Origin of the steep power-law scaling of breakdown rate

Measured breakdown rate per pulse per unit length in conditioned Cu structures follows $\mathrm{BDR} \sim E^{n} \tau_{p}^{m}$ with n approximately 30 and m approximately 5 (CLIC test-stand data), and BDR at fixed field decreases slowly with accumulated pulse number (conditioning). Derive n, m and the conditioning curve from a microscopic model, and state whether the power law persists at BDR below $10^{-7}$ per pulse per meter of structure.

A model whose predicted n, m and conditioning curve match test-stand data at two or more frequencies without refitting.