Modeling of reference operating scenario of GOL-NB multiple-mirror trap

Currently, the GOL-NB multiple-mirror trap is being developed at the Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences. The main scientific goal pursued by building GOL-NB is direct demonstration of suppression of longitudinal losses of particles and energy from the trap by using sections with a multiple-mirror magnetic field, which can be attached to the central gas-dynamic trap. Plasma heating in GOL-NB will be accomplished by neutral beam injection with a power of up to 1.5MW. The paper presents the first results of modeling the dynamics of the plasma parameters and fast ions under the reference operating scenario of the trap in which traditional short magnetic mirrors, rather than multiple-mirror sections, are attached to the central trap. In such a configuration, the plasma lifetime in the trap is expected to be minimal. The modeling was performed by using the DOL kinetic code. As a result, the initial conditions of the experiments are refined and the requirements to the system of maintaining the particle balance in the trap are determined.     

Nonstationary kinetic theory of ion transport in plasma with small perturbations

A theory of charged particle transport for small potential perturbations in a fully ionized plasma is developed on the basis of solving a linearized kinetic equation with the Landau collision integral. This theory is free of any constraints on the characteristic time and spatial scales of perturbations. Ion fluxes appropriate for an arbitrary ion-ion collision frequency that can ensure nonlocal space-time transport in the plasma are calculated. The obtained ion transport coefficients are used to calculate the partial contribution of ions to the longitudinal permittivity of collisional plasma. The resulting expression for the plasma permittivity is applicable in the entire range of frequencies and wavenumbers.     

Plasma outflow from a corrugated trap in the kinetic regime

The problem of stationary plasma outflow from an open corrugated trap in the kinetic regime is considered with allowance for pair collisions in the framework of a kinetic equation with the Landau collision integral. The distribution function is studied in the limit of small-scale corrugation and a large mirror ratio. In considering a single corrugation cell, a correction for the distribution function is calculated analytically. An equation describing variations of the distribution function along the system is derived and used to study the problem of plasma outflow into vacuum.     

Formation of a narrow radial density profile of fast ions in the GDT device

The radial density profile of fast ions with a mean energy of 10 keV is measured in experiments with a two-component high-β plasma in the GDT device. Fast ions are produced by injecting neutral beams into a warm plasma. The measured fast-ion density profile is found to be narrower than that calculated with allowance for the neutral beam trapping and Coulomb scattering. Special experiments with a movable limiter have indicated that the formation of a narrow fast-ion density profile in GDT cannot be attributed to the loss of fast ions. Possible mechanisms responsible for this effect are discussed.     

Modeling of Coulomb collisions in a kinetic description of the electron cyclotron resonance plasma heating

The electron distribution function is modeled numerically with allowance for Coulomb collisions and quasilinear effects under cyclotron resonance conditions by solving a two-dimensional kinetic equation containing the quasilinear diffusion operator and the Coulomb collision operator in the Landau form. Two simplified model collision integrals that make it possible to describe electron heating by microwave radiation are considered. The first model collision operator is obtained by introducing the parametric time dependence of the temperature of the background Maxwellian electrons into the linear collision integral. It is shown that the heating of the bulk electrons can be described in a noncontradictory way if the temperature dynamics of the background electrons is calculated from the equation of energy balance, which is governed by the amount of the microwave power absorbed by the resonant electrons with the distribution function modified due to quasilinear effects. This conclusion is confirmed in a more rigorous fashion by comparing the solutions obtained using the first model Coulomb collision integral with those obtained using the second model integral, namely, the nonlinear operator derived by averaging the distribution function of the scattering electrons over pitch angles. The time-dependent linear collision integral is used to obtain analytic solutions describing quasi-steady electron heating with allowance for the quasilinear degradation of microwave power absorption.     

Adiabatic model of field reversal by fast ions in an axisymmetric open trap

A model of field reversal by fast ions has been developed under the assumption of preservation of fast-ion adiabatic invariants. Analytical solutions obtained in the approximation of a narrow fast-ion layer and numerical solutions to the evolutionary problem are presented. The solutions demonstrate the process of formation of a field reversed configuration with parameters close to those of the planned experiment.     

Iterative algorithms for processing experimental data

The need to solve linear and nonlinear integral equations arise, e.g., in recovering plasma parameters from the data of multichannel diagnostics. The paper presents an iterative method for solving integral equations with a singularity at the upper limit of integration. The method consists in constructing successive approximations and calculating the integral by quadrature formulas in each integration interval. An example of application of the iterative algorithm to numerically solve an integral equation similar to those arising in recovering the plasma density profile from reflectometry data is presented.     

