Near- and far-field centroid-oscillation diagnostics of straight and curved discharge plasma waveguides

Discharge capillary plasma waveguides are key components for long-distance laser guiding, multi-GeV laser wakefield acceleration, and staged accelerator coupling. Their optical axis, matched spot size, and effective channel depth directly affect laser guiding quality and beam pointing stability, while in curved waveguides the geometric centerline is not necessarily the optical equilibrium trajectory. Here we extend the established laser centroid-oscillation diagnostic by adding a far-field angular measurement to the conventional near-field exit-position measurement. Combining the two measurements reduces the phase ambiguity of position-only diagnostics and gives a more constrained inversion of the centroid-oscillation phase. In a straight discharge capillary, the two measurements give consistent phases near 154 degrees, corresponding to a matched spot size of about 53.3 μm and an effective channel depth of about 1.25×10^18 cm^-3 under the selected guiding condition. The same diagnostic is applied to a curved capillary with a 1.25 m curvature radius, where the far-field response indicates a preferred nonzero relative injection offset. This combined measurement provides an in situ phase-space diagnostic for straight and curved plasma waveguides.