Fast-rising high voltage impulses, gas-dielectric interfaces, and electrode topologies which generate significant electric field nonuniformity are features often encountered within pulsed power applications. The consideration of pre-breakdown and breakdown processes, especially those across gas-solid interfaces in divergent electric fields, is important for the operation and optimization of different pulsed power and low temperature plasma systems. In this work, primary ionization waves across a sub-mm solid-gas interface have been modelled in a 2D approximation using the drift-diffusion approach. They have been initiated from a needle electrode of 80 micrometers radius, partially embedded inside a solid dielectric, and partially exposed to air. The gap separation studied in this work was 250 micrometers, in which positive and negative ramp voltages were applied with rising slopes of 25,16.67,12.5, and 10kV/ns, emulating the rising edge of impulses with different rates of voltage rise. The resulting spatiotemporal evolution of the electric field and nonthermal plasma channel has been obtained and discussed. The obtained results can help in the development of pulsed power and nonthermal plasma systems, and further contributes to the fundamental understanding of the mechanisms driving gas-solid interfacial discharge under fast impulses with high dV/dt
