Plasma dynamics of an explosive emission center - ecton of a cathode spot in external tangential magnetic field

Abstract

The plasma dynamics of an explosive-emission center demonstrates the plasma polarization in applied external magnetic field, induced by dense plasma spherical expansion across the magnetic field. The additional positive space charge appears at the retrograde side of the dense plasma due to the polarization current j <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">φ</sub> =σBv/c ≈10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> BT [A/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ]. Probability of initiation of a new explosive emission center increases at the retrograde side and decreases at the amperian side due to this polarization. Velocity of a cathode spot retrograde motion (for considered copper cathode) vretr was estimated as v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">retr</sub> ~0.3·v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</sub> ·BT. For a clean surface v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">random</sub> ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> cm/s, hence v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">retr</sub> ~0.3B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gs</sub> [cm/s]. The “Robson angle” function was derived from simple geometrical reasons of the spot-cell (explosive-emission-center) plasma polarization, i.e. ζ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> =arctan(A·tanθ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</sub> ), where A≡tanα <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pl</sub> /cosα <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pl</sub> and α <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pl</sub> = 20°-40° - plasma-jet-expansion parameter. Therefore, considering of a plasma dynamics of the explosive-emission center can give an explanation of the vacuum-arc cathode-spot retrograde motion in frames of the ecton model.