Calculation and optimization of plasma-optic focusing devices

(i) The focusing of an ion beam by a Morozov lens formed by a current ring in a plasma is calculated using an exact expression for the magnetic field and taking into account the nonparaxial character of the focused beam. The possible ways of optimizing such a lens are considered. (ii) Different versions of extended plasmaoptic devices in which spherical aberrations are minimized are analyzed. It is proposed to optimize extended plasma-optic devices by changing the magnetic field from the entrance end to the exit end of the solenoid in such a way that the boundary magnetic surface always coincides with the boundary surface of the focused beam. It is shown that, under the same conditions, the focusing power of the optimized devices is one to two orders of magnitude higher than that of traditional thin plasma lenses. (iii) The problem of creating a magnetic field whose strength is optimized as a function of the longitudinal coordinate is solved by the Tikhonov regularization method. (iv) An extended plasma-optic device with an optimized solenoid for focusing 1-MeV ion beams is calculated, and the ion trajectories in the device are traced. (v) It is proved expedient to develop special-purpose computer codes aimed at modeling and optimizing the existing and planned experimental plasma-optic focusing devices.     

The possible role of contact current in cancer risk associated with residential magnetic fields

Residential electrical wiring safety practices in the US result in the possibility of a small voltage (up to a few tenths of a volt) on appliance surfaces with respect to water pipes or other grounded surfaces. This "open circuit voltage" (V(OC)) will cause "contact current" to flow in a person who touches the appliance and completes an electrical circuit to ground. This paper presents data suggesting that contact current due to V(OC) is an exposure that may explain the reported associations of residential magnetic fields with childhood leukemia. Our analysis is based on a computer model of a 40 house (single-unit, detached dwelling) neighborhood with electrical service that is representative of US grounding practices. The analysis was motivated by recent research suggesting that the physical location of power lines in the backyard, in contrast to the street, may be relevant to a relationship of power lines with childhood leukemia. In the model, the highest magnetic field levels and V(OC)s were both associated with backyard lines, and the highest V(OC)s were also associated with long ground paths in the residence. Across the entire neighborhood, magnetic field exposure was highly correlated with V(OC) (r = 0.93). Dosimetric modeling indicates that, compared to a very high residential level of a uniform horizontal magnetic field (10 mu T) or a vertical electric field (100 V/m), a modest level of contact current (approximately 18 mu A) leads to considerably greater induced electric fields (> 1 mV/m) averaged across tissue, such as bone marrow and heart. The correlation of V(OC) with magnetic fields in the model, combined with the dose estimates, lead us to conclude that V(OC) is a potentially important exposure with respect to childhood leukemia risks associated with residential magnetic fields. These findings, nonetheless, may not apply to residential service used in several European countries or to the Scandinavian studies concerned with populations exposed to magnetic fields from overhead transmission lines.     

Extremely low frequency electric fields and cancer: Assessing the evidence

Much of the research and reviews on extremely low frequency (ELF) electric and magnetic fields (EMFs) have focused on magnetic rather than electric fields. Some have considered such focus to be inappropriate and have argued that electric fields should be part of both epidemiologic and laboratory work. This paper fills the gap by systematically and critically reviewing electric‐fields literature and by comparing overall strength of evidence for electric versus magnetic fields. The review of possible mechanisms does not provide any specific basis for focusing on electric fields. While laboratory studies of electric fields are few, they do not indicate that electric fields should be the exposure of interest. The existing epidemiology on residential electric‐field exposures and appliance use does not support the conclusion of adverse health effects from electric‐field exposure. Workers in close proximity to high‐voltage transmission lines or substation equipment can be exposed to high electric fields. While there are sporadic reports of increase in cancer in some occupational studies, these are inconsistent and fraught with methodologic problems. Overall, there seems little basis to suppose there might be a risk for electric fields, and, in contrast to magnetic fields, and with a possible exception of occupational epidemiology, there seems little basis for continued research into electric fields. Bioelectromagnetics 31:89–101, 2010. © 2009 Wiley‐Liss, Inc.     

