Following some recent unexpected hints of neutron production in setups like high-voltage atmospheric discharges and plasma discharges in electrolytic cells, we present a measurement of the neutron flux in a configuration similar to the latter. We use two different types of neutron detectors, poly-allyl-diglicol-carbonate (PADC, aka CR-39) tracers and Indium disks. At 95% C.L. we provide an upper limit of 1.5 neutrons cm^-2 s^-1 for the thermal neutron flux at ~5 cm from the center of the cell. Allowing for a higher energy neutron component the largest allowed flux is 64 neutrons cm^-2 s^-1. This upper limit is two orders of magnitude smaller than what previously claimed in an electrolytic cell plasma discharge experiment. Furthermore the behavior of the CR-39 is discussed to point our possible sources of spurious signals.
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