Stimulated ionization scattering of a wave beam forming a discharge channel in a magnetic mirror trap

The stimulated scattering of a whistler wave beam forming an extended discharge channel in a magnetic mirror trap is discovered and investigated experimentally. It is shown that the beam is scattered by relaxaction oscillations of the lattice of plasma inhomogeneities excited by the beam field. The spectrum of the pump field in the RF discharge plasma is found to broaden considerably and to contain individual modulation peaks corresponding to lattice oscillations. The peaks are observed at working gas pressures at which the electron mean free path is close to the wavelength of the standing wave forming the discharge channel. A physical model describing the phenomena observed is developed.     

Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

Nonlinear oscillations of a semiconductor plasma with a nonrelativistic electron beam

Nonlinear oscillations of a semiconductor plasma with a low-density electron beam in the absence of an external magnetic field are studied in the hydrodynamic approximation. The beam is assumed to be nonrelativistic and monoenergetic. Cases are studied in which the Langmuir frequency of the electron oscillations in a semiconductor is much higher or much lower than the electron momentum relaxation rate. The self-similar solution obtained for the first case describes the damping of the nonlinear oscillations of the wave potential. Numerical analysis of the second case shows that the electric field distribution in the beam may correspond to that in a shock wave.     

Passage of electromagnetic waves through the critical surface

A study is made of the passage of electromagnetic waves through the critical surface at small angles between the plasma density gradient and the magnetic field. Expressions are derived for the transmission and reflection coefficients of electromagnetic oscillations that are periodic in the direction transverse to the density gradient. The penetration of wave beams is also analyzed. In the case of a wide beam, the incident and transmitted ray trajectories are shown to be mirror-image about the resonance surface. Behind the resonance surface, a narrow incident wave beam generates a beam propagating along the magnetic field.     

Space-charge lens for focusing a negative-ion beam

Results are presented from experimental and theoretical studies of a space-charge lens for focusing a negative-ion beam. The space-charge field and the beam ion trajectories are numerically calculated for the lens used in the experiments. The results of calculations are compared with the experimental data. It is shown theoretically and experimentally that the proposed device allows one to achieve the main operating conditions of the space-charge lens: the inertial confinement of positive ions and the removal of electrons by an external electric field. The focusing field of the lens attains ～100 V/cm, which provides a focal length of <20 cm.     

The accuracy of digital image-based finite element models.

Digital image-based finite element meshing is an alternative approach to time-consuming conventional meshing techniques for generating realistic three-dimensional (3D) models of complex structures. Although not limited to biological applications, digital image-based modeling has been used to generate structure-specific (i.e., non-generic) models of whole bones and trabecular bone microstructures. However, questions remain regarding the solution accuracy provided by the digital meshing approach, particularly at model or material boundaries. The purpose of this study was to compare the accuracy of digital and conventional smooth boundary models based on theoretical solutions for a two-dimensional (2D) compression plate and a 3D circular cantilever beam. For both the plate and beam analyses, the predicted solution at digital model boundaries was characterized by local oscillations, which produced potentially high errors within individual boundary elements. Significantly, however, the digital model boundary solution oscillated approximately about the theoretical solution. A marked improvement in solution accuracy was therefore achieved by considering average results within a region composed of several elements. Absolute errors for Von Mises stress averaged over the beam cross section, for example, converged to less than 4 percent, and the predicted free-end displacement of the cantilever beam was within 1 percent of the theoretical solution. Analyses at several beam orientations and mesh resolutions suggested a minimum discretization of three to four digital finite elements through the beam cross section to avoid high numerical stiffening errors under bending.     

Space-charge lens for focusing negative ion beams by means of an additional electron ionizer

A space-charge lens created at the Institute of Physics, National Academy of Sciences of Ukraine, to focus negative ion beams using an additional electron ionizer is investigated. In the previous version of the lens, in which the gas was ionized by the ion beam itself, the focal power was quite high (the focal length was ? ≤ 20 cm) but the gas pressure was too great (P ～ 10^?3 torr), which resulted in significant charge-exchange losses of the beam ions. The experimental and theoretical study reported here shows that the use of a 100-eV electron beam as an auxiliary ionizer allows the working pressure in the lens to be significantly reduced. As a result, a simple, inexpensive, and efficient lens has been developed that can be used in systems for transportation of negative ion beams.     

Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.     

Method to increase efficiency of irradiation of biological objects by electron beams

The method has been proposed for active control of distribution of the dose caused by an electron beam passed through the medium. The method is based on the influence of magnetic field on charged particles and it allows concentrating of the absorbed dose in the prescribed area. To investigate this method the Monte-Carlo simulations were carried out for 20-70 MeV electrons in 0.5-3 T magnetic field using GEANT program. From the obtained results it follows that in the uniform magnetic field the maximum in distribution of the electron beam dose appears and its shape is similar to Bregg's peak for heavy charged particles. The location of the maximum may be changed by varying beam energy and magnetic fields configuration. For 60-70 MeV beam the maximum may be obtained at the depth of 10-15 cm that is convenient for radiotherapeutic usage.     

