Suppression of the current instability by decay processes

A study is made of the instability of lower hybrid waves in an isothermal magnetized current-carrying plasma. It is assumed that the dynamic suppression of the current instability is associated with the excitation of a quasi-monochromatic wave near the instability threshold and its subsequent decay into two strongly damped lower hybrid waves. It is shown that the decay process results in the onset of either a quasi-periodic or stochastic nonlinear stabilization regime involving a small number of modes. The anomalous resistance is estimated.     

Generation of ion-acoustic and magnetoacoustic waves in an RF helicon discharge

A study is made of the generation of ion-acoustic and magnetoacoustic waves in a discharge excited in an external magnetic field by an electromagnetic wave in the whistler frequency range (ω_LH ? ω ? ω_He, where ω_LH = $\sqrt {\omega _{He} \omega _{Hi} } $ and ω_He and ω_Hi are the electron and ion gyrofrequencies, respectively). The excitation of acoustic waves is attributed to the decay of a high-frequency hybrid mode forming a plasma waveguide into low-frequency acoustic waves and new high-frequency waves that satisfy both the decay conditions and the waveguide dispersion relations. The excitation of acoustic waves is resonant in character because the conditions for the generation of waveguide modes and for the occurrence of the corresponding nonlinear wave processes should be satisfied simultaneously. An unexpected effect is the generation of magnetoacoustic waves by whistlers. A diagnostic technique is proposed that allows one to determine the thermal electron velocity by analyzing decay conditions and dispersion relations for waves in the discharge channel.     

Nonlinear damping of zonal flows

The modulatonal instability theory for the generation of large-scale (zonal) modes by drift modes has been extended to the second order including the effects of finite amplitude zonal flows, ? _q . The nonlinear (second-order) sidebands are included in the perturbative expansion to derive the nonlinear equation for the evolution of ? _q . It is shown that effects of finite ? _q reduce the growth rate of zonal flow with a possibility of oscillatory regimes at a later stage.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Threshold effects observed in conformation changes induced by electric fields

Single-stranded polynucleotides are used as model systems for the investigation of conformational changes induced by electric fields. It is demonstrated that the single-strand helix–coil transition in poly(A), poly(dA), and poly(C) can be induced by application of high electric fields. The transition is measured by UV absorbance using polarized light at an angle of 54.8° with respect to the vector of the electric field and by electrodichroism. A linear increase of the absorbance, reflecting the helix-to-coil transition, is observed at increasing field strength. When ions are added to the polymer, electric fields do not induce conformation changes, unless a threshold value of the electric field strength E₀ is exceeded. At field strengths above this threshold, the degree of transition is a linear function of the increase in field strength. The threshold values E₀ show a linear increase with the logarithm of the ion concentration. Bivalent ions cause thresholds at much lower ion concentrations than mo-novalent ions. The shielding efficiency of ions is correlated to the binding affinity of these ions to the polymer. The conformation changes induced by the field and the existence of thresholds can be explained on the basis of dissociation field effects. Similar threshold effects may be expected for other macromolecules as well as for membrane structures and may be important in the regulation of bioelectricity.     

Nonlinear dynamics of beam–plasma instability in a finite magnetic field

The nonlinear dynamics of beam–plasma instability in a finite magnetic field is investigated numerically. In particular, it is shown that decay instability can develop. Special attention is paid to the influence of the beam?plasma coupling factor on the spectral characteristics of a plasma relativistic microwave accelerator (PRMA) at different values of the magnetic field. It is shown that two qualitatively different physical regimes take place at two values of the external magnetic field: B ₀ = 4.5 kG (Ω ~ ωB _p ) and 20 kG (Ω _B ? ω_p). For B ₀ = 4.5 kG, close to the actual experimental value, there exists an optimal value of the gap length between the relativistic electron beam and the plasma (and, accordingly, an optimal value of the coupling factor) at which the PRMA output power increases appreciably, while the noise level decreases.     

Analysis of the efficiency of lower hybrid current drive in the FT-2 tokamak

Results are presented from experimental studies of the efficiency of lower hybrid current drive (LHCD) in the FT-2 tokamak. The dependence of the LHCD efficiency on the grill phasing Δφ and RF oscillator power was determined experimentally in a wide range of plasma densities. It is shown that, at high plasma currents (i.e., at sufficiently high electron temperatures), current drive is suppressed when the plasma density reaches its resonance value n _LH for the pumping wave frequency, rather than when parametric decay comes into play (as was observed in regimes with lower plasma currents and, accordingly, lower electron temperatures T _e ). In order to analyze the experimentally observed effect of LHCD and its dependence on the value and sign of the antenna phasing, the spectra of the excited LH waves, P(N _z ), were calculated. Simulations using the FRTC code with allowance for the P(N _z ) spectrum and the measured plasma parameters made it possible to calculate the value and direction of the LH-driven current, which are determined by the spectrum of the excited LH waves. It is shown that the synergetic effect caused by the interaction between different spectral components of the excited RF wave plays a decisive role in the bridging of the gap in the wave spectrum.     

