The Advanced Wakefield Experiment, or AWAKE, is an experiment based at CERN (European Organization for Nuclear Research) whose purpose is to demon- strate the acceleration of electrons using plasma wakefields driven by a charged par- ticle bunch. As a proof-of-principle experiment, AWAKE will be propagating a high- energy proton bunch through 10 meters of plasma to drive the wakefields for electron acceleration. To accelerate the electrons, we want to inject them into regions of both focusing and acceleration within these wakefields behind the proton bunch. In order for the electrons to stay within this optimal accelerating/focusing region, we need to maintain uniform plasma density within 0.2%, and we need to inject when the wakefield phase-velocity is constant. To preserve uniform plasma density, we use a liquid heat-exchanging pipe which can maintain stable temperatures, and therefore uniform rubidium vapor/plasma densities, to within 0.2%. We show that this is pos- sible using Galden HT270 as a heat-exchanging liquid. We also show that additional components required for this system will need external heating to prevent heat-loss, and therefore temperature non-uniformity. Furthermore, using the PIC simulation OSIRIS, we study how changing size parameters of the initial proton bunch by ±5% a ects the phase-velocity of the wakefield. It is seen that these parameter variations will not significantly affect the optimal region size and energy gain of injected elec- trons; so long as the electrons are injected at regions of ξ near σzb of the proton bunch and after 4 m of bunch propagation length in the plasma. / Graduate

An ongoing experiment is described to demonstrate the principle of multi-pulse laser wakefield acceleration, in which a plasma wakefield is resonantly excited by a train of laser pulses, spaced by the plasma wavelength. Particle-in-cell simulations of the initial single-pulse experimental setup are presented, in order to calculate the expected signal. Preliminary results are presented and future plans, based on work done so far, are discussed. Part of this work involves the implementation of a single-shot wakefield diagnostic - frequency-domain holography, which records the phase shift caused by passage of a probe pulse through the plasma. This implementation is described in detail, along with the associated analysis procedure. Practical difficulties encountered while implementing the diagnostic are discussed, along with possible ways of mitigating them in the future. A method is presented by which the noise level in the resulting phase measurements can be predicted, much more accurately than any previously published method for this technique. Methods of generating pulse trains for use in future multi-pulse laser wakefield acceleration experiments are presented. These include techniques proposed for use in this demonstration experiment, as well as one intended for use in a dedicated high-efficiency, high repetition-rate, multi-pulse driver laser. This last method, based on programmable pulse shaping using a spatial light modulator, requires a suitable mask to be computed based on the parameters of the required pulse train; an algorithm is described to perform this computation.