Somatic evoked high-frequency magnetic oscillations reflect activity of inhibitory interneurons in the human somatosensory cortex

High-frequency potential oscillations in the range of 300–900 Hz have recently been shown to concur with the primary response (N20) of the somatosensory cortex in awake humans. However, the physiological mechanisms of the high-frequency oscillations remained undetermined. We addressed the issue by analyzing magnetic fields during wakefulness and sleep over the left hemisphere to right median nerve stimulation with a wide bandpass (0.1–2000 Hz) recording with subsequent high-pass (> 300 Hz) and low-pass (< 300 Hz) filtering. With wide bandpass recordings, high-frequency magnetic oscillations with the main signal energy at 580–780 Hz were superimposed on the N20m during wakefulness. Isofield mapping at each peak of the high-pass filtered and isolated high-frequency oscillations showed a dipolar pattern and the estimated source for these peaks was the primary somatosensory cortex (area 3b) very close to that for the N20m peak. During sleep, the high-frequency oscillations showed dramatic diminution in amplitude while the N20m amplitude exhibited a moderate increment. This reciprocal relation between the high-frequency oscillations and the N20m during a wake-sleep cycle suggests that they represent different generator substrates. We speculate that the high-frequency oscillations represent a localized activity of the GABAergic inhibitory interneurons of layer 4, which have been shown in animal experiments to respond monosynaptically to thalamo-cortical input with a high-frequency (600–900 Hz) burst of short duration spikes. On the other hand, the underlying N20m represents activity of pyramidal neurons which receive monosynaptic excitatory input from the thalamus as well as a feed-forward inhibition from the interneurons.     

On the nature of global plasma oscillations in a tokamak. Part II: Spatial structure and propagation of perturbations observed at the T-10 tokamak

Large-scale plasma oscillations (so-called MHD oscillations) observed at the T-10 tokamak are investigated. The central electron cyclotron heating was used to enhance oscillations at the m/n = 1/1 mode with the goal of determining the internal characteristics of the process. The spatially resolved electron cyclotron emission diagnostics allowed analyzing the propagation characteristics of plasma perturbations. The experiments have revealed that excitation of oscillations in a particular mode occur simultaneously in the entire area located within the corresponding rational magnetic surface. The propagation of plasma perturbations along the torus is found to be inhomogeneous. The electron cyclotron emission diagnostics allowed finding eigen (resonance) frequencies of plasma oscillations from the parameters of their inhomogeneous propagation in the plasma core and comparing them with spectra of oscillations of the magnetic field induced by the plasma current in the edge plasma, which were recorded by magnetic probes. It is established that the frequencies of eigenmodes are independent of the electron temperature, plasma density, and auxiliary heating power. Even spatial harmonics of the principal magnetic surface are observed under strong excitation of oscillations. The rational magnetic surfaces that determine oscillation harmonics retain their position during the entire steady-state phase of the total plasma current in spite of the strong sharpening of the temperature profile due to central heating.     

Specific features of virtual cathode formation and dynamics with allowance for the magnetic self-field of a relativistic electron beam

The conditions and mechanisms of virtual cathode formation in relativistic and ultrarelativistic electron beams are analyzed with allowance for the magnetic self-field for different magnitudes of the external magnetic field. The typical behavior of the critical current at which an oscillating virtual cathode forms in a relativistic electron beam is investigated as a function of the electron energy and the magnitude of the uniform external magnetic field. It is shown that the conditions for virtual cathode formation in a low external magnetic field are determined by the influence of the magnetic self-field of the relativistic electron beam. In particular, azimuthal instability of the electron beam caused by the action of the beam magnetic self-field, which leads to a reduction in the critical current of the relativistic electron beam, is revealed.     

Low frequency electromagnetic fields and the Belousov-Zhabotinsky reaction

Low frequency magnetic fields can influence biochemical reactions and consequently physiological rhythms and oscillations. To test this for a model reaction we used the chemical Belousov-Zhabotinsky (BZ) reaction, which is one of the simplest chemical oscillators. The oscillation frequency of the reaction was tracked optically by the absorption of blue light. Field treatment was carried out at room temperature in the middle of two Helmholtz coils. After starting the reaction, for 5 min the oscillations were monitored as control measurement, then during the next 10 min monitoring was with a magnetic field switched on, followed by a period of 5 min with the field switched off. A variety of exposure conditions have been tested: the frequency was varied between 5 and 1000 Hz, the field strength was varied up to 2.7 mT, different pulse shapes were used, the influence of the exposure temperature was tested, and the influence of the optimum exposure conditions (static magnetic field and the frequency of the dynamic field) as predicted by the ion parametric resonance (IPR) model has been measured. In conclusion, in no case any statistical significant influence of the magnetic treatment on the oscillation frequency of the BZ reaction could be detected (P > .05, t-test).     

