High-power stabilized pinches are subject to magnetic disturbances and leakage of energetic particles. A diffusion theory describing the leakage in terms of interconnection of flux surfaces is consistent with the experimental data. Direct observation of the leakage phenomenon was realized in a 4-in., 100- kamp linear pinch tube, along which is passed a 200-kv, 10-mamp electron beam of 0.1- mu sec duration. Prior to onset of magnetic disturbances, the beam delineates regular nested magnetic-flux surfaces at the phosphor end-window. When the beam is injected on a flux surface where magnetic disturbances have begun, the trace becomes erratic, and subsequently all transmission ceases. The loss of beam containment within the pinch begins at the current layer and propagates inward. By addition of a hard core to the pinch tube, suppression of magnetic disturbances can be achieved in inverse stabilized pinches. Correspondingly, regular beam traces are obtainable throughout the pinch cycle, at levels of current density where transmission through stabilized pinches cannot be maintained at all. The successful containment of particles in hard-core geometry is being given a further test by means of a newly completed 400-kamp levitron (toroidal pinch with ring core) of 12-in. minor diameter. The electron- beam probe provedmore » highly useful for diagnosis of the magnetic structure of pinch discharges even in their stable state. The magnetic pitch on a flux surface can be derived from the angle rotation of the beam image about the pinch axis. The time rate of rotation measures the interdiffusion of magnetic-field components. The magnetic shear can be derived directly from the elongation of the beam image along the flux surface. Experimental tests of this measurement of shear confirm that the results are nearly independent of beam energy and duration, and of absolute magnetic field strengih. In stabilized pinches regions of low shear are found prior to onset of the magnetic disturbances. In inverse stabilized pinches substantial shear can be maintained at all radii. (auth)« less