Cathode region of a transitory discharge inCO2. I. Theory of the cathode region

The inception of the cathode region of a transitory discharge in ${\mathrm{CO}}_2$ is studied by means of a spatio-temporal second-order hydrodynamic model (continuity equations for electrons and ions, momentum and energy equations for electrons). The electric field is calculated by Poisson equation. This first paper deals particularly with the formalism developed for this study. A term-to-term analysis of the equations allows the characterization of the physical mechanisms governing each part of the cathode region. The balance between the electric field acting as a source of energy and the elastic and inelastic collisions acting as loss processes is studied. The whole collective phenomena in the discharge (diffusion and work of electronic pressure strength which are made explicit by the gradients in the equations) play a regulating role in relation to the energy-gain or -loss processes. In a place where the field action is significant, i.e., in the cathode fall, they contribute to reduce this action and are energy- and velocity-loss processes for the electrons, whereas, in the negative glow, they compensate for the quasinull action of the electric field, and thus they are the only processes maintaining the energy and the velocity of the electrons in this zone. The cathode-fall–negative-glow transition zone is defined as the zone where the action of the energetic collective phenomena (total diffusion, work of electron pressure) is reversed.