The new results concerning neutron emission detection from a laboratory high-voltage discharge in the air are presented. Data were obtained with a combination of plastic scintillation detectors and $^3$He filled counters of thermal neutrons. Strong dependence of the hard x-ray and neutron radiation appearance on the field strength near electrodes, which is determined by their form, was found. We have revealed a more sophisticated temporal structure of the neutron bursts observed during of electric discharge. This may indicate different mechanisms for generating penetrating radiation at the time formation and development of the atmospheric discharge.
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