Some Aspects of Breakdown Streamers

Photomultiplier and oscillographic study of positive breakdown streamers yields values of current and distance of tip advance as a function of time. From these the relatively constant number $n$ of excess positive ions left behind by the streamer per cm advance and the tip velocity $v_t$ are obtained. These are related to the linear electron density $n_c$ per cm of streamer channel plasma and the electron drift velocity $v_c$ in the channel by $n_c{v}_c=n{v}_t$, with $v_t>v_c$. Since $v_c$ is related to the gradient $X_c$ in the channel by well-known drift velocity data, it is possible to limit the range of values of $n_c$ and $v_c$. The limiting conditions are that $n_c>n$, $\int 0^x{X}_c\mathrm{dx}<V_x$, where $V_x$ is the applied potential, and finally that $X_c$ must be sufficiently large to maintain the channel conducting despite dissociative recombination and dissociative attachment losses. In longer channels heating cannot be neglected. The dense positive space charge left behind by the electron current in the ionized channel of radius $R$ causes a radial expansion of the excess space charge to a radius $R^{\prime }$ by incoming electron avalanches leading to a broad transient luminosity for some distance behind the tip. The tip and the conducting channel taking the return stroke, however, retain their small radius $R$.