Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons

A nonlinear theory is constructed that describes steady-state ion-acoustic waves in an ideal plasma in which the electron component is a degenerate Fermi gas and the ion component is a classical gas. The parameter ranges in which such a plasma can exist are determined, and dispersion relations for ion-acoustic waves are obtained that make it possible to find the linear ion-acoustic velocity. Analytic gas-dynamic models of ion sound are developed for a plasma with the ion component as a cold, an isothermal, or an adiabatic gas, and moreover, the solutions to the equations of all the models are brought to a quadrature form. Profiles of a subsonic periodic and a supersonic solitary wave are calculated, and the upper critical Mach numbers of a solitary wave are determined. For a plasma with cold ions, the critical Mach number is expressed by an explicit exact formula.     

Nonlinear ion acoustic waves in a quantum degenerate warm plasma with dust grains

A study is made of the propagation of ion acoustic waves in a collisionless unmagnetized dusty plasma containing degenerate ion and electron gases at nonzero temperatures. In linear theory, a dispersion relation for isothermal ion acoustic waves is derived and an exact expression for the linear ion acoustic velocity is obtained. The dependence of the linear ion acoustic velocity on the dust density in a plasma is calculated. An analysis of the dispersion relation reveals parameter ranges in which the problem has soliton solutions. In nonlinear theory, an exact solution to the basic equations is found and examined. The analysis is carried out by Bernoulli’s pseudopotential method. The ranges of the phase velocities of periodic ion acoustic waves and the velocities of solitons are determined. It is shown that these ranges do not overlap and that the soliton velocity cannot be lower than the linear ion acoustic velocity. The profiles of the physical quantities in a periodic wave and in a soliton are evaluated, as well as the dependence of the critical velocity of solitons on the dust density in a plasma.     

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.     

Nonlinear theory of ion-acoustic waves in an electron-positron-ion plasma

An analytical nonlinear gasdynamic theory of ion-acoustic waves in an e-p-i plasma is developed for the case in which all the plasma components in the wave undergo polytropic compression and rarefaction. An exact solution to the basic equations is found and analyzed by the Bernoulli pseudopotential method. The parameter range in which periodic waves can propagate and the range in which solitary waves (solitons) exist are determined. It is shown that the propagation velocity of a solitary is always higher than the linear ion sound velocity. The profiles of all the physical quantities in both subsonic and supersonic waves are calculated. The results obtained agree well with both the data from other papers and particular limiting cases.     

On the minimal set of plasma parameters to determine the dispersion law of electron whistler waves

The minimal sufficient set of plasma parameters is presented to describe the dispersion properties of electron whistler waves (helicons) in a wide frequency range above the ion cutoff frequency, provided that the wave frequency is significantly lower than the electron plasma frequency. When the gyrofrequency of the lightest ions is much higher than those of heavier ions, it is sufficient to know the relative content of the lightest ions, the highest ion cutoff frequency, the lower hybrid resonance frequency, and the electron gyro- and plasma frequencies. In this case, the frequency of electron whistler waves is determined by the upper root of the biquadratic equation derived, whereas the lower root corresponds to a resonant mode with its refractive index increasing when the frequency tends toward the highest ion gyrofrequency from below. The developed approach is also efficient in plasmas containing a substantial amount of negative ions and/or heavy dust particulates. The accuracy of the approximate solution of the total cold plasma dispersion relation is illustrated graphically.     

Theory of the ICR heating of a plasma column: Methodological note

A set of wave equations is derived that describes electromagnetic waves at frequencies on the order of the ion gyrofrequency in a plasma column with an arbitrary electron temperature. This set takes into account, in particular, the resonant interaction of electrons with waves in the transit-time magnetic pumping regime. The effect of the amplification of the electromagnetic fields of current-carrying antennas by the plasma is analyzed. The evolution of the fields with an increase of plasma density from a zero value (vacuum) is considered. The main parameters are determined for minority ion cyclotron resonance heating in the planned EPSILON system.     

ECE measurements via B-X-O mode conversion: A proposal to diagnose the q profile in spherical tokamaks

Generation of electron Bernstein waves by the ordinary-extraordinary-Bernstein (O-X-B) mode conversion process has been successfully demonstrated on W7-AS. According to Kirchoff’s law, the inverse process of plasma EC emission by B-X-O mode conversion at particular angles must take place in tokamak plasmas. The optical depth at electron cyclotron harmonics is generally very high for electron Bernstein waves in tokamak plasmas. Consequently the O-mode ECE spectrum measured below the plasma frequency will show steps in the emitted power when each EC harmonic coincides with the upper hybrid resonance zone, where the mode conversion occurs, giving a local measurement of the relationship between the total magnetic field and plasma density. In a spherical tokamak, there are several EC harmonics below the plasma frequency, so several such steps can be observed via the B-X-O mode conversion mechanism. This is a very promising way to get information about the q profile in ST plasmas.     

