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Fusion Science and Technology
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In transition: Commercializing fusion power
Commercial fusion power is closer than ever. There are now around 30 U.S. fusion companies, several of which claim to be on track to connect to the grid as early as the 2030s.
Tokamak and laser inertial confinement approaches benefit from decades of research at facilities such as the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory and ITER, with alternative concepts including stellarator, magnetic mirror, and Z-pinch confinement also making notable progress as private and government funding for fusion increases.
Donald J. Dudziak
Nuclear Science and Engineering | Volume 47 | Number 2 | February 1972 | Pages 230-234
Technical Note | doi.org/10.13182/NSE72-A22402
Articles are hosted by Taylor and Francis Online.
A derivation of the time-dependent forward stochastic equation is sketched for a point reactor with linear feedback and an arbitrary finite fission neutron frequency distribution. Certain pathological characteristics of possible stochastic trajectories are discussed, and limiting conjectures are made based on physical considerations. The time-independent forward stochastic equation with negative reactivity feedback is solved in the classical manner, leading to a recursion relation for the long-run probabilities. Next, all factorial moments of the long-run distribution are shown to be finite, and the corresponding probabilities, P(N,∞), are thus o(N-k) for any integer k. Following this, a more tractable recursion relation is presented for the simpler case of binary fission. For this simpler model, the equivalence to an independent analysis of the Kolmogorov forward matrix equations, as presented in a previous paper, is demonstrated. Finally, a simple recursion relation among factorial moments of the long-run distribution is derived for the binary fission model.