An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions

For many years, low mode asymmetry in inertially confined fusion (ICF) implosions has been recognized as a potential performance limiting factor, but analysis has been limited to using simulations and searching for data correlations. Herein, an analytically solvable model based upon the simple picture of an asymmetric piston is presented. Asymmetry of the shell driving the implosion, as opposed to asymmetry in the hot-spot, is key to the model. The model provides a unifying framework for the action of mode-1 shell asymmetry and the resulting connections between various diagnostic signatures. A key variable in the model is the shell asymmetry fraction, f, which is related to the areal density variation of the shell surrounding the hot-spot. It is shown that f is simply related to the observed hot-spot mode-1 velocity and to the concept of residual energy in an implosion. The model presented in this paper yields explicit expressions for the hot-spot diameter, stagnation pressure, hot-spot energy, inertial confinement-time, Lawson parameter, hot-spot temperature, and fusion yield under the action of mode-1 asymmetry. Agreement is found between the theory scalings when compared to ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations, making the theory a useful tool for interpreting data. The theory provides a basis for setting tolerable limits on asymmetry.