Numerical Studies of Self-modulation Instability in the Beam-Driven Plasma Wakefield Experiments

Abstract

The plasma wakefield accelerator is one of promising and advanced particle accelerator models. It can make particle accelerator more compact and cheaper. A beam bunch propagating through plasma excites the plasma wakefield at some conditions. The optimum wake is obtained for k_p*σ_z = sqrt(2) and k_p*σ_r ≤ 1. Where k_p is plasma wave number and σ_z (or σ_r) is RMS beam length (or RMS beam radius). But we are interested in using CERN’s long and high-energy proton beams. The CERN’s proton beams are much longer (~12 cm) than the optimum driving beam length (in order of plasma wavelength λ_p). Here we focus on the instability which occurs based on the interaction between beam and plasma electrons. By this instability, the long driving beam is modulated along the propagation direction, so it makes the beam satisfy the optimum size for excitation of plasma waves. What we should know is that the plasma oscillation which is initially and axi-symmetrically excited by beam head will seed self-modulation of driving beam. Therefore, we first study fundamental theories of excitation of plasma waves by the charged particle beam. It’s about the response of plasma electrons to driving beam. The driving beam doesn’t interact with and only affects plasma. Here excited plasma wakefields should be considered. As the next step, the dynamics of plasma wakefield accelerator is introduced. Evolution of beam envelope in time could result in beam centroid offset or radius pinching. Where the two phenomena, centroid offset and radius pinching of the beam in plasma are called ‘Self-modulation instability’ and ‘Hose instability’. Those two instabilities compete each other. As the last step, the parameters of Injector Test Facility (ITF) at Pohang Accelerator Laboratory (PAL) is used to demonstrate the self-modulation instability.