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\section{Creation of a Magnetosphere}  In order to retain this atmosphere, we will need to create a magnetosphere to shield Mars from solar wind and harmful cosmic radiation. Assuming Mars has constant density and a solid inner core and liquid outer core proportionally identical to the Earth's, we can create a dynamo by detonating nuclear weapons in Mars' inner core, thus inducing convection in Mars outer core.  To shield Mars from the same amount of cosmic radiation as the Earth, we want Mars' magnetopause to be approximately 20 Mars radii away from its center: about the same distance from Earth's center to its magnetopause.  $R_(Magnetopause)=[2B_0^2/(\mu_0\rho_(sw*v_sw^2)]^(1/6)$ where $B_0$ is the magnetic dipole moment of the planet.  Because the convecting currents which generate the magnetosphere are complex and occur within the spherical outer core, we will simplify our calculations by approximating Mars' outer core as a single gigantic rotating cylinder with radius $(R_"outer core" - R_"inner core")/2$ and height $2R_"outer core"$. With this approximation, we find Mars' magnetic dipole moment to be  $$B_0 = \rho_c\omega\mu_0[(R_"outer core"-R_"inner core")/2]^4*2R_"outer core"/16\pi$$