Generalized theory of second-harmonic orthogonally polarized dispersion interferometry and implementation for pulsed power electrode plasma measurements.

We present a generalized theoretical framework for Second-Harmonic Orthogonally Polarized Dispersion Interferometry (SHOP-DI) and the diagnostic's implementation for time-resolved electron areal-density measurements of pulsed-power Magnetically Insulated Transmission Line (MITL) electrode plasmas. The theoretical treatment extends standard SHOP-DI analysis by deriving the detected intensity response for arbitrary second-harmonic polarization angles, establishing a detector-bandwidth-limited criterion for the maximum trackable rate of change in electron areal density, modeling a counter-rotating phase-control-window system that enables reproducible phase-offset calibration, and introducing a power-normalized analysis method which separates refractive-index-induced phase shifts from static channel imbalance and common-mode optical-power fluctuations. Guided by these developments, the diagnostic was redesigned for operation on Sandia National Laboratories' (SNL's) 1 MA Mykonos accelerator, where MITL plasmas evolve on nanosecond time scales within sub-mm Anode-Cathode (A-K) gaps. The implemented system combines a 2 GHz bandwidth, corresponding to a maximum measurable areal-density rate of change of 4.8 × 1016 1/cm2/ns, with an overlapping 1/e2 probing beam waist diameter of ∼100μm. Improved optical throughput and optomechanical stiffness enabled the experiments at Mykonos to achieve a noise-limited 1σ areal-density uncertainty of 1.6 × 1014 1/cm2. These results provide design criteria for future SHOP-DI systems and demonstrate a high-bandwidth, high-sensitivity design useful for pulsed-power electrode plasma measurements.