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.

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We demonstrate the experimental feasibility of probing the fully nonperturbative regime of quantum electrodynamics with a 100 GeV-class particle collider. By using tightly compressed and focused electron beams, beamstrahlung radiation losses can be mitigated, allowing the particles to experience extreme electromagnetic fields. Three-dimensional particle-in-cell simulations confirm the viability of this approach. The experimental forefront envisaged has the potential to establish a novel research field and to stimulate the development of a new theoretical methodology for this yet unexplored regime of strong-field quantum electrodynamics.The interaction of light and matter is governed by quantum electrodynamics (QED), which is the most successfully tested theory in physics. According to the present understanding of QED, the properties of matter change qualitatively in the presence of strong electromagnetic fields. The importance of strong-field quantum effects is determined by the Lorentz invariant parameter χ = E * /E cr [1, 2] (also called beamstrahlung parameter in the context of particle colliders), which compares the electromagnetic field in the electron/positron rest frame E * with the QED critical field E cr = m 2 c 3 /(e ) ≈ 1.32×10 18 V/m. Here, m and e are the electron/positron mass and charge, c is speed of light, and is reduced Planck constant, respectively. Whereas classical electrodynamics is valid if χ 1, quantum effects like the recoil of emitted photons (quantum radiation reaction) and the creation of matter from pure light become important in the regime χ 1. Eventually, the interaction between light and matter becomes fully nonperturbative if χ 1. The behavior of matter near QED critical field strengths (i.e., the regime χ ∼ 1) is important in astrophysics (e.g., gamma-ray bursts, pulsar magnetosphere, supernova explosions) [3][4][5], at the interaction point of future linear particle colliders [6][7][8][9][10][11][12][13], and in upcoming high energy density physics experiments, where laserplasma interactions will probe quantum effects [14]. Experimental investigations of strong-field QED have just approached χ 1, e.g., by combining highly energetic particles with intense optical laser fields. This experimental scheme, first realized in the SLAC E-144 experiment [15,16], has been recently revisited [17,18]. Notable alternatives are x-ray free electron lasers [19], highly charged ions [20], heavy-ion collisions [21], and strong crystalline fields [22]. The success of QED in the regime χ 1 is based on the smallness of the fine-structure *

The cross section for deeply virtual Compton scattering in the reaction ep → eγp has been measured with the ZEUS detector at HERA using integrated luminosities of 95.0 pb −1 of e + p and 16.7 pb −1 of e − p collisions. Differential cross sections are presented as a function of the exchanged-photon virtuality, Q 2 , and the centre-of-mass energy, W , of the γ * p system in the region 5 < Q 2 < 100 GeV 2 and 40 < W < 140 GeV. The measured cross sections rise steeply with increasing W . The measurements are compared to QCD-based calculations.