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Unformatted text preview: Physics 498/MMA Handout 7 Fall 2007 Mathematical Methods in Physics I http://w3.physics.uiuc.edu/ ∼ mstone5 Prof. M. Stone 2117 ESB University of Illinois 1) Critical Mass : An infinite slab of fissile material has thickness L . The neutron density n ( r ) in the material obeys the equation ∂n ∂t = D ∇ 2 n + λn + μ, where n is zero at the surface of the slab at x = 0 , L . Here D is the neutron diffusion constant, the term λn describes the creation of new neutrons by induced fission, and μ is the rate of production per unit volume of neutrons by spontaneous fission. Assume that n depends only on x . a) Expand n as a series n ( x, t ) = X m a m ( t ) ϕ m ( x ) where the ϕ m are a complete set of functions you think suitable for solving the problem. b) Find an explicit expression for the coefficients a m ( t ) in terms of their intial values a m (0). c) Determine the critical thickness, L crit , above which the slab will explode....
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This homework help was uploaded on 01/29/2008 for the course PHYS 598 taught by Professor Stone during the Fall '07 term at University of Illinois at Urbana–Champaign.
 Fall '07
 Stone
 Mass, Neutron

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