Publications

Formulation And Implementation Of A 1.75D Streamer Model

Jorgenson, Roy E.; Warne, Larry K.

Streamers are a type of ionization wave occurring during the early time phase of a gas discharge. They are typically launched when the evolving space charge of an electron avalanche reaches a certain critical level, beyond which the fi eld of the space charge itself is su ffi cient to drive further evolution of the ionization process. One of the most common ways to model streamers is known as a 1.5D model where the fi eld of a uniformly charged set of discs of chosen radius is evaluated along the cylinder axis. This fi eld drives a one-dimensional kinetic ionization process, which results in the nonlinear evolution of the streamer. This model is e ffi cient, but has the drawback of fi xing the radius and requiring it as an input parameter. Previously, we tried to extend t he 1.5D model to include evolution of its radius by developing a two-step process of axial and radial exp ansion but we encountered stability issues with the model that we thought could have been due to decoupling the two steps. In this report we introduce a new formulation of a streamer model that includes radial expansion. The goal is to take radial moments of the starting axisymmetric fl uid equations and thereby include the radial evolution of the streamer naturally and self-consistently from the beginning. We fi rst develop the fl uid model moments without electron attachment. We review the calculation of the electric fi elds required for the model and investigate approximations to improve computational e ffi ciency. We discuss the code implementation of the model and fi nally, we add attachment to allow the treatment of electronegative gases. Intentionally Left Blank