[en] Results of investigation into running away current-plasma sheath (CPS) of noncylindrical Z-pinch are given. Experimental chamber was filled with neon up to 3 torr pressure. Store of energy was equal to 20 kJ. CPS radiation spectrum scanning was recorded in the phase of its convergence to the system axis by means of an electron-optical converter of the AGAT type. Electron temperature in the inflection region on CPS constituted 3 eV. Possibilities of magnetic field diffusion through neon CPS and appearance of CPS running away mode are shown. CPS plasma spectra indicated that radiation can be recorded only from a CPS head near-anode part and its external peripheral regions moving from the axis and emitting considerably less quantity of radiation