School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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Nonlinear conservation laws with moving boundaries often arise in applications such as gas dynamics and more recently in the context of nuclear fusion reactors. Gaining insight into the nature of solutions to such models and their dependence upon design parameters is often done numerically. We use formal asymptotics to study a model of a magnetized target fusion reactor for producing energy. We will asymptotically solve the compressible Euler equations with two free moving boundaries, with an algebraic coupling of fluid pressure at one of the free boundaries. The model consists of an intense pressure being imparted on the boundary of a large sphere holding molten lead-lithium over a very short time scale, in the middle of which is a smaller concentric sphere containing plasma. A localized disturbance quickly propagates toward the plasma, whereby part of the energy is reflected and part compresses the plasma. The plasma pressure is modeled by a magnetic pressure, dependent upon its radius. Both the outer boundary of the lead-lithium sphere and the plasma boundary are free. Using matched asymptotics and various techniques for solving linear hyperbolic systems including Riemann invariants and using the velocity potential formulation of the linear acoustic equations, we estimate the maximum compression of the plasma. This estimation gives insights into the factors relevant in designing an energy-producing reactor.


Copyright 2015 Society for Industrial and Applied Mathematics

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SIAM Journal on Applied Mathematics



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Mathematics Commons



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