Kinetic Theory Model for Ion Movement through Biological Membranes: I. Field-Dependent Conductances in the Presence of Solution Symmetry

A model for ion movement through specialized sites in the plasma membrane is presented and analyzed using techniques from nonequilibrium kinetic theory. It is assumed that ions traversing these specialized regions interact with membrane molecules through central conservative forces. The membrane molecules are approximated as massive spherical scattering centers so that ionic fractional energy losses per collision are much less than one. Equations for steady-state membrane ionic currents and conductances as functions of externally applied electric field strength are derived and numerically analyzed, under the restriction of identical solutions on each size of the membrane and constant electric fields within the membrane. The analysis is carried through for a number of idealized ion-membrane molecule central force interactions. For any interaction leading to a velocity-dependent ion-membrane molecule collision frequency, the membrane chord conductance is a function of the externally applied electric field. Interactions leading to a collision frequency that is an increasing (decreasing) function of ionic velocity are characterized by chord conductances that are decreasing (increasing) functions of field strength. For ion-neutral molecule interactions, the conductance is such a rapidly decreasing function of field strength that the slope conductance becomes negative for all field strengths above a certain value.     

Numerical modeling of the formation of steady-state nonequilibrium distributions of particles interacting through a power-law potential

The formation of a steady-state nonequilibrium distribution function of particles interacting through the repulsive potential U ~ α/r ^β(1≤β≤4), which operates at an infinite range, is studied numerically. The collisional particle dynamics in such a system is investigated using a spatially homogeneous nonlinear collision integral in the Landau-Fokker-Planck form, which is a model Boltzmann collision integral for arbitrary potentials of interaction accompanied by little momentum transfer between particles in collisions. Numerical modeling is based on completely conservative difference schemes. It is shown that the principal condition for the existence of steady-state nonequilibrium distributions is the presence of a particle or an energy flux oriented in the proper manner in momentum space. A steady-state local distribution exists inside the momentum interval between the energy source and sink and has the form of a gradually decreasing function. Since a radical change in the distribution function under nonequilibrium conditions leads to an anomalous enhancement of the conduction of a medium and its emission characteristics, the results obtained can be used, e.g., to predict the behavior of semiconductors with an intrinsic or extrinsic conductivity under the action of particle fluxes or electromagnetic radiation.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Generation of dense multicharged ion flows from an ECR plasma confined in a quasi-gas-dynamic magnetic cusp trap

The possibility of generating dense multicharged ion beams with a current density as high as ～1 A/cm² from an ECR plasma confined in a quasi-gas-dynamic cusp trap is studied both theoretically and experimentally. The most important advantages of this type of ion source are that the plasma in the cusp is stabile against MHD perturbations and that a trap intended to operate at fairly high pump-field frequencies (above 30 GHz) is relatively inexpensive. A theoretical model of confinement of a high-density nonequilibrium ECR plasma (T _e ? T _i ) in an open magnetic trap is proposed and results are presented from model experiments with an ～30-cm-long cusp trap (here, by the cusp length is meant the volume of a paraxial magnetic tube divided by the area of its cross sections in magnetic mirrors) pumped by a pulsed microwave field with a frequency of 37.5 GHz and power of 100 kW. The possibility of achieving a quasi-gas-dynamic regime of plasma confinement of an ECR plasma in a cusp trap is demonstrated. Ion beams with a average ion charge number of 2–4 (depending on the sort of working gas) and current densities unprecedented for ECR sources are obtained. Good agreement between theoretical and experimental results makes it possible to reliably predict the ion beam parameters that can be achieved at even higher microwave frequencies.     

Transverse and longitudinal permittivities of a gaseous plasma with an electron collision frequency proportional to the electron velocity

The transverse and longitudinal plasma permittivities, ?^tr and ? ^l , are analyzed for the case where the electron collision frequency in the Bhatnagar-Gross-Krook collision integral is proportional to the absolute value of the electron velocity. It is found that, in both the low-and high-frequency limits, the expressions for ?^tr and ? ^l derived for the case of a variable electron collision frequency coincide with the classical formulas obtained under the assumption of a constant collision frequency, whereas for frequencies close to the electron collision frequency, these expressions differ significantly from the classical ones.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Development of Left Ventricular Longitudinal Speckle Tracking Echocardiography in Very Low Birth Weight Infants with and without Bronchopulmonary Dysplasia during the Neonatal Period

Objectives

In preterm infants, postnatal myocardial adaptation may be complicated by bronchopulmonary dysplasia (BPD). We aimed to describe the development of left ventricular function by serial 2D, Doppler, and speckle tracking echocardiography (2D-STE) in infants with and without BPD during the neonatal period and compare these to anthropometric and conventional hemodynamic parameters.

Study Design

Prospective echocardiography on day of life (DOL) 1, 7, 14, and 28 in 119 preterm infants <1500 g birth weight of whom 36 developed BPD (need for oxygen supplementation at 36 weeks gestational age). Non-BPD and BPD infants differed significantly in median (IQR) gestational age (25.5(24–26.5) weeks vs. 29(27–30) weeks, p<0.001) and birth weight (661(552–871) g vs. 1100(890–1290) g, p<0.001).

