Many models of ultra-high energy cosmic-ray production involve acceleration in linear accelerators located in gamma-ray bursts, magnetars, or other sources. These transient sources have short lifetimes, which necessitate very high accelerating gradients, up to 10 super(13) keV cm super(-1). At gradients above 1.6 keV cm super(-1), muons produced by hadronic interactions undergo significant acceleration before they decay. This muon acceleration hardens the neutrino energy spectrum and greatly increases the high-energy neutrino flux. Using the IceCube high-energy diffuse neutrino flux limits, we set two-dimensional limits on the source opacity and matter density, as a function of accelerating gradient. These limits put strong constraints on different models of particle acceleration, particularly those based on plasma wake-field acceleration, and limit models for sources like gamma-ray bursts and magnetars.