High-harmonic generation (HHG) provides short-wavelength light that is useful for precision spectroscopy and probing ultrafast dynamics. We report efficient, phase-coherent harmonic generation up to 9th-order (333 nm) in chirped periodically poled lithium niobate waveguides driven by phase-stable $leq$12-nJ, 100 fs pulses at 3 $mu$m with 100 MHz repetition rate. A mid-infrared to ultraviolet-visible conversion efficiency as high as 10% is observed, amongst an overall 23% conversion of the fundamental to all harmonics. We verify the coherence of the harmonic frequency combs despite the complex highly nonlinear process. Numerical simulations based on a single broadband envelope equation with quadratic nonlinearity give estimates for the conversion efficiency within approximately 1 order of magnitude over a wide range of experimental parameters. From this comparison we identify a dimensionless parameter capturing the competition between three-wave mixing and group-velocity walk-off of the harmonics that governs the cascaded HHG physics. These results can inform cascaded HHG in a range of different platforms.
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