Current action integral for the electrical explosion of tungsten fuzz nanostructure

The following article examines plasma formation via electrical explosion of the tungsten fuzz nanostructure. The electrical resistivity of the helium-filled tungsten nanowire structure obtained in the previous research [Tsventoukh and Kulagin, Phys. Plasmas 31, 092509 (2024)] has been applied to evaluate the specific electrical current action integral and the parameters of arcing explosive cycles. The resistivity was estimated to be ρ1nw(T) = 0.265 mΩ cm × (1 + T/15 kK) for a helium-filled tungsten nanowire and η−2/3 × ρ1nw(T) for a layer of nanowires of relative density η. The electric current action integral for a single helium-filled nanowire h was calculated to be h1nw = 1.2 × 108 A2 cm−4 s and that for the whole nanostructure layer is h = η5/3 × h1nw, which is less than 106 A2 cm−4 s for fuzz layers several μm thick of density η < 1/20. Explosive electron emission (ecton cycle) has been estimated to be in the nanosecond range based on the experimentally measured current density. The average current density during the ecton pulse has been estimated as η2/3/(1 + 2η) × h1nw/(enl) = η2/3/(1 + 2η) × 125 MA cm−2/(l/μm), which depends only on the experimental value of the fuzz burnout depth l (a few μm) and agrees with the experimentally measured values of the average current density. The research showed that an ensemble of “sharp needles,” comprising about 1/10 of the total number of nanowires at the arc crater, can (i) provide a total current approximately equal to the arc current (a few amperes) and (ii) form plasma within tens of picoseconds via explosion by a current density of a few GA/cm2.