Stability of a stationary double layer

Electrostatic oscillations in a stationary beam double layer are studied in the hydrodynamic approximation. An analysis of the solutions to the linearized equations for perturbations shows that the double layer in an unbounded plasma may be subject only to convective instability, in which case the perturbations localized inside the region of the potential jump escape from the plasma without distorting the steady field structure. The double layer in a bounded plasma is investigated numerically by a particle-in-cell method. It is established that, as is the case in the Pierce system, the governing role in the stability of the double layer is played by the field of the charges induced on the surfaces of the conducting electrodes.     

Dissipation-free jumps for the magnetosonic branch of cold plasma motion

Dissipation-free jumps are studied in a hydrodynamic model of a cold plasma moving at about magnetosonic speed. The jumps described by the generalized Korteweg-de Vries equation, which possesses similar nonlinear and dispersion properties, are considered. In particular, jumps with emission and solitonlike jumps are considered. The assumption that our model possesses jumps of the same type as those for the generalized Korteweg-de Vries equation is justified by numerically investigating the problem of the decay of an initial discontinuity in a cold plasma. An analytic method is described that makes it possible to predict the structure of such jumps in the general case.     

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.     

Spectral properties of an N-pole helical structure consisting of like-charged equal-size dust grains

The oscillations and stability of an N-pole helical structure that consists of like-charged equal-size dust grains and is confined in a plasma in an axisymmetric potential well are studied theoretically. Self-confining structures, as well as their linear collective modes corresponding to three coupled types of grain displacements (change in the radius of the structure, change in the distance between neighboring lattice planes of the structure, and angular displacements in the lattice planes), are found. On the whole, the coupled oscillations have the form of wormlike perturbations. Dispersion relations for the oscillation modes of helical structures composed of N interwoven helices are derived and solved numerically.     

Diastolic calcium release controls the beating rate of rabbit sinoatrial node cells: numerical modeling of the coupling process

Recent studies employing Ca2+ indicators and confocal microscopy demonstrate substantial local Ca2+ release beneath the cell plasma membrane (subspace) of sinoatrial node cells (SANCs) occurring during diastolic depolarization. Pharmacological and biophysical experiments have suggested that the released Ca2+ interacts with the plasma membrane via the ion current (INaCa) produced by the Na+/Ca2+ exchanger and constitutes an important determinant of the pacemaker rate. This study provides a numerical validation of the functional importance of diastolic Ca2+ release for rate control. The subspace Ca2+ signals in rabbit SANCs were measured by laser confocal microscopy, averaged, and calibrated. The time course of the subspace [Ca2+] displayed both diastolic and systolic components. The diastolic component was mainly due to the local Ca2+ releases; it was numerically approximated and incorporated into a SANC cellular electrophysiology model. The model predicts that the diastolic Ca2+ release strongly interacts with plasma membrane via INaCa and thus controls the phase of the action potential upstroke and ultimately the final action potential rate.     

Numerical simulation of the instability of a nonuniform plasma flow: Nonlinear dynamics of slipping instability

A kinetic model is proposed that describes the nonlinear dynamics of the instabilities of a transversely nonuniform plasma flow. It is shown that, in the linear approximation, the model yields the familiar boundary-value problem for the scalar potential in plasma. The slipping instability in a plane waveguide is considered as an example. The general dispersion relation for a flow with a stepwise uniform density profile and with a tangential discontinuity in its longitudinal velocity is analyzed qualitatively. The dynamics of the slipping instability is investigated numerically for a flow that is detached from the waveguide walls and whose longitudinal velocity obeys a linear, a sinusoidal, or a discontinuous distribution. In the nonlinear stage of the instability, the flow expands in such a way as to come into contact with the walls, the spread in the longitudinal velocities remains smaller than the initial velocity variation, and the longitudinal velocities of different transverse layers in the flow are not completely equalized.     

Interaction of a high-current electron beam with hybrid waveguide and plasma modes in a dielectric Cherenkov maser with a plasma layer

The characteristics of a high-current electron beam-driven microwave amplifier—a dielectric Cherenkov maser—are investigated in the framework of linear theory for the case of a plasma layer present at the surface of the maser slow-wave structure. The dispersion relation for axisymmetric perturbations is obtained for the conventional configuration (a circular dielectric-lined waveguide and a thin annular beam propagating within the vacuum region inside the annular plasma) in the model of a fully magnetized plasma and beam. The results of numerically solving the dispersion relation for different beam and plasma parameters are presented, and an analysis based on these results is given with regard to the features of the beam interaction with the hybrid waves of the system (both hybrid waveguide and hybrid plasma modes). For the hybrid waveguide mode, the dependences of the spatial growth rate on the frequency demonstrate an improvement in the gain at moderate plasma densities, along with narrowing the amplification band and shifting it toward higher frequencies. For the hybrid plasma mode, the interaction with a mildly relativistic (200–250 keV) beam, when the wave phase velocity is close to the speed of light in the dielectric medium, is most interesting and, therefore, has been studied in detail. It is shown that, depending on the beam and plasma parameters, different regimes of the hybrid plasma mode coupling to the hybrid waveguide mode or a usual, higher order plasma mode take place; in particular, a flat gain vs. frequency dependence is possible over a very broad band. The parameters at which the ?3-dB bandwidth calculated for the 30-dB peak gain exceeds an octave are found.     

