Time-Dependent Transport via the Continued Fraction Approximation.
Technical rept. Jan 72-May 73,
AIR FORCE WEAPONS LAB KIRTLAND AFB N MEX
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The time-dependent neutral particle transport problem of an isotropic Greens function source in homogeneous, isotropic, spherically symmetric media is examined using the infinite set of time-dependent P-N equations and integral transform techniques. The approximate Greens function solutions in transform space for the all-angle flux corresponding to the P-N approximation of order N are determined to order P-9, and demonstrate a multiple wave nature upon inversion. An examination of the set of P-N solutions leads to the development of the complete P-infinity continued fraction solution in transform space. For pure absorbing media the continued fraction is related to an analytic function which, upon inversion, yields the exact analytical solution to the problem. For cases with low-order scattering moments the continued fraction solution yields closed form functions in transform space, but these have not yielded to useful inversion. However, a continued fraction approximation technique is developed and yields simple closed form approximate solutions for the case of isotropic scatter. Modified author abstract
- Nuclear Physics and Elementary Particle Physics