It is demonstrated that the performance of the self-modulated proton driver plasma wakefield accelerator (SM-PDPWA) is strongly affected by the reduced phase velocity of the plasma wave. Using analytical theory and particle-in-cell simulations, we show that the reduction is largest during the linear stage of self-modulation. As the instability nonlinearly saturates, the phase velocity approaches that of the driver. The deleterious effects of the wake's dynamics on the maximum energy gain of accelerated electrons can be avoided using side-injections of electrons, or by controlling the wake's phase velocity by smooth plasma density gradients.

This report describes the conceptual steps in reaching the design of the AWAKE experiment currently under construction at CERN. We start with an introduction to plasma wakefield acceleration and the motivation for using proton drivers. We then describe the self-modulation instability -a key to an early realization of the concept. This is then followed by the historical development of the experimental design, where the critical issues that arose and their solutions are described. We conclude with the design of the experiment as it is being realized at CERN and some words on the future outlook. A summary of the AWAKE design and construction status as presented in this conference is given in [1].

Abstract. New acceleration technology is mandatory for the future elucidation of fundamental particles and their interactions. A promising approach is to exploit the properties of plasmas. Past research has focused on creating large-amplitude plasma waves by injecting an intense laser pulse or an electron bunch into the plasma. However, the maximum energy gain of electrons accelerated in a single plasma stage is limited by the energy of the driver. Proton bunches are the most promising drivers of wakefields to accelerate electrons to the TeV energy scale in a single stage. An experimental program at CERN -the AWAKE experiment -has been launched to study in detail the important physical processes and to demonstrate the power of proton-driven plasma wakefield acceleration. Here we review the physical principles and some experimental considerations for a future proton-driven plasma wakefield accelerator.

An accurate description of noise levels is of crucial importance for the correct simulation of instabilitydriven processes, such as the density modulation of a long proton bunch traversing a plasma. To insure that the correct instability develops, a seed field must be larger than the cumulative shot noise. We develop an analytical theory of the noise field and compare it with multidimensional simulations. We find that the natural noise wakefield generated in a plasma by the CERN Super Proton Synchrotron bunches is very low, at the level of 10 kV=m. This fortunate fact eases the requirements on the seed. Our threedimensional simulations show that even a few tens MeV electron bunch precursor of a very moderate intensity is sufficient to seed the proton bunch self-modulation in plasma.

In this paper we present a new three dimensional (3D) full electromagnetic relativistic hybrid plasma code H-VLPL (hybrid virtual laser plasma laboratory). The full kinetic particlein-cell (PIC) method is used to simulate low density hot plasmas while the hydrodynamic model applies to the high density cold background plasma. To simulate the linear electromagnetic response of the high density plasma, we use a newly developed form of an exponential integrator method. It allows us to simulate plasmas of arbitrary densities using large time steps. The model reproduces the plasma dispersion and gives correct spatial scales like the plasma skin depth even for large grid cell sizes. We test the hybrid model validity by applying it to some physical examples.