Nonlinear ion flux caused by a periodic ion-acoustic wave in plasma with two-temperature electrons

The propagation of periodic ion-acoustic waves in plasma with two-temperature electrons and cold ions is analyzed. The equations for the wave potential are derived in the first- and second-orders of the perturbation theory, and their nonsecular periodic solutions are obtained. The average nonlinear ion flux is determined, and its properties are studied as functions of the ratios between the densities and temperatures of the cold and hot electron components. The conditions are analyzed under which the ion flux is co- or counter-directed to the wave propagation direction. For the case in which, depending on the plasma parameters, the ion flux at a given wave amplitude can be either positive or negative, the domains of existence of positive and negative ion fluxes in the “temperature ratio-density ratio” plane are determined.     

Threshold Energy Density of Lower Hybrid Waves in the Freja Experiment

Data from the Freja satellite experiment on the lower hybrid turbulence in the Earth’s magnetosphere are analyzed. It is shown that the observed threshold energy density of lower hybrid waves required for the excitation of localized wave packets is in good agreement with theoretical predictions.     

Flutter in collapsible tubes: a theoretical model of wheezes

A mathematical analysis of flow through a flexible channel is examined as a model of flow-induced flutter oscillations that pertain to the production of wheezing breath sounds. The model provides predictions for the critical fluid speed that will initiate flutter waves of the wall, as well as their frequency and wavelength. The mathematical results are separated into linear theory (small oscillations) and nonlinear theory (larger oscillations). Linear theory determines the onset of the flutter, whereas nonlinear theory determines the relationships between the fluid speed and both the wave amplitudes and frequencies. The linear theory predictions correlate well with data taken at the onset of flutter and flow limitation during experiments of airflow in thick-walled collapsible tubes. The nonlinear theory predictions correlate well with data taken as these flows are forced to higher velocities while keeping the flow rate constant. Particular ranges of the parameters are selected to investigate and discuss the applications to airway flows. According to this theory, the mechanism of generation of wheezes is based in the interactions of fluid forces and friction and wall elastic-restoring forces and damping. In particular, a phase delay between the fluid pressure and wall motion is necessary. The wave speed theory of flow limitation is discussed with respect to the specific data and the flutter model.     

Feasibility of using bernstein modes for current drive in toroidal devices

The feasibility of using Bernstein modes for producing electron cyclotron current drive in toroidal devices is examined. It is shown that the negative role of trapped particles may reduce upon increasing the longitudinal slowing-down factor of waves. Numerical geometrical-optics calculations of the propagation and absorption of waves were performed for the scheme in which radiation is launched from the low-field side as an ordinary wave, linearly converted into an extraordinary wave, and finally converted into Bernstein mode. An analysis is performed for medium-sized toroidal devices. Based on numerical simulation, the parameters determining the efficiency of current drive, namely, the characteristic values of the resonant energies and the longitudinal slowing-down factor of waves in the region where most of the microwave power dissipates, are found.     

Multimode parametric instability during electron cyclotron heating

A study is made of the generation of electron Bernstein waves in the interaction of a microwave field with a magnetized plasma during electron cyclotron heating. Parametric resonance accompanied by simultaneous conversion of microwave-field energy into the energy of numerous waves is analyzed. The relevant dispersion relation is investigated using the Hill method, which has recently been applied for the first time to examine the parametric interaction between high-power microwave radiation and plasmas. It is shown that the dispersion relation can be used to describe the onset of modulational instability at multimode parametric resonance. The growth rate of the modulational instability is obtained. Efficient energy transfer from the microwave field into Bernstein modes and, accordingly, into plasma electrons may be one of the main mechanisms for electron cyclotron resonance plasma heating.     

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

Low-frequency electromagnetic waves propagating perpendicular to the gradients of the density and magnetic field in an inhomogeneous dusty plasma whose mass density is determined primarily by the dust component are analyzed. It is shown that, in analyzing the dispersion properties of inhomogeneous plasma, it is important to take into account the dynamic properties of ions in the vicinity of the dust-ion hybrid resonance. The conditions for the onset of instability of a magnetic drift wave are investigated for different relations between parameters of the inhomogeneity and the value of the Alfvén velocity. The differences from the previous results, as well as possible astrophysical applications, are discussed.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Electromagnetically induced transparency in a magnetized plasma during oblique propagation of radiation

The parametric effect of electromagnetically induced transparency (EIT) is studied in the case of quasi-transverse propagation of an extraordinary wave in the vicinity of the upper hybrid resonance in a cold plasma. The question is investigated of whether the waves that propagate in a smoothly inhomogeneous medium (from the transparency region in the vicinity of the upper hybrid resonance into vacuum or in the opposite direction) can reach the EIT region. The features of the quasi-transverse propagation of an extraordinary wave at the electron cyclotron resonance frequency in the quasi-EIT regime are also considered. It is shown that, in this situation, the parametric effects modify the polarization of the wave, with the result that its absorption increases substantially (by one to two orders of magnitude).     

