Voltage-pulse-profile characteristics with space charge of a loaded pulsed ionization chamber

An analytical model describing the voltage pulse profile of a pulsed ionization chamber and its relationship to the electron density in a field drift dominated plasma is formulated. The differential equation derived from the equations of motion and conservation of electron density combined with Poisson's equation for the electric space-charge field in the system is solved analytically for the cylindrical-electrode geometry with an external RC circuit. The numerical analysis for the given initial and boundary conditions yields the anode voltage-signal pulse profiles for the period of electron collection as a function of the initial electron density, the gas pressure, and ion-chamber radii and length. Thus, the theory permits the determination of the electron density from the observed voltage signal.