross-section is a complex mathematical problem that remains to be solved.

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’.

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.

By combining the linear theory and numerical simulations, we study the response of a radially bounded axisymmetric plasma to relativistic charged particle beams in a wide range of plasma densities. We present analytical expressions for the magnetic field generated in the dense plasma, prove vanishing of the wakefield potential beyond the trajectory of the outermost plasma electron, and follow the wakefield potential change as the plasma density decreases. At high plasma densities, wavefronts of electron density and radial electric field are distorted because of beam charge and current neutralization, while wavefronts of wakefield potential and longitudinal electric field are not. At plasma densities lower than or of the order of beam density, multiple electron flows develop in and outside the plasma, resulting in nonzero wakefield potential around the plasma column.

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.