Effect of parametric resonance on the formation of waves with a broad multiharmonic spectrum during the development of two-stream instability

A cubically nonlinear multiharmonic theory of two-stream instability in a two-velocity relativistic electron beam is constructed with allowance for parametric resonance between harmonics of longitudinal waves of different types, as well as between wave harmonics of the same type. The effect of these two kinds of parametric resonance interaction on the development of two-stream instability is investigated. It is shown that parametric resonance between different types of longitudinal waves excited in a two-velocity beam can substantially affect the development of physical processes in the system under study. It is proposed to use parametric resonance between longitudinal waves of different types to form waves with a prescribed broad multiharmonic spectrum.     

Capturing the Dynamics of a Hybrid Multiscale Cancer Model with a Continuum Model

Cancer is a complex disease involving processes at spatial scales from subcellular, like cell signalling, to tissue scale, such as vascular network formation. A number of multiscale models have been developed to study the dynamics that emerge from the coupling between the intracellular, cellular and tissue scales. Here, we develop a continuum partial differential equation model to capture the dynamics of a particular multiscale model (a hybrid cellular automaton with discrete cells, diffusible factors and an explicit vascular network). The purpose is to test under which circumstances such a continuum model gives equivalent predictions to the original multiscale model, in the knowledge that the system details are known, and differences in model results can be explained in terms of model features (rather than unknown experimental confounding factors). The continuum model qualitatively replicates the dynamics from the multiscale model, with certain discrepancies observed owing to the differences in the modelling of certain processes. The continuum model admits travelling wave solutions for normal tissue growth and tumour invasion, with similar behaviour observed in the multiscale model. However, the continuum model enables us to analyse the spatially homogeneous steady states of the system, and hence to analyse these waves in more detail. We show that the tumour microenvironmental effects from the multiscale model mean that tumour invasion exhibits a so-called pushed wave when the carrying capacity for tumour cell proliferation is less than the total cell density at the tumour wave front. These pushed waves of tumour invasion propagate by triggering apoptosis of normal cells at the wave front. Otherwise, numerical evidence suggests that the wave speed can be predicted from linear analysis about the normal tissue steady state.     

Nonlinear broadband doubling of the extraordinary wave frequency in inhomogeneous magnetoactive plasma

The nonlinear resonance doubling of radio wave frequencies in inhomogeneous plasma is studied as applied to the ionosphere under the conditions of the phase synchronism between an extraordinary pump wave and its second harmonic. The synchronism is not related to plasma resonances, but is determined by the magnetic field and plasma electron density in the transparency region. The generation efficiency of the second harmonic of a transversely propagating wave is calculated for a wide frequency band lying higher than the lower hybrid resonance frequency. It is shown that this effect is physically analogous to the generation of the second harmonic of laser radiation in a nonlinear crystal. The generation efficiency of the second harmonic is determined for inhomogeneous ionospheric plasma in which the synchronism condition is satisfied in a limited frequency range. It is shown that this effect can be used for remote nonlinear diagnostics of the upper ionospheric plasma, in which the characteristic size of the synchronism region can reach several kilometers. It is proposed to use a combination of satellite and ground-based ion probes in experiments on transionospheric probing. Even if the frequency of the wave emitted from the satellite is lower than the critical frequency in the ionosphere, the frequency of its second harmonic can exceed the critical frequency, so that it can be recorded by a ground-based ion probe or a specially designed receiver. The reflected second-harmonic signal can also be detected at the satellite by using a broadband radio-frequency spectrometer.     

Resonance oscillations in the human arterial system]

The paper summarizes the results of the experiments aimed at obtaining sphygmograms of peripheral and carotid arteries with due regard to the values of longitudinal dimensions of body and extremities in healthy subjects. Mathematical equations expressing the fact that dicrotic waves recorded on sphygmograms are the reflections of blood eigentones coinciding with resonance oscillations have been derived. It is proved that at least two partial vibration systems oscillating with different own frequencies are present in human arteries. Conditions under which the resonance of constituent frequencies of pulsatile pressure waves and output waves in arteries occurs have been determined. From this point of view a new explanation for the well-known phenomenon of the pulsatile wave amplitude increase from the heart towards peripheric regions is proposed.