Numerical investigations and analysis on the effects of geometrical parameters on the group velocity of transverse magnetic pump mode and free electron laser instability

In this paper, we have numerically investigated the effects of various geometrical parameters of a backward wave oscillator, filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate R ₀ of a seeded free electron laser. On changing mean radius corrugation amplitude h and corrugation period z ₀ of backward wave oscillator; the ponderomotive potential of space charge wave changes. This in turn, changes the coupling strength of TM mode with negative beam space charge mode and hence the growth rate of parametric instability of free electron laser. A dispersion relation is derived and numerically solved for various geometrical parameters of backward wave oscillator and beam profile. A relation for Γ is also derived and computed numerically. The instability growth scales directly to the square root of beam density and inversely as seven power of relativistic gamma factor γ₀. Published in Russian in Fizika Plazmy, 2009, Vol. 35, No. 2, pp. 179–184. This text was submitted by the authors in English.     

Nonlinear propagation of agonist-induced cytoplasmic calcium waves in single astrocytes

In astrocytes in primary culture, activation of neurotransmitter receptors results in intracellular calcium signals that propagate as waves across the cell. Similar agonist-induced calcium waves have been observed in astrocytes in organotypic cultures in response to synaptic activation. By using primary cultured astrocytes grown on glass coverslips, in conjunction with fluorescence microscopy we have analyzed agonist-induced Ca²⁺ wave initiation and propagation in individual cells. Both norepinephrine and glutamate elicited Ca²⁺ signals which were initiated focally and discretely in one region of the cell, from where the signals spread as waves along the entire length of the cell. Analysis of the wave propagation and the waveform revealed that the propagation was nonlinear with one or more focal loci in the cytoplasm where the wave was regeneratively amplified. These individual loci appear as discrete focal areas 7–15 μm in diameter and having intrinsic oscillatory properties that differ from each other. The wave initiation locus and the different amplification loci remained invariant in space during the course of the experiment and supported an identical spatiotemporal pattern of signalling in any given cell in response to multiple agonist applications and when stimulated with different agonists which are coupled via InsP₃. Cytoplasmic Ca²⁺ concentration at rest was consistently higher (17 ± 4nM, mean ± S.E.M.) in the wave initiation locus compared with the rest of the cytoplam. The nonlinear propagation results from significant changes in signal rise times, amplitudes, and wave velocity in cellular regions of active loci. Analysis of serial slices across the cell revealed that the rise times and amplitudes of local signals were as much as three- to fourfold higher in the loci of amplification. A phenomenon of hierarchy in local amplitudes of the signal in the amplification loci was observed with the wave initiation locus having the smallest and the most distal locus having largest amplitude. By this mechanism locally very high concentrations of Ca²⁺ are achieved in strategic locations in the cell in response to receptor activation. While the average wave velocity calculated over the length of the cell was 10–15 μm/s, in the active loci rates as high as 40 μm/s were measured. Wave velocity was fivefold lower in regions of the cell separating active loci. The differences in the intrinsic oscillatory periods give rise to local Ca²⁺ waves that show the properties of collision and annihilation. It is hypothesized that the wave front provokes regenerative Ca²⁺ release from specialized areas in the cell where the endoplasmic reticulum is endowed with higher density of InsP₃ receptor channels. Thus wave propagation is achieved by a process of diffusion and regenerative Ca²⁺ release in multiple cellular loci provoked by the advancing wave front; in this way, wave propagation is nonlinear and saltatory. Regenerative Ca²⁺ wave propagation from distal atrocytic processes to the cell body and neighboring cells is likely to provide an important signalling mechanism in the nervous system. 1994 John Wiley & Sons, Inc.     

Impact of fear effect on the growth of prey in a predator-prey interaction model

Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r₀ as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r₀. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.     

Estimation of the levels of radiation-induced <Emphasis Type="Italic">P</Emphasis>-element transposition in <Emphasis Type="Italic">Drosophila melanogaster</Emphasis> experimental populations and laboratory strains

When experimental P + M populations were exposed to chronic γ-irradiation (0.31 mGy/h), the highest instability level of the singed-weak (sn _w ) locus was observed in F₃–F₁₀ with a subsequent decrease and stabilization of the mutation rate. The sn ^w mutation rate was within the range of spontaneous variation in conditions of P-M hybrid dysgenesis and irradiation of males of the Harwich laboratory strain with active P elements at 1.61 mGy/h. The instability of the sn ^w locus was significantly higher at lower dose rates (0.23 and 0.31 mGy/h), suggesting a nonlinear dose-effect relationship.     

