Proton Beam Defocusing as a Result of Self-Modulation in Plasma

TL;DR

This paper investigates how self-modulation in plasma causes proton beam defocusing, and proposes a diagnostic method using imaging screens to confirm the development of plasma wakefields in the AWAKE experiment.

Contribution

It provides numerical analysis of proton defocusing due to self-modulation and suggests a practical measurement approach for wakefield confirmation.

Findings

Maximum defocusing angles around 1 mrad indicate successful SMI development.

Measurement of defocusing angles can confirm GV/m plasma wakefield creation.

Numerical simulations predict proton behavior and diagnostic outcomes.

Abstract

The AWAKE experiment will use a \SI{400}{GeV/c} proton beam with a longitudinal bunch length of $\sigma_z = 12\,\rm{cm}$ to create and sustain GV/m plasma wakefields over 10 meters . A 12 cm long bunch can only drive strong wakefields in a plasma with $n_{pe} = 7 \times 10^{14}\,\rm{electrons/cm}^3$ after the self-modulation instability (SMI) developed and microbunches formed, spaced at the plasma wavelength. The fields present during SMI focus and defocus the protons in the transverse plane \cite{SMI}. We show that by inserting two imaging screens downstream the plasma, we can measure the maximum defocusing angle of the defocused protons for plasma densities above $n_{pe} = 5 \times 10^{14}\,\rm{electrons/cm}^{-3}$. Measuring maximum defocusing angles around 1 mrad indirectly proves that SMI developed successfully and that GV/m plasma wakefields were created. In this paper we present numerical studies on how and when the wakefields defocus protons in plasma, the expected measurement results of the two screen diagnostics and the physics we can deduce from it.