Multistage Fusion Reaction Rates in an Adiabatically Compressed Plasma

We consider a dense gas of deuterium to undergo a rapid, adiabatic compression by a piston in a chamber. A reduction in the degrees of freedom of the plasma particles, such as may be effected by an electric discharge during the compression or by the application of magnetic fields, results in a higher final temperature for a given compression ratio. In model calculations we consider the adiabatic compression of one mole of molecular deuterium modeled as a van der Waals gas initially at room temperature and we compare the subsequent fusion energy release with the work done by the piston for various values of compression ratio and degrees of freedom. Prior work considered fusion to occur only at the end of the compression while the present work considers fusion energy released at various stages during the compression. Higher final temperatures and ratios of output to input energy result from this refinement of the model.