Realization of biophysical models of cardiac electrical activity

Considered are the principles of realization of biophysical models of heart ventricle electrical activity in the form of a double electric layer on the surface of the electrically active myocardium (epicardium and endocardium) and the boundary surfaces dividing the model compartments with different electrophysiological characteristics. The model parameters are the electrophysiological and anatomical characteristics of the heart such as the geometry of the ventricles and the specialized His-Purkinje conduction system, the velocity of depolarization spread over myocardium, the ratio of the velocities of excitation transmission through the Myocardium / His / Purkinje elements of the model, the shape of transmembrane action potentials on the boundary surfaces, the orientation of the intrinsic anatomical axes of the heart relative to the initial set of coordinates, and some other biophysical characteristics of the myocardium. This model is the main unit of a computer simulation system, which includes databases of real and simulated electrocardiosignals.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

Does a cell perform isoelectric focusing?

A model of intracellular electrical sorting of enzymes and organelles in the cytosol, based on isoelectric focusing, is proposed. The focusing is suggested to take place over a centrally symmetric pH gradient which in the cytosol of the yeast Saccharomyces cerevisiae is known to be 7.2-6.4. From published data on the energetic capacity and from the computed electric resistance of the S. cerevisiae cell, the maximum value of the electric field that can be maintained in the cytosol was estimated. The results showed that the strength of a centrally symmetric intracytosolic electric field could be as high as 90 mV/cm, which is sufficient to account for sorting of cytosolic proteins according to their isoelectric points. Although direct experimental evidence for intracellular isoelectric focusing is still missing, several phenomena of physiological importance can be understood on the assumption of its real existence.     

Focusing of heavy ion beams by a high-current plasma lens

Results are presented from studies of the focusing of wide-aperture low-energy (100–400 eV) and moderate-energy (5–25 keV) beams of heavy-metal ions by a high-current electrostatic plasma lens. It is found experimentally that, because of the significant electron losses, the efficient focusing of such beams can be achieved only if the external potentials at the plasma-lens electrodes are maintained constant. Static and dynamic characteristics of the lens are studied under these conditions. It is shown that, as the beam current and the electrode voltage increase, the maximum electrostatic field in the lens tends to a certain limiting value because of the increase in the spatial potential near the lens axis. The role of spherical and moment aberrations in the focusing of wide-aperture low-divergence ion beams is revealed. It is shown that, even when spherical aberrations are minimized, unremovable moment aberrations decrease the maximum compression ratio of a low-energy heavy-ion beam because of the charge separation of multiply charged ions in the focal region. At the same time, as the ion energy increases, the role of the moment aberrations decreases and the focusing of high-current heavy-ion beams by a plasma lens becomes more efficient than the focusing of light-ion (hydrogen) beams. This opens up the possibility of using electrostatic plasma lenses to control ion beams in high-dose ion implanters and high-current accelerators of heavy ions.     

Physical nature of the electric current produced by the asymmetry of particle motion in toroidal magnetic confinement systems

A new type of longitudinal electric current is revealed by analyzing the drift trajectories of charged particles in a tokamak—the current that may be referred to as the asymmetry current because it is associated with the asymmetry of the boundary between trapped and transit particles in phase space. The generation of this current is explained by the fact that the motions of the particles that cross the magnetic surface at a given point in opposite directions are qualitatively different. The asymmetry current results from the toroidal variations of the magnetic field and is maintained by the radial momentum flux of transit particles. The contribution of the particles of different species to the asymmetry current density is proportional to their pressure, is independent of the gradients of the plasma parameters, is maximum at the magnetic axis, and decreases toward the plasma periphery. In contrast to standard neoclassical theory, the asymmetry current can be found only from exact particle trajectories. The asymmetry current is calculated for tokamaks with differently shaped magnetic surfaces and for a model stellarator. By exploiting the newly revealed asymmetry current, together with the bootstrap current, it may be possible to substantially simplify the problem of creating a tokamak reactor.     