Phosphate has dual roles in cross-bridge kinetics in rabbit psoas single myofibrils

In this study, we aimed to study the role of inorganic phosphate (P_i) in the production of oscillatory work and cross-bridge (CB) kinetics of striated muscle. We applied small-amplitude sinusoidal length oscillations to rabbit psoas single myofibrils and muscle fibers, and the resulting force responses were analyzed during maximal Ca²⁺ activation (pCa 4.65) at 15°C. Three exponential processes, A, B, and C, were identified from the tension transients, which were studied as functions of P_i concentration ([P_i]). In myofibrils, we found that process C, corresponding to phase 2 of step analysis during isometric contraction, is almost a perfect single exponential function compared with skinned fibers, which exhibit distributed rate constants, as described previously. The [P_i] dependence of the apparent rate constants 2πb and 2πc, and that of isometric tension, was studied to characterize the force generation and P_i release steps in the CB cycle, as well as the inhibitory effect of P_i. In contrast to skinned fibers, P_i does not accumulate in the core of myofibrils, allowing sinusoidal analysis to be performed nearly at [P_i] = 0. Process B disappeared as [P_i] approached 0 mM in myofibrils, indicating the significance of the role of P_i rebinding to CBs in the production of oscillatory work (process B). Our results also suggest that P_i competitively inhibits ATP binding to CBs, with an inhibitory dissociation constant of ∼2.6 mM. Finally, we found that the sinusoidal waveform of tension is mostly distorted by second harmonics and that this distortion is closely correlated with production of oscillatory work, indicating that the mechanism of generating force is intrinsically nonlinear. A nonlinear force generation mechanism suggests that the length-dependent intrinsic rate constant is asymmetric upon stretch and release and that there may be a ratchet mechanism involved in the CB cycle.     

Agonist-induced calcium waves in oscillatory cells: A biological example of Burgers' equation

Oscillations in cytosolic Ca²⁺ concentrations in living cells are often a manifestation of propagating waves of Ca²⁺. Numerical simulations with a realistic model of inositol 1, 4, 5-trisphosphate (IP₃)-induced Ca²⁺ wave trains lead to wave speeds that increase linearly at long times when (a) IP₃ levels are in the range for Ca²⁺ oscillations, (b) a gradient of phase is established by either an initial ramp or pulse of IP₃, and (c) IP₃ concentrations asymptotically become uniform. We explore this phenomenon with analytical and numerical methods using a simple two-variable reduction of the De Young-Keizer model of the IP₃ receptor that includes the influence of Ca²⁺ buffers. For concentrations of IP₃ in the oscillatory regime, numerical solution of the resulting reaction diffusion equations produces nonlinear wave trains that shows the same asymptotic growth of wave speed. Due to buffering, diffusion of Ca²⁺ is quite slow and, as previously noted, these waves occur without appreciable bulk movement of Ca²⁺. Thus, following Neu and Murray, we explore the behavior of these waves using an asymptotic expansion based on the small size of the buffered diffusion constant for Ca²⁺. We find that the gradient in phase of the wave obeys Burgers' equation asymptotically in time. This result is used to explain the linear increase of the wave speed observed in the simulations.     

Measurement of oscillatory flow pressure gradient in an elastic artery model

In vitro experiments were conducted to measure the oscillatory flow pressure gradient along an elastic tube in order to assess the recent nonlinear theory of Wang and Tarbell. According to this theory, in an elastic tube with oscillatory flow, the mean (time-averaged) pressure gradient cannot be calculated using Poiseuille's law. The effect of wall motion creates a nonlinear convective acceleration, and an induced mean pressure gradient is required to balance the convective acceleration. The induced mean pressure gradient depends on the diameter variation over a cycle, the pulsatility and unsteadiness of the flow, and the phase difference between the pressure wave form and the flow wave form. The amplitude of the pressure gradient also depends on these parameters and may deviate significantly from Womersley's rigid tube theory. A flow loop was constructed to produce oscillatory flow in an elastic tube. Flow wave forms were measured with an ultrasonic flow probe, and ultrasonic diameter crystals were used to measure wall movement. A special device for pressure drop measurement was constructed using Millar catheter tip transducers to obtain both forward and backward pressure drops that were then averaged. This averaging method eliminated the static error of the pressure transducers. The pressure-flow phase angle was varied by clamping a distal elastic section at various locations. Pressure gradients were obtained for a range of phase angles between −55 ° and +49 °. The mean and amplitude of the measured pressure gradient were compared to theoretical values. Both positive and negative induced mean pressure gradients were measured over the range of phase angles. The measured pressure gradient amplitudes were always lower than predicted by Womersley's rigid tube theory. The experimental means and amplitudes are in good agreement with the elastic tube theoretical values. Thus, the experiments verify the theory of Wang and Tarbell.     

