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Gaseous Helium at cryogenic temperatures < 11 K and both liquid and gaseous He at 4.2 K < T <5.2 K at high pressures (0.1-6) MPa was excited using a corona discharge both for negative and positive high voltages. The properties of the corona discharge were study by electro-physical and spectral methods. The electro-physical investigations (measurements of corona current as a function of applied voltage) gave information about mobility of charged particles in such peculiar medium The corona current is very small < 10-7 A. Measured current-voltage characteristic allow to calculate mobility of charged particles (electrons for negative corona and positive ions for positive corona). The mobility is a function of external pressure both for supercritical fluid and for liquid. It is due to micro-cavities around electrons in such conditions. Light emitted from the ionization zone of the discharge was analyzed. Both atomic lines and molecular bands were observed. Distortion of the spectral specimen was analyzed. Parameters of lines (shift and width) depend on applied pressure both in supercritical fluid and in liquid. The phenomenon is due to empty cavities around excited atom or molecule.