Topic/Type: 1.2 Fusion Plasmas (magnetic & inertial confinement), Poster

### A numerical model of pre-explosive heating of microprotrusion by plasma-wall interaction and ohmic heating consisted with thermo-field emission

S. A. Barengolts, G. A. Mesyats, M. M. Tsventoukh

Lebedev Physical Institute RAS, Leninsky ave. 53, 119991 Moscow, The Russian Federation

The evolution of fast ($\small \sim 10$ns) overheating of microprotrusion ($\small \sim 1 \mu$m) at the plasma-surface boundary is considered. An intense power flux from plasma to the wall leads to the electron emission and ohmic heating by emission current. The heating of surface by plasma ions and electrons, cooling/heating by emission (according to Nottingham effect), and ohmic heating were taken into account. The thermo-field emission current density and average energy of emitted electrons (their energy distribution function) were calculated numerically in WKB-approximation. The electric field at the emitting surface was defined by Mackeowen-like equation. Considered range of plasma densities $\small 10^{14-20}$cm$\small ^{-3}$ electron temperatures 0.1eV?10keV.
The ability was shown of microprotrusion explosive overheating consistent with emission. It was found that the explosive threshold is defined by the power flux to the surface. The threshold value corresponds to $\small q_0\sim 200$MW/cm$\small ^2$. (What is close to the energy transferred to surface due to the dust-particle impact.) The 'explosive' heating means both achieving high temperature and current density: $\small T\sim10^4$K, $\small j\sim 10^8$A/cm$\small ^2$, and increasing of their growth: $\small tial T/tial t > 0$, $\small tial^2 T/tial t^2 > 0$, $\small tial j /tial t > 0$ ($\small tial J /tial t > 0$). With plasma density less than $\small (3-5)\times10^{18}$cm$\small ^{-3}$, (with $\small q > 200$MW/cm$\small ^2$), the emission cooling is insufficient (as the electron emission is strongly restricted by a space charge). Therefore an overheating of a microprotrusion up to $\small \sim 10^4$K occurs much earlier - at $\small \sim 1$ns. But in this case the intense surface vaporization and metal vapor ionization lead to the significant plasma density growth at the surface and, hence, to the transition of the heating evolution into the explosive regime, described above.
Considered conditions for the microexplosion initiation with a strong emission pulse ? the ecton ($\small \sim 10^{10}-10^{11}$ electrons per pulse), can be realized in plasma interaction with cathode, anode, or isolated wall; and can lead to the arc spots formation.