Numerical simulations of a high-current plasma lens

The dynamic processes by which an electrostatic plasma lens with a wide-aperture ion beam and electrons produced from the secondary ion-electron emission relaxes to a steady state is investigated for the first time by the particle-in-cell method. The parameters of a two-dimensional mathematical model were chosen to correspond to those of actual plasma lenses used in experimental studies on the focusing of high-current heavy-ion beams at the Institute of Physics of the National Academy of Sciences of Ukraine (Kiev, Ukraine) and the Lawrence Berkeley National Laboratory (Berkeley, USA). It is revealed that the ion background plays a fundamental role in the formation of a high potential relief in the cross section of a plasma lens. It is established that, in the volume of the plasma lens, a stratified electron structure appears that is governed by the nonuniform distribution of the external potential over the fixing electrodes and the insulating magnetic field. The stratification is very pronounced because of the finite sizes of the cylindrical fixing electrodes of the lens. It is shown that the presence of such a structure limits the maximum compression ratio for an ion beam to values that agree with those observed experimentally.     

Reflection and transmission coefficients for radio waves incident obliquely on N identical plane plasma layers and zebra patterns in the spectrum of solar radio emission

The reflection and transmission coefficients for quasi-monochromatic radio waves incident at an arbitrary angle on an arbitrary number of identical piecewise-homogeneous plane plasma layers are calculated analytically and numerically. It is shown that alternating transparency and opacity stripes in the spectrum of radio waves passing through such a plasma structure (the zebra pattern effect) can be observed at any angle of incidence. The opacity stripes for ordinary waves are wider than those for extraordinary waves. For the zebra pattern to be well pronounced, the radio wave flux in the Sun??s atmosphere should be narrowly directed, which is possible during bursts.     

Structure of the fronts of strong collisional shock waves in an ideal two-temperature electron-ion plasma with ions of arbitrary charge

Solutions in the form of plane running waves are investigated numerically in the framework of a two-temperature hydrodynamic model of a fully ionized ideal plasma with ions of arbitrary charge number Z₀. Most simulations were carried out for simple boundary conditions corresponding to a cold immobile plasma at the front of a running wave. All the solutions obtained have a discontinuity in the form of an isoelectronic-thermal jump, whose parameters relax to their steady-state values in the course of calculation. The problem of finding numerical solutions in which all the quantities at infinity take on finite (equilibrium) values actually reduces to the problem of the front structure of a strong shock wave. For a plasma with singly changed ions (Z₀ = 1), numerical solutions were found to coincide with the previously known solution. For a plasma with arbitrarily charged ions (Z₀ > 1), numerical solutions were obtained for the first time on the basis of justified formulas for the electron thermal conductivity.     

Numerical Simulation of Whistler Waves in Magnetized Plasma with Small-Scale Irregularities

Propagation of whistler-mode waves in magnetized plasma in the presence of small-scale field-aligned irregularities with enhanced or depressed plasma density is simulated numerically. The numerical experiments have demonstrated the effect of guided propagation of whistler-mode waves in plasma regions occupied by irregularities with transverse dimensions smaller than the whistler wavelength in uniform plasma. It is shown that not only individual irregularities but also the entire modified region, which serves as a specific guiding structure, exhibit waveguide properties.     

Numerical modeling of L-H transitions in the presence of a radial current at the edge of a tokamak plasma

Hydrodynamic equations describing wall plasma turbulence are analyzed numerically using a two-dimensional four-field model. Turbulent transport coefficients are calculated with consideration of the radial current. Numerical analysis revealed a possible scenario for L-H transitions that is associated with the radial current driven by nonambipolar processes. It is shown that the transition of a plasma to an improved confinement mode can also be triggered by other mechanisms.     

Nonlinear dispersion in a plasma with a relativistic electron beam

The nonlinear interaction of a relativistic electron beam with a plasma is investigated numerically on the basis of the extended notions of the physical quantities that enter the linear dispersion relation. Extending the notions of the wave frequency, wavenumber, and wave phase velocity to the nonlinear stage of an instability makes it possible to analyze the evolution of the Cherenkov and plasma resonances and to study how they affect the saturation of the wave amplitude. A model of the beam-plasma instability in which the growth rate is calculated from the corresponding linear hydrodynamic formula on the basis of the results obtained using a numerical kinetic model makes it possible to establish the applicability range of the hydrodynamic approximation for beams with different energies.     

