Unipolar arcing: Difference between revisions

The electron emission at the cathode spot occurs in the form of discrete explosive electron emission splashes, so-called 'ectons'. These quanta of the explosive process represent the minimum actions required for the explosive events. The duration of one ecton is about <math>\sim</math>10 ns, the current $\sim$1 A, and the size of the emission centers is about $\sim1$ $\upmu$m. The explosion leaves a micro crater with a diameter of about $\sim1$ $\upmu$m.

According to the ecton model, arc operation is self-sustained, and occurs in stages \cite{Bar2011} (Figure \ref{fig:arc_mech}). The first stage is the appearance of dense primary erosion plasma due to the external action, e.g. a laser pulse or ELM-plasma, onto the target. This dense plasma action results in a strong emission pulse ($10^8$ A/cm$^2$) that leads to a thermal explosion of the emitting local area, the start of stage two. The created dense plasma produces two important effects: 1) the sheath thickness reduces, leading to an increase in the electric field at the surface, and 2) (due to the electric field) the ion bombardment heating increases. Now, if the local electric field is additionally enhanced by the fine structure of the surface, e.g. tungsten fuzz, this can all together intensify the local energy input, leading to a thermal run-away process. If the energy input rate exceeds the energy removing rate, this can lead to a micro-explosion. The micro-explosion creates another dense erosion plasma, and hence creates another emission site, so this causes repeating ignition of micro-explosions. The dense plasma provides the conditions for the ignition while 'choking' the already operating emission center by its limited conductivity \footnote{During the explosive gas phase, material is evaporated which increases the gas density in front of the emission site. Since gas is a bad conductor, the current transfer capability suffers.}. Ignition in this sense is not just the triggering of the arc discharge but the arc's perpetual mechanism to 'stay alive.' The probabilistic distribution of ignition of emission centers can be associated with a fractal spot model\footnote{Fractals are mathematical or physical objects invariant to scaling, so called 'self-similar'. They occur in phenomena which are nonlinear, aperiodic, and chaotic, such as arcing \cite{And2008}.}

where $\tau$ is a time interval over which observation is averaged, $E_{phon}$ is the phonon energy (heat)transferred to the cathode material, $E_{CE}$ the cohesive energy needed to transfer the cathode material from the solid phase to the vapor phase, $E_{ionization} $ is the energy needed to ionize the vaporized cathode material, $E_{kin,i} $ is the kinetic energy given to the ions due tot the pressure gradient and other acceleration mechanisms, $E_{ee}$ is the energy needed to emit electrons from the solid to the plasma, $E_{th,e}$ the thermal energy (enthalpy) of electron in the plasma, $E_{MP}$ is the energy invested in melting, heating, and acceleration of marcoparticles, and $E_{rad}$ is the energy emitted by radiation. The input energy is mostly transferred to heat the cathode, to emit and heat electrons, and to produce and accelerate ions.