This paper is a sequel to the 1998 review paper “Scientific status of the Dense Plasma Focus” with 16 authors belonging to 16 nations, whose initiative led to the establishment of the International Center for Dense Magnetized Plasmas (ICDMP) in the year 2000. Its focus is on understanding the principal defining characteristic features of the plasma focus in the light of the developments that have taken place in the last 20 years, in terms of new facilities, diagnostics, models, and insights. Although it is too soon to proclaim with certainty what the plasma focus phenomenon is, the results available to date conclusively indicate what it is demonstrably not. The review looks at the experimental data, cross-correlated across multiple diagnostics and multiple devices, to delineate the contours of an emerging narrative that is fascinatingly different from the standard narrative, which has guided the consensus in the plasma focus community for several decades, without invalidating it. It raises a question mark over the Fundamental Premise of Controlled Fusion Research, namely, that any fusion reaction having the character of a beam-target process must necessarily be more inefficient than a thermonuclear process with a confined thermal plasma at a suitably high temperature. Open questions that need attention of researchers are highlighted. A future course of action is suggested that individual plasma focus laboratories could adopt in order to positively influence the future growth of research in this field, to the general benefit of not only the controlled fusion research community but also the world at large.
We introduce a general class of generating functionals for the calculation of quantum-mechanical expectation values of arbitrary functionals of fluctuating paths with fixed end points in configuration or momentum space. The generating functionals are calculated explicitly for harmonic oscillators with time-dependent frequency, and used to derive a smearing formulas for correlation functions of polynomial and nonpolynomials functions of time-dependent positions and momenta. These formulas summarize the effect of thermal and quantum fluctuations, and serve to derive generalized Wick rules and Feyn-man diagrams for perturbation expansions of nonpolynomial interactions.
A broad class of (N+1) -species ratio-dependent predator-prey stochastic models, which consist of one predator population and N prey populations, is considered. The effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise. In the framework of the mean-field theory, approximate self-consistency equations for prey-populations mean density and for predator-population density are derived (to the first order in the noise variance). In some cases, the mean field exhibits Hopf bifurcations as a function of noise correlation time. The corresponding transitions are found to be reentrant, e.g., the periodic orbit appears above a critical value of the noise correlation time, but disappears again at a higher value of the noise correlation time. The nonmonotonous dependence of the critical control parameter on the noise correlation time is found, and the conditions for the occurrence of Hopf bifurcations are presented. Our results provide a possible scenario for environmental-fluctuations-induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature.
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