Kelvin-Helmholtz instability of a cylindrical plasma flow with an arbitrary temperature

The dispersion relation for Kelvin-Helmholtz magnetohydrodynamic instability of a cylindrical plasma flow in a longitudinal magnetic field is studied with allowance for plasma compressibility. Stability of the system in a wide range of plasma parameters is thoroughly analyzed in the incompressible plasma approximation. Using the results obtained, a diagram of the system stability is constructed in terms of the magnetic field and the ratio between the plasma densities in the flow and the ambient space. It is shown by numerically solving the dispersion relation for the case of a compressible plasma that perturbations with scale lengths on the order of the flow diameter and larger can develop even at a zero temperature. For low ion-sound velocities, c _S ²/U ₀² < 0.25, the growth rate of the axisymmetric mode with m = 0 is much smaller than that of non-axisymmetric modes. It is shown that, in an incompressible plasma, the eigenmodes are damped monotonically with distance from the flow. In plasma with a finite temperature, the character of damping is oscillatory; in this case, the lower the plasma temperature, the larger the distance at which the ambient plasma is perturbed.     

Stability of hybrid modes of a single-component electron plasma containing an admixture of background gas ions

The spectrum of eigenmodes of a waveguide completely filled with a cold electron plasma containing a small admixture of ions produced due to electron-impact ionization of background gas atoms is calculated numerically. The calculations were performed within the entire range of allowable values of the radial electric and longitudinal magnetic fields for both magnetized and unmagnetized ions by using the earlier derived nonlocal dispersion relation [Plasma Phys. Rep. 36, 563 (2010)]. The spectrum consists of three families of electron modes with frequencies equal to the Doppler-shifted upper and lower hybrid frequencies and modified ion cyclotron (MIC) modes. When the Doppler shift caused by electron rotation in the crossed electric and magnetic fields compensates for the hybrid frequency, the electron modes become low-frequency modes and interact with the ion modes. For m = 1, only the lower hybrid modes can be low-frequency ones, whereas at m ≥ 2, both lower and upper hybrid modes can be low-frequency ones. The spectrum of modes having the azimuthal number m = 2 is thoroughly analyzed. It is shown that, in this case, the lower hybrid modes behave similar to the m = 1 modes. The dispersion curves of the upper hybrid modes intersect with all harmonics of the MIC frequency (positive, negative, and zero) and are unstable in the vicinities of the intersections. The maximum value of the instability growth rate is several times higher than the ion plasma frequency. The MIC modes are unstable within a wide range of the field strengths, and their growth rates are two orders of magnitude slower. Instabilities are caused by the relative motion of electrons and ions (the transverse current) and the anisotropy of the ion distribution function.     

Nonlinear regimes of Farley-Buneman instability

The dynamic suppression of the instability of a quasi-monochromatic wave by nonlinear wave-wave interaction is considered. It is shown that, near the threshold of linear instability, the process of decay into two strongly damped waves leads to the onset of a quasi-periodic or a stochastic nonlinear stabilization regime involving a small number of modes. A case study is made of the Farley-Buneman instability in an isothermal magnetized current-carrying plasma in which particle collisions play an important role. Typical characteristic features of different stabilization regimes are analyzed as functions of current and other plasma parameters.     

Plasma decay in high-voltage nanosecond discharges in oxygen-containing mixtures

Plasma decay in high-voltage nanosecond discharges in CO₂: O₂ and Ar: O₂ mixtures at room gas temperature and a pressure of 10 Torr is studied experimentally and theoretically. The time dependence of the electron density during plasma decay is measured using microwave interferometry. The time evolution of the charged particle density, ion composition, and electron temperature is simulated numerically. It is shown that, under the given conditions, the discharge plasma is dominated for the most time by O ₂ ⁺ ions and plasma decay is determined by dissociative and three-body electron?ion recombination. As in the previous studies performed for air and oxygen plasmas, agreement between measurements and calculations is achieved only under the assumption that the rate of three-body recombination of molecular ions is much greater than that for atomic ions. The values of the rate constant of three-body recombination of electrons with О₂ ⁺ ions in a wide range of electron temperatures (500–5500 K), as well as for thermal (300 K) electrons, are obtained by processing the experimental results.     

Nonlinear electromagnetic pulse with a superwide frequency bandwidth

A nonlinear equation is derived and its analytic solution describing a soliton-like perturbation propagating at velocity close to the speed of light is found. It is shown that the rate at which the amplitude of a soliton excited by a cold electron beam in a magnetized plasma-filled waveguide grows is proportional to (n _b/n ₀)^1/3, as is the linear growth rate of the beam-plasma instability.