High speed numerical calculation method of rate equations for abruptly recombining plasmas

The changes in the electron density and ion density in a plasma become significant as recombining of the plasma proceeds to the extent that laser oscillation begins to take place. These densities and population densities are generally calculated by using a rate equation and an equation expressing the law of conservation of particles. The present study proposes a new procedure that serves for rapid numerical calculation of a non-linear rate equation. The procedure uses the differentiated form of the particle conservation equation to eliminate the need of repeated calculation. Numerical calculations are made of the time variation of the electron density and reduced population densities of a recombining hydrogen plasma. Calculations are also made for a recombining helium plasma. The present numerical calculation procedure is compared with a conventional one with repect to the required calculation time. Results show that the calculation time can be reduced down to several 10s percent for a recombining hydrogen plasma. Furthermore, the time is found to be decreased by one to two orders of magnitude for plasmas containing two types of ions, such as helium plasma. (Nogami, K.)