Process of compensation of the space charge of a negative ion beam in a gas

The process of compensation of the space charge of a negative ion beam propagating through a neutral gas is investigated numerically. A comparison of the results obtained with experimental data unambiguously proves that, at high gas pressures, when the beam space charge is overcompensated, the electric field within the beam is determined by Coulomb collisions of the beam ions with plasma electrons. At low pressures, when the space charge is undercompensated, the field within the beam is determined by the dynamic processes related to oscillations of the beam current.     

Investigation of the chaotic dynamics of an electron beam with a virtual cathode in an external magnetic field

The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring in an electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beam and interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased, the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation and interaction of spatiotemporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator is achieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.     

Investigation of low-frequency waves in plasma-filled microwave oscillators

The excitation of microwave oscillations by an electron beam in a hybrid plasma waveguide—a slow-wave structure (a sequence of inductively coupled resonators) with a plasma-filled transport channel—is studied both experimentally and theoretically. It is shown that the governing role in the generation of microwaves and their transmission to a feeder line is played by the spatial and temporal plasma-density variations associated with low-frequency ion plasma oscillations. The microwave pressure gives rise to low-frequency plasma oscillations with a rise time shorter than their period. This nonlinear mechanism for the excitation of low-frequency oscillations has a threshold in terms of the microwave power. The unsteady character of the spatial distribution of the plasma density results in intermittent microwave generation and shortens the duration of microwave pulses.     

Nonlinear modulation of an extraordinary wave under the conditions of parametric decay

A self-consistent set of Hamilton equations describing nonlinear saturation of the amplitude of oscillations excited under the conditions of parametric decay of an elliptically polarized extraordinary wave in cold plasma is solved analytically and numerically. It is shown that the exponential increase in the amplitude of the secondary wave excited at the half-frequency of the primary wave changes into a reverse process in which energy is returned to the primary wave and nonlinear oscillations propagating across the external magnetic field are generated. The system of ??slow?? equations for the amplitudes, obtained by averaging the initial equations over the high-frequency period, is used to describe steady-state nonlinear oscillations in plasma.     

Nonlinear theory of coupled waves exemplified by beam-plasma instability

The nonlinear stage of instability of an annular electron beam spatially separated from an annular plasma is investigated. The equations describing coupled waves for an arbitrary ratio between the beam and plasma densities are derived. It is shown that instability saturates at distances on the order of several inverse spatial growth rates. The saturation is caused by relativistic nonlinearity, generation of the second harmonic, and low-frequency modulation of the electromagnetic field. At larger distances, resonant generation of low-frequency beam oscillations becomes a dominant factor. In the case of a low-density beam, an expression for the maximum power of the generated plasma wave is obtained in an explicit form.     

Simulation of oscillatory processes in a beam-plasma system with a virtual cathode in gas-filled interaction space

Physical processes occurring in an intense electron beam with a virtual cathode in an interaction space filled with neutral gas are studied in a two-dimensional model. A mathematical model is proposed for investigating complicated self-consistent processes of neutral gas ionization by the beam electrons and the dynamics of an electron beam and heavy positive ions in the common space charge field with allowance for the two-dimensional motion of charged particles. Three characteristic dynamic regimes of the system are revealed: complete suppression of oscillations of the virtual cathode as a result of neutralizing its space charge by positive ions; the pulsed generation regime, in which the ions dynamics repeatedly suppresses and restores the virtual cathode oscillations; and the continuous generation regime with an anomalously high level of noisy oscillations.     

Possibility of using active secondary charge-exchange particle diagnostics for measuring the magnetic field direction in the plasma of a magnetic fusion reactor

An active particle diagnostic method based on the secondary charge exchange of hydrogen atoms of a probing (diagnostic) beam is proposed for local measurements of the magnetic field direction in the plasma of a thermonuclear fusion reactor. Experiments with new-generation large devices require searching for novel methods for measuring the direction of the total magnetic field in a plasma at different points along the radius of the plasma column. The main idea of the method proposed, which holds great promise for large devices, is outlined. The possibility of using the method on ITER—a large fusion reactor that is now at the design stage—is illustrated by carrying out relevant numerical simulations. The results obtained for one of the main discharge scenarios, with the injection geometry and probing beam energy (100 eV) that are now adopted for the ITER design, show that the method can provide local measurements of the magnetic field direction (the magnetic pitch angle) and of the spatial variations of the field vector. Further analysis has revealed, however, that, from the standpoint of signal intensity and signal-to-noise ratio, it is expedient to increase the energy of the beam atoms to 200–250 keV. With such probing beams, the method ensures a spatial (radial) resolution of about 10 cm in the plasma core during a signal acquisition time of 10 ms. The magnetic pitch angle can be measured with an accuracy of 5 × 10^?3 rad. An important advantage of the method proposed is its ability to directly measure the pitch angle of the magnetic field lines.