Electromagnetic plasma acceleration in an inverse Z-pinch geometry

Results are presented from experimental studies of the electromagnetic acceleration of a hydrogen or deuterium plasma in an inverse Z-pinch geometry. The acceleration dynamics of the plasma shell was simulated in a zero-dimensional model and was measured with magnetic probes. The ion energy spectrum in the plasma flow was determined with the help of ion collectors by the time-of-flight technique.     

Dynamics of an Al wire corona of a megaampere Z-pinch

It is shown that the development of instabilities in a Z-pinch plasma formed by loading a relatively thick Al wire (an initial diameter of 120 μm and a maximum discharge current of 2–3 MA) is slowed down due to the high plasma density in the wire corona. A cylindrically symmetric, regular, and stable corona surrounding the wire contains a helical formation with a dense, cold, and magnetized plasma. X-ray pulses with a photon energy of several keV and an FWHM duration of 10–20 ns are generated by a few imploded neck structures in the pinch phase of the corona evolution (70–100 ns after the current onset). The main part of X radiation emitted by individual bright spots in the photon energy range 1.5–2.4 keV (up to 40 J at a peak power of 4 GW) consists of the continuum and the bound-bound transition radiation from H-and He-like Al ions. A possible scenario for the axial magnetic field evolution during an X-ray pulse is outlined. __________ Translated from Fizika Plazmy, Vol. 28, No. 4, 2002, pp. 329–336. Original Russian Text Copyright ? 2002 by Kubeš, Renner, Krousky, Kravárik, Bakshaev, Blinov, Chernenko, Gordeev, Dan’ko, Korolev, Shashkov.     

The truthful signalling hypothesis: an explicit general equilibrium model

In mating competition, the truthful signalling hypothesis (TSH), sometimes known as the handicap principle, asserts that higher-quality males signal while lower-quality males do not (or else emit smaller signals). Also, the signals are "believed", that is, females mate preferentially with higher-signalling males. Our analysis employs specific functional forms to generate analytic solutions and numerical simulations that illuminate the conditions needed to validate the TSH. Analytic innovations include: (1) A Mating Success Function indicates how female mating choices respond to higher and lower signalling levels. (2) A congestion function rules out corner solutions in which females would mate exclusively with higher-quality males. (3) A Malthusian condition determines equilibrium population size as related to per-capita resource availability. Equilibria validating the TSH are achieved over a wide range of parameters, though not universally. For TSH equilibria it is not strictly necessary that the high-quality males have an advantage in terms of lower per-unit signalling costs, but a cost difference in favor of the low-quality males cannot be too great if a TSH equilibrium is to persist. And although the literature has paid less attention to these points, TSH equilibria may also fail if: the quality disparity among males is too great, or the proportion of high-quality males in the population is too large, or if the congestion effect is too weak. Signalling being unprofitable in aggregate, it can take off from a no-signalling equilibrium only if the trait used for signalling is not initially a handicap, but instead is functionally useful at low levels. Selection for this trait sets in motion a bandwagon, whereby the initially useful indicator is pushed by male-male competition into the domain where it does indeed become a handicap.     

Nonquasineutral relativistic current filaments and their X-ray emission

Nonquasineutral electron current filaments with the azimuthal magnetic field are considered that arise due to the generation of electron vorticity in the initial (dissipative) stage of evolution of a current-carrying plasma, when the Hall number is small (σB/en _e c ? 1) because of the low values of the plasma conductivity and magnetic field strength. Equilibrium filamentary structures with both zero and nonzero net currents are considered. Structures with a zero net current type form on time scales of t < t _sk = (r ₀ω _pe /c)² t _st, where t _sk is the skin time, t _st is the typical time of electron-ion collisions, and r ₀ is the radius of the filament. It is shown that, in nonquasineutral filaments in which the current is carried by electrons drifting in the crossed electric (E _r ) and magnetic (B _θ) fields, ultrarelativistic electron beams on the typical charge-separation scale r _B = B/(4πen _e ) (the so-called magnetic Debye radius) can be generated. It is found that, for comparable electron currents, the characteristic electron energy in filaments with a nonzero net current is significantly lower than that in zero-net-current filaments that form on typical time scales of t < t _sk. This is because, in the latter type of filaments, the oppositely directed electron currents repel one another; as a result, both the density and velocity of electrons increase near the filament axis, where the velocities of relativistic electrons are maximum. Filaments with a zero net current can emit X rays with photon energies ? ω up to 10 MeV. The electron velocity distributions in filaments, the X-ray emission spectra, and the total X-ray yield per unit filament length are calculated as functions of the current and the electron number density in the filament. Analytical estimates of the characteristic lifetime of a radiating filament and the typical size of the radiating region as functions of the plasma density are obtained. The results of calculations are compared with the available experimental data.     

