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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We present an alternative method for constructing the exact and approximate solutions of electromagnetic wave equations whose source terms are arbitrary order multipoles on a curved spacetime. The developed method is based on the higher-order Green's functions for wave equations which are defined as distributions that satisfy wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. The constructed solution is applied to the study of various geometric effects on the generation and propagation of electromagnetic wave tails to first order in the Riemann tensor. Generally the received radiation tail occurs after a time delay which represents geometrical backscattering by the central gravitational source. It is shown that for an arbitrary weak gravitational field it is valid that the truly nonlocal wave-propagation correction (the tail term) has a universal form which is independent of multipole structure of the gravitational source. In a particular case when the electromagnetic radiation pulse is generated by the wave source during a finite time interval, the structure of the wave tail at the time after the direct pulse has passed the gravitational source is in the first approximation independent of the higher multipole moments of the source of

Higher-order fundamental solutions are defined as the distributions that satisfy the wave equations with inhomogeneous terms which are point distributions of the corresponding order. Starting from the Hadamard fundamental solution, the construction of the local higherorder fundamental solutions of the covariant scalar wave equation on a causal domain is considered. A simple recurrent algorithm for calculating such solutions is found.

Complete recurrent algorithms for calculating the higher-order fundamental solutions of covariant linear wave equations for scalar and tensor wave fields on an arbitrary curved spacetime are derived. The higher-order fundamental solutions are the distributions that satisfy the wave equations with the corresponding order covariant derivatives of the Dirac delta function as the source terms. Like the classical Green's function for a scalar wave equation, the higher-order fundamental solutions contain the terms which have support on, and only on, the lightcone as well as tail terms which have support inside the lightcone. With the help of the higher-order fundamental solutions found it is possible to compute the exact multipole solutions of wave equations in a form convenient for practical computations. As applications we consider the exact field of a dipole source of variable strength travelling in an arbitrary curved spacetime and the tail term of scalar multipole waves in the Friedman dust-dominated universe for the case of minimal coupling.