Behavior of a dust grain in the double layer of an electric probe in a gas-discharge plasma

Equations for the motion of an individual dust grain in the double layer of a negatively charged cylindrical probe in a glow discharge plasma are derived and solved numerically. The distribution of the electric potential near the probe is determined, and the grain charge is calculated as a function of the distance from the probe for different probe potentials. The trajectories of grains with different initial energies are traced. An analysis of the grain trajectories shows that, at a certain distance from the probe, high-energy grains may be recharged; i.e., the grain charge may change sign. The grains are found to have no direct effect on the probe current in a dusty plasma of a glow discharge.     

Plasma asymmetric dipole antenna excited by a surface wave

A study is made of a quarter-wave asymmetric dipole antenna in which the conducting rod is replaced by a plasma column with an electron density much higher than the critical density. The parameters of such an antenna are determined by the exited surface wave, which affects the electromagnetic field structure in the near-field zone. It is shown analytically, numerically, and experimentally that the resonant length of the plasma dipole antenna is close to one-quarter of the length of the surface wav and that the conversion efficiency of plasma antenna power into radiation can be no worse than that of a metal dipole antenna. It is also shown experimentally that the plasma in a dipole antenna can be self-consistently excited by an RF oscillator and that the excited RF oscillations can be efficiently radiated into the surrounding space.     

Investigation of the charge and potential of a dust grain in a low-pressure plasma with allowance for ionization in the intergrain space

The formation of the ion flow to a dust grain and the distribution of the electric potential in a low-pressure dusty plasma are investigated theoretically with allowance for ionization in the intergrain space. Poisson’s equation similar to the Langmuir plasma-sheath equation is solved numerically with the use of partial analytic solutions at the boundary of the Seitz-Wigner cell and in thin layers in the intergrain space. The charge and potential of a dust grain are found as functions of the grain radius and cell size. The grain potential and the total cell potential energy as functions of the cell size display weak minima, whose positions correspond to the observed intergrain distance in dusty crystals.     

Theory of propagation of ordinary surface cyclotron waves

The dispersion properties of ordinary surface cyclotron waves in a semiinfinite nonuniform plasma are investigated. The waves propagate across the external magnetic field directed along the plasma surface in a metal waveguide the internal surface of which is covered with a dielectric. The problem is solved analytically in the framework of a kinetic model for plasma particles under the assumption of weak spatial dispersion. The influence of the parameters of the dielectric layer separating the plasma from the metal wall, the shape of the plasma density profile, and the value of the external magnetic field on the dispersion properties of surface cyclotron waves is studied both numerically and analytically.     

Thermodynamic equilibrium of pure electron plasmas in a Malmberg-Penning trap

A new class of annular confinement configurations of a single-charged plasma corresponding to global thermodynamic equilibria in a cylindrical Malmberg-Penning trap with an axial conductor is investigated both numerically and analytically. In the case of an infinite plasma length, the density turns out to be essentially constant inside a surface of revolution and to fall off abruptly outside of it. Analytical limiting cases are calculated explicitly in the limit of small Debye lengths. In the case of a finite plasma length, the self-consistent solution to Poisson's equation describing thermodynamic equilibrium is obtained numerically and the dependence of the plasma density distribution on the various parameters of the system is investigated.     

Kelvin-Helmholtz instability for a bounded plasma flow in a longitudinal magnetic field

Kelvin-Helmholtz MHD instability in a plane three-layer plasma is investigated. A general dispersion relation for the case of arbitrarily orientated magnetic fields and flow velocities in the layers is derived, and its solutions for a bounded plasma flow in a longitudinal magnetic field are studied numerically. Analysis of Kelvin-Helmholtz instability for different ion acoustic velocities shows that perturbations with wavelengths on the order of or longer than the flow thickness can grow in an arbitrary direction even at a zero temperature. Oscillations excited at small angles with respect to the magnetic field exist in a limited range of wavenumbers even without allowance for the finite width of the transition region between the flow and the ambient plasma. It is shown that, in a low-temperature plasma, solutions resulting in kink-like deformations of the plasma flow grow at a higher rate than those resulting in quasi-symmetric (sausage-like) deformations. The transverse structure of oscillatory-damped eigenmodes in a low-temperature plasma is analyzed. The results obtained are used to explain mechanisms for the excitation of ultra-low-frequency long-wavelength oscillations propagating along the magnetic field in the plasma sheet boundary layer of the Earth’s magnetotail penetrated by fast plasma flows.