Nonquasineutral current equilibria as elementary structures of plasma dynamics

A study is made of the fundamental features of current filaments with a nonzero electron vorticity Ω _e ≡ B − (c/e) ▿ × p _ee ≠ 0 and the corresponding Lagrangian invariant I _e . Such current structures can exist on spatial scales of up to ω _pi ⁻¹. It is shown that the dissipative stage of the plasma evolution and the violation of Thomson’s theorem on vorticity conservation in an electron fluid are of fundamental importance for the onset of electron current structures. A key role of the screening of electric and magnetic fields at distances on the order of the magnetic Debye radius r _B = B/(4πen _e )—the main property of such current structures in a Hall medium with σB/(en _e c) ≫ 1—is stressed. Since the minimum size of a vortex structure is the London length c/ω _pe , the structures under consideration correspond to the condition r _B > c/ω _pe or B ² > 4πn _e m _e c ², which leads to strong charge separation in the filament and relativistic electron drift. It is demonstrated that the specific energy content in current structures is high at a filament current of 10–15 kA: from 100 J/cm³ at a plasma density of 10¹⁴ cm⁻³ (the parameters of a lightning leader) to 10⁷ J/cm³ for a fully ionized atmospheric-pressure air. Estimates are presented showing that the Earth’s ionosphere, circumsolar space, and interstellar space are all Hall media in which current vortex structures can occur. A localized cylindrical equilibrium with a magnetic field reversal is constructed—an equilibrium that correlates with the magnetic structures observed in intergalactic space. It is shown that a magnetized plasma can be studied by using evolutionary equations for the electron and ion Lagrangian invariants I _e and I _i . An investigation is carried out of the evolution of a current-carrying plasma in a cylinder with a strong external magnetic field and with a longitudinal electron current turned on in the initial stage—an object that can serve as the simplest electrodynamic model of a tokamak. In this case, it is assumed that the plasma conductivity is low in the initial stage and then increases substantially with time. Based on the conservation of the integral momentum of the charged particles and electromagnetic field in a plasma cylinder within a perfectly conducting wall impenetrable by particles, arguments are presented in support of the generation of a radial electric field in a plasma cylinder and the production of drift ion fluxes along the cylinder axis. A hypothesis is proposed that the ionized intergalactic gas expands under the action of electromagnetic forces.     

A model of the sex ratio in flying ants with an unexpected equilibrium and an expected ESS

A model of an ant population is presented in which each colony has one queen and one worker. The worker then rears to adulthood one reproductive individual and has complete control of its sex. If a stable polymorphism is allowed to occur between two alleles, one causing the worker to rear a male, the other causing the worker to rear a female, then the sex ratio at equilibrium will be different from the three females to one male predicted by Trivers and Hare. However, if a rare mutant is introduced whose homozygous worker has a $\text{3}\text{4}$; probability of producing a female reproductive (and a $\text{1}\text{4}$ probability of producing a male reproductive), then the sex ratio will equilibrate at three females to one male as the new mutant goes to fixation. Several details related to this observation are discussed.     

General equilibrium of an ecosystem

Ecosystems and economies are inextricably linked: ecosystem models and economic models are not linked. Consequently, using either type of model to design policies for preserving ecosystems or improving economic performance omits important information. Improved policies would follow from a model that links the systems and accounts for the mutual feedbacks by recognizing how key ecosystem variables influence key economic variables, and vice versa. Because general equilibrium economic models already are widely used for policy making, the approach used here is to develop a general equilibrium ecosystem model which captures salient biological functions and which can be integrated with extant economic models. In the ecosystem model, each organism is assumed to be a net energy maximizer that must exert energy to capture biomass from other organisms. The exerted energies are the "prices" that are paid to biomass, and each organism takes the prices as signals over which it has no control. The maximization problem yields the organism's demand for and supply of biomass to other organisms as functions of the prices. The demands and supplies for each biomass are aggregated over all organisms in each species which establishes biomass markets wherein biomass prices are determined. A short-run equilibrium is established when all organisms are maximizing and demand equals supply in every biomass market. If a species exhibits positive (negative) net energy in equilibrium, its population increases (decreases) and a new equilibrium follows. The demand and supply forces in the biomass markets drive each species toward zero stored energy and a long-run equilibrium. Population adjustments are not based on typical Lotka-Volterra differential equations in which one entire population adjusts to another entire population thereby masking organism behavior; instead, individual organism behavior is central to population adjustments. Numerical simulations use a marine food web in Alaska to illustrate the model and to show several simultaneous predator/prey relationships, prey switching by the top predator, and energy flows through the web.     

