Faraday rotation study of plasma bubbles in GeV wakefield accelerators

We visualize plasma bubbles driven by 0.67 PW laser pulses in plasma of density $n_e \approx 5\times10^{17}$ ${\rm cm}^{-3}$ by imaging Faraday rotation patterns imprinted on linearly-polarized probe pulses of wavelength $\lambda_{pr} = 1.05 \mu$m and duration $\tau_{pr} = 2$ ps or $1$ ps that cross the bubble's path at right angles. When the bubble captures and accelerates tens to hundreds of pC of electron charge, we observe two parallel streaks of length $c\tau_{pr}$ straddling the drive pulse propagation axis, separated by $\sim45$ $\mu$m, in which probe polarization rotates by $0.3^\circ$ to more than $5^\circ$ in opposite directions. Accompanying simulations show that they result from Faraday rotation within portions of dense bubble side walls that are pervaded by the azimuthal magnetic field of accelerating electrons during the probe transit across the bubble. Analysis of the width of the streaks shows that quasi-monoenergetic high-energy electrons and trailing lower energy electrons inside the bubble contribute distinguishable portions of the observed signals, and that relativistic flow of sheath electrons suppresses Faraday rotation from the rear of the bubble. The results demonstrate favorable scaling of Faraday rotation diagnostics to $40\times$ lower plasma density than previously demonstrated.