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Fluid instabilities arise in a variety of contexts and are often unwantedresults of engineering imperfections. In one particular model for a magnetizedtarget fusion reactor, a pressure wave is propagated in a cylindrical annuluscomprised of a dense fluid before impinging upon a plasma and imploding it.Part of the success of the apparatus is a function of how axially-symmetric thefinal pressure pulse is upon impacting the plasma. We study a simple model forthe implosion of the system to study how imperfections in the pressure impartedon the outer circumference grow due to geometric focusing. Our methodologyentails linearizing the compressible Euler equations for mass and momentumconservation about a cylindrically symmetric problem and analyzing theperturbed profiles at different mode numbers. The linearized system gives riseto singular shocks and through analyzing the perturbation profiles at varioustimes, we infer that high mode numbers are dampened through the propagation. Wealso study the Linear Klein-Gordon equation in the context of stability oflinear cylindrical wave formation whereby highly oscillatory, bounded behaviouris observed in a far field solution.

Assessment of the Effects of Azimuthal Mode Number Perturbations upon the Implosion Processes of Fluids in Cylinders