Mutational equilibrium model of genome size evolution

The paper describes a mutational equilibrium model of genome size evolution. This model is different from both adaptive and junk DNA models of genome size evolution in that it does not assume that genome size is maintained either by positive or stabilizing selection for the optimum genome size (as in adaptive theories) or by purifying selection against too much junk DNA (as in junk DNA theories). Instead the genome size is suggested to evolve until the loss of DNA through more frequent small deletions is equal to the rate of DNA gain through more frequent long insertions. The empirical basis for this theory is the finding of a strong correlation and of a clear power-function relationship between the rate of mutational DNA loss (per bp) through small deletions and genome size in animals. Genome size scales as a negative 1.3 power function of the deletion rate per nucleotide. Such a relationship is not predicted by either adaptive or junk DNA theories. However, if genome size is maintained at equilibrium by the balance of mutational forces, this empirilical relationship can be readily accommodated. Within this framework, this finding would imply that the rate of DNA gain through large insertions scales up a quarter-power function of genome size. On this view, as genome size grows, the rate of growth through large insertions is increasing as a quarter power function of genome size and the rate of DNA loss through small deletions increases linearly, until eventually, at the stable equilibrium genome size value, rates of growth and loss equal each other. The current data also suggest that the long-term variation is genome size in animals is brought about to a significant extent by changes in the intrinsic rates of DNA loss through small deletions. Both the origin of mutational biases and the adaptive consequences of such a mode of evolution of genome size are discussed.     

Ventricle equilibrium position in healthy and normal pressure hydrocephalus brains using an analytical model

The driving force that causes enlargement of the ventricles remains unclear in case of normal pressure hydrocephalus (NPH). Both healthy and NPH brain conditions are characterized by a low transparenchymal pressure drop, typically 1 mm Hg. The present paper proposes an analytical model for normal and NPH brains using Darcy's and Biot's equations and simplifying the brain geometry to a hollow sphere with an internal and external radius. Self-consistent solutions for the large deformation problem that is associated with large ventricle dilation are presented and the notion of equilibrium or stable ventricle position is highlighted for both healthy and NPH conditions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and it is shown that both CSF seepage through the ependyma and parenchymal permeability play a key role. Although very simple, the present model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions.     

On the spectrum of Z-pinch plasma neutrons

Generation of neutrons from Z-pinch discharges in a deuterated gas medium has been studied. It is shown that a power-law energy dependence of the number of high-energy deuterons in Z-pinch plasma explains the observed broadening of the neutron spectrum in these systems. It is established that, at an average ion energy below 3 keV in Z-pinch plasma, neutrons are mostly generated due to the interaction of high-energy (∼100-keV) deuterons with the main plasma components.     

The range of time delay and the global stability of the equilibrium for an IVGTT model

Diabetes mellitus has become a prevalent disease in the world. Diagnostic protocol for the onset of diabetes mellitus is the initial step in the treatments. The intravenous glucose tolerance test (IVGTT) has been considered as the most accurate method to determine the insulin sensitivity and glucose effectiveness. It is well known that there exists a time delay in insulin secretion stimulated by the elevated glucose concentration level. However, the range of the length of the delay in the existing IVGTT models are not fully discussed and thus in many cases the time delay may be assigned to a value out of its reasonable range. In addition, several attempts had been made to determine when the unique equilibrium point is globally asymptotically stable. However, all these conditions are delay-independent. In this paper, we discuss the range of the time delay and provide easy-to-check delay-dependent conditions for the global asymptotic stability of the equilibrium point for a recent IVGTT model through Liapunov function approach. Estimates of the upper bound of the delay for global stability are given in corollaries. In addition, the numerical simulation in this paper is fully incorporated with functional initial conditions, which is natural and more appropriate in delay differential equation systems.     

Measurements of neutron emission from a Z-pinch constriction

Results are presented from measurements of neutron emission generated during discharges with current amplitudes of up to 3 MA and a current rise time of ～100 ns through profiled loads 10 mm in height and 4–5 mm in diameter. The experiments were performed with the S-300 eight-module high-power generator. To enhance the effect of energy accumulation, a≤1-mm-diameter neck was made in the central region of the load. An agar-agar foam of mass density 0.1 g/cm³ with an additive of deuterated polyethylene was used as a plasma-forming material. The formation of a hot plasma in the Z-pinch constriction was accompanied by the emission of soft X-ray (E = 1–10 keV), hard X-ray (E ≥ 30 keV), and neutron pulses with a minimum pulse duration of ≤10 ns. The neutron energy measured by the time-of-flight technique in three directions relative to the load axis (0°, 90°, and 180°) was found to be 2.5 ± 0.3 MeV, which corresponds to the dd reaction. The total neutral yield during the development of one constriction with a characteristic size of 100 μm attained 10⁸ neutrons per pulse.     

