We present a new model for the synchrotron compact nebular emissions for Vela and PSR B1706-44, and derive fundamental pulsar/plerion parameters such as the pair production multiplicity, M, and wind magnetization parameter, σ. The pair cascade above the pulsar polar cap, combined with the energy from the pulsar wind, injects a pair plasma into the surrounding environment. This wind, consisting of particles and fields, is shocked by the environment, resulting in synchrotron emission from "thermalized" pairs in a compact nebula. The broadband nebular spectrum depends crucially on the spin-down power, distance, pair multiplicity, pulsar wind shock radius, and σ at this shock. We construct such a model for the particle spectra in the compact X-ray nebulae of Vela and PSR B1706-44. Fits to the multiwavelength spectra of these sources indicate that 300 M 1000, whereas 0.05 σ 0.5 for Vela. The same σ interval (as for Vela) was independently derived from the radial gradients of the X-ray compact nebular emission from both Vela and PSR B1706-44, giving us confidence in our results. The M we derive for Vela is too small to be explained by curvature losses in the open magnetosphere of Vela, but the presence of optical pulsed photons could modify the predicted multiplicity.
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