Betatron radiation diagnostics for AWAKE Run 2

AWAKE Run 2 aims to preserve the transverse normalised emittance of an externally injected electron beam throughout acceleration, requiring a new diagnostic to measure the beam emittance after the accelerating plasma stage. Spectroscopy of the betatron emission from the electron beam could be suitable for this case. The method of trace-space reconstruction from a measured betatron spectrum is described via a simplified analytical model in order to assess its suitability the AWAKE experiment. The expected betatron emission from witness electrons at AWAKE is characterised using 3D quasi-static PIC simulations, revealing a measurable quantity of UV to soft x-ray emission. Practical challenges for the measurement are discussed.