The formalism of Analytic Multi-Regge Theory is developed as a basis for the study of abstract Critical and Super-Critical Pomeron high-energy behavior and for related studies of the Regge behavior of spontaneously broken gauge theories and the Pomeron in QCD. Asymptotic domains of analyticity for multiparticle amplitudes are shown to follow from properties of Field Theory and S-Matrix Theory. General asymptotic dispersion relations are then derived for such amplitudes in which the spectral components are described by the graphical formalism of hexographs. Further consequences are distinct Sommerfeld-Watson representations for each hexograph spectral component, together with a complete set of angular momentum plane unitarity equations which control the form of all multi-Regge amplitudes. Because of this constraint of Reggeon Unitarity'' the Critical Pomeron solution of the Reggeon Field Theory gives the only known non-trivial'' unitary high-energy S-Matrix. By exploiting the full structure of multi-Regge amplitudes as the Pomeron becomes Super-Critical, the simultaneous modification of hadrons and the Pomeron can be studies. The result is a completely consistent description of the Super-Critical Pomeron appearing in hadron scattering. Reggeon Unitarity is satisfied in the Super-Critical Phase by the appearance of a massive gluon'' (Reggeised vector particle) coupling pair-wise to the Pomeron.

We are constructing a diagnostic system to measure the electric field (>100 kV/cm) of a free-electron laser (FEL) beam when injected into the plasma of the Microwave Tokamak Experiment (MTX). The apparatus allows a crossed-beam measurement, with 2-cm spatial resolution in the plasma, involving the FEL beam (with 140-GHz, {approx}1-GW ECH pulses), a neutral-helium beam, and a dye-laser beam. After the laser beam pumps metastable helium atoms to higher excited states, their decay light is detected by an efficient optical system. Because of the Stark effect arising from the FEL electric field ({rvec E}), a forbidden transition can be strongly induced. The intensity of emitted light resulting from the forbidden transition is proportional to E{sup 2}. Because photon counting rates are estimated to be low, extra effort is made to minimize background and noise levels. It is possible that the lower {rvec E} of an MTX gyrotron-produced ECH beam with its longer-duration pulses can also be measured using this method. Other applications of the apparatus described here may include measurements of ion temperature (using charge-exchange recombination), edge-density fluctuations, and core impurity concentrations.