Results

The intra- and inter-observer variability of the 2D-STE parameters measured did not depend on time of measurement, although there were significant differences in the reproducibility of the parameters. Low intra- and inter-observer variability was seen for longitudinal systolic strain and strain rate mid septum with a median CV (coefficient of variation) of <4.6%. Much higher CVs (>10%) were seen for the apical segment. While anthropometric parameters show rapid development during the first 4 weeks of life, the speckle tracking parameters did not differ statistically significantly during the neonatal period. Infants with and without BPD differed significantly (p<0.001) in the development of anthropometric parameters, conventional hemodynamic parameters except for heart rate, and 2D-STE parameters: global longitudinal systolic strain rate (GLSSR) and longitudinal systolic strain for the mid left wall (LSSR). The largest differences were seen at DOL 1 and 7 in GLSSR (p<0.001) and in LSSR (p<0.01).

Conclusions

Reproducible 2D-STE measurements are possible in preterm infants <1500 g. Cardiac deformation reveals early (DOL 1 and 7) ventricular changes (GLSSR and LSSR) in very low birth weight infants who develop BPD.     

Anomalous Fast-Ion Transport During Neutral Beam Injection on EAST

The fast-ion transport during neutral beam injection on the Experimental Advanced Superconducting Tokamak (EAST) is studied. Based on the NUBEAM and TRANSP codes, it is found that fast-ion transport is anomalous when the minimum safety factor (q_min) is about 2, while it is neoclassical when q_min is around 1. Neutral beam injection heating efficiency, plasma stored energy, and the total heating power are reduced when the fast ion transport is anomalous. The Alfvén continuum spectrum and the mode structures of toroidal Alfvén eigenmodes (AEs) are also calculated for comparison between neoclassical fast-ion transport and anomalous fast-ion transport. High-q_min discharge with anomalous fast-ion transport has more AE activity than that of lower q_min discharge with neoclassical fast-ion transport.     

Dynamics of ion heating in a gas-dynamic trap during neutral beam injection

The dynamics of the ion temperature of the target plasma in a gas-dynamic trap during high-power neutral beam injection is measured by using the Rutherford scattering technique. A comparison of the experimental results with the results of simulations by a model based on the theory of pair Coulomb collisions indicates no significant anomalous losses from the ion plasma component.     

The role of aggregation kinetics in the sedimentation of erythtocytes

The well-known S-shaped settling curves are obtained as solutions of an autonomic dynamical system deduced mathematically from the generalized Stokes formula, the blood volume conservation law, and the Smoluchowski theory of particle coagulation. Numerical computations and parametric analysis of the deduced two nonlinear differential equations for the plasma zone thickness and aggregate size are given. It is shown that the model presented makes it possible, on the basis of experimentally recorded sedimentation curves and aggregate size growth, to identify quantitatively the values of the essential physical parameters of the coupled processes of erythrocyte aggregation and sedimentation. This method of identification could be used as a diagnostic test in hematological laboratories.     

Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.     

The random walk of Azospirillum brasilense

The bacterium Azospirillum brasilense has been frequently studied in laboratory experiments. It performs movements in space where long forward and backward runs on a straight line occur simultaneously with slow changes of direction of the line. A model is presented in which a correlated random walk on a line is joined to diffusion on a sphere of directions. For this transport system, a hierarchy of moment approximations is derived, ranging from a hyperbolic system with four dependent variables to a scalar damped wave equation (telegraph equation) and then to a single diffusion equation for particle density. The original parameters are compounded in the diffusion quotient. The effects of these parameters, such as particle speed or turning rate, on the diffusion coefficient are discussed in detail.     

Motion of nanobeads proximate to plasma membranes during single particle tracking

Drag and torque on nanobeads translating within the pericellular layer while attached to glycolipids of the plasma membrane are calculated by a novel hydrodynamic model. The model considers a bead that translates proximate to a rigid planar interface that separates two distinct Brinkman media. The hydrodynamic resistance is calculated numerically by a modified boundary integral equation formulation, where the pertinent boundary conditions result in a hybrid system of Fredholm integrals of the first and second kinds. The hydrodynamic resistance on the translating bead is calculated for different combinations of the Brinkman screening lengths in the two layers, and for different viscosity ratios. Depending on the bead-membrane separation and on the hydrodynamic properties of both the plasma membrane and the pericellular layer, the drag on the bead may be affected by the properties of the plasma membrane. The Stokes-Einstein relation is applied for calculating the diffusivity of probes (colloidal gold nanobeads attached to glycolipids) in the plasma membrane. This approach provides an alternative way for the interpretation of in vitro observations during single particle tracking procedure, and predicts new properties of the plasma membrane structure.