Predator-mediated coexistence: an equilibrium interpretation

I have constructed a spatially distributed analytical model of predators, superior prey competitors, and inferior prey competitors, based on the limiting deterministic version of a simulation model by Caswell (1978). Persistence regions for the three populations are mapped in parameter space. Conceptually shrinking the system from infinite size (i.e. infinitely many spatial “cells”) to some finite size introduces demographic stochasticity, increasing the chance of extinction of one or more populations within a given time interval. But some of the finite (stochastic) system's behavior, such as any tendency to damp perturbations, can be related to the behavior of the deterministic system at the same location in parameter space.     

Spin-state equilibrium in the model complexes of azide hemoprotein

Addition of NaN3 to ferric protohemin biscoordinated with 1-methylimidazole (1-MeIm) or 2-methylimidazole (2-MeIm) in (CH3)2SO resulted in sizeable visible absorption changes, corresponding to the formation of the mixed ligand complexes, hemin X N-3 X 1-MeIm and hemin X N-3 X 2-MeIm. The visible absorption spectrum of the 1-MeIm complex was closely similar to those of azide hemoproteins, while the 2-MeIm derivative exhibited intensified 500 and 625 nm bands and depressed 540 and 570 nm peaks. The iron-bound N-3 of the model complexes exhibited two infrared stretching bands, which were assigned to the high- and low-spin peaks. The intensity of the high-spin infrared peaks increased at higher temperature. From the analyses of the infrared spectral changes, the thermodynamic values of the thermal spin equilibria were determined to be delta H = -3920 cal/mol and delta S = -11.1 e.u. for hemin X N-3 X 1-MeIm and delta H = -2150 cal/mol and delta S = 7.9 e.u. for hemin X N-3 X 2-MeIm. The thermodynamic values of the 1-MeIm complex are similar to the reported values for azide metmyoglobin, suggesting that the contribution from the nonbonded porphyrin-globin contacts to the spin equilibrium is small in azide metmyoglobin. Comparison of the delta H and delta S values among model systems indicates that delta H and delta S compensation similar to that observed in hemoprotein also holds in the models. This may suggest an underlying common denominator for the spin-equilibrium mechanisms in hemins and hemoproteins.     

Theoretical model for the equilibrium behavior of DNA superhelices

A statistical-mechanical model for superhelical DNA is presented. The partition function for a DNA superhelix is written by using a combinatorial approach in order to allow for the known relation between the number of superhelical twists and the states of the base pairs in the double helix. While the theory allows any factors which might contribute to the free energy of superhelical twisting to be included in the statistical weights of the superhelical twists, only the reduction in configurational entropy is considered in this paper. Similarities between an imperfectly matched DNA double helix and a DNA superhelix are used in the derivation of expressions for the entropy of superhelical DNA. Although the partition function is presented in a general form, permitting many equilibrium properties of DNA superhelices to be treated, the application considered in this paper is the calculation of helix–coil transition curves. Several experimentally observed features of such transitions are predicted. For example, the curves are bimodal, with an early and a late transition relative to that of a nicked molecule. The results are very sensitive to the volume within which two parts of the double helix must meet when forming a superhelical twist. The free energy of superhelix formation is calculated, and the results are compared with those obtained from the data of Bauer and Vinograd for ethidium bromide intercalation. In the present model, the free energy increases less sharply with an increase in the number of superhelical twists than observed experimentally, indicating that factors other than configurational entropy probably make important contributions to the free energy of superhelix formation.     

Multichannel vacuum arc discharge used for Z-pinch formation

Results are presented from experimental studies of the implosion dynamics and radiative characteristics of an aluminum Z-pinch formed from a plasma shell (PS). The PS with an initial diameter of 4 cm was produced with the help of a multichannel vacuum arc discharge and formed due to the evaporation of the electrode material in ten parallel arc discharges. The PS composition depended on the electrode material in the arc discharge. The described experiments were performed with aluminum electrodes. The total arc current was 80 kA. The PS implosion was provided by an IMRI-5 high-current generator with a current amplitude of 450 kA and rise time of 500 ns. The PS implosion resulted in the formation of a 0.2-cm-diameter plasma column with an electron temperature of 700?C900 eV and average ion density of (5?C8) × 10¹⁷ cm^?3. The maximum radiation power per unit length in aluminum K-lines reached 300 MW/cm, the duration of the radiation pulse being 20 ns.