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| An analytical model of a collisional plasma being compressed by a cylindrical liner is proposed and solved in a magnetized liner inertial fusion-like context. The implosion is assumed to be isobaric, and the plasma is initially magnetized. The model reduces to a system of two partial differential equations for temperature and magnetic field. This system is controlled by the Péclet number, magnetic Reynolds number and the electron Hall parameter. Depending on their initial value, the imploding plasma tends to either an unmagnetized diffusive state or a magnetized state. Scaling laws for temperature, magnetic field, hot spot mass increase and magnetic field losses are obtained. Effects of finite thermal to magnetic pressure ratio are also considered. Special attention is given to the effect of the Nernst term on the degradation of the total magnetic flux conservation. It is found that due to the Nernst term, the magnetic field is advected outwardly and piled up against the liner, enhancing the diffusion. The magnetic flux losses get independent of the magnetic Reynolds number in a large Reynolds limit. It is shown how the plasma magnetization reduces the effect of the Nernst velocity. | |
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