Reconstruction of FXR beam conditions

Beam-envelope radius, envelope angle, and beam emittance can be derived from measurements of beam radius for at least three different transport conditions. We have used this technique to reconstruct exit parameters from the FXR injector and accelerator. We use a diamagnetic loop (DML) to measure the magnetic moment of the high current beam. With no assumptions about radial profile, we can derive the beam mean squire radius from the moment under certain easily met conditions. Since it is this parameter which is required for the reconstruction, it is evident that the DML is the ideal diagnostic for this technique. The simplest application of this technique requires at least three shots for a reconstruction but in reality requires averaging over many more shots because of shot to shot variation. Since DML measurements do not interfere with the beam, single shot time resolved measurements of the beam parameters appear feasible if one uses an array of at least three DMLs separated by known transport conditions.