Mathematical model for transient isoelectric focusing of simple ampholytes

A mathematical model describing transient processes in isoelectric focusing (IEF) of L biprotic ampholytes is presented. The model is a generalization of our previous research on steady slate in IEF and consists of L nonlinear partial differential equations coupled with 2L+2 algebraic equations. Constraints imposed by the mode of operation, viz., constant current. voltage or power, are described. Due to the nonlinearity of the equations, analysis of the model requires computer simulation. Model equations suitable for computer implementation are derived.     

Induced electric field and current density patterns in bone fractures

We have used the low frequency solver of the computer program SEMCAD‐X to model the induced electric field and current density patterns in simple models of a fractured femur embedded off‐center in cylindrical muscle tissue; a 1 cm fracture gap is filled with callus. The model is exposed to a 1 kHz, 1 mT sinusoidal magnetic field. The frequency chosen is typical of the major Fourier components of many waveforms used to stimulate fracture healing using pulsed magnetic fields; the intensity is also a typical level. Models include fractures perpendicular to the bone and at an angle from the perpendicular, each exposed to a field applied parallel to the bone or parallel to either of the two axes perpendicular to it. We find that all directions of applied magnetic fields produce essentially parallel induced electric fields and current densities through the plane of the callus, but that a magnetic field applied parallel to the bone induces considerably higher fields and currents than the same strength field applied in either perpendicular direction. Because investigations of pulsed‐field devices, including modeling of induced fields and currents, peaked more than a decade ago, this is the first application to our knowledge of the current capabilities of computer modeling systems to biological systems at low frequencies. Bioelectromagnetics 33:585–593, 2012. © 2012 Wiley Periodicals, Inc.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

Cell type-specific quantitative predictions of radiation-induced chromosome aberrations: a computer model approach

A quantitative computer model was applied to simulate the three-dimensional (3D) spatial organization of chromatin in human cell nuclei under defined conditions of virtual irradiation to explore the implications of spatial organization on chromosome aberrations. To calibrate the virtual irradiation algorithm, a dose-dependent spectrum of radiation-induced chromosome aberrations such as dicentrics, translocations and centric rings was calculated for low-LET radiation doses ranging from 0.5 to 5 Gy. This was compared with the results from experimental studies. While the dose-response curves calculated from model simulations agree well with experimental dose-response curves for dicentrics and translocations, centric rings are significantly more frequent in the model simulation than in experiments despite taking into account exclusive arm territories in the applied Spherical 1 Mbp Chromatin Domain (SCD) computer model explicitly. Taking into account the non-random positioning of chromosome territories observed in lymphocyte cell nuclei (a so-called gene density-correlated arrangement of chromosome territories), aberration frequencies were calculated with the calibrated irradiation algorithm to investigate the impact of chromosome territory neighborhood effects (proximity effects). The absolute frequencies of pairwise exchanges agree well with those found in an experimental study. In conclusion, the results obtained using the computer model approach presented here based on only a few adjustable parameters correlated well with those of experimental studies of chromosome aberration frequencies. Thus the model may be a useful tool in radiation-induced cancer risk estimates in combination with epidemiological studies.     

Experimental study of electron vortex structures in an electrostatic plasma lens

Results are presented from experimental studies of electron vortex bunches in a cold ion-beam plasma consisting of strongly magnetized electrons and a beam of almost free positive ions. The existence of electron vortex bunches was detected from local minima of the electric potential on surfaces perpendicular to the magnetic field lines. It is found that the vortices have the form of magnetic-field-aligned filaments, in which electrons rotate with a velocity significantly exceeding both the velocity of the vortex as a whole and the electron velocity in the ambient plasma. It is shown that, in a sufficiently strong magnetic field, the accumulation of electrons in the vortices terminates when the condition for the longitudinal confinement of electrons by the electric field fails to hold.     

Experimental studies of the behavior of the ion plasma component during disruptive instability in a tokamak

Results are presented from experimental studies of the behavior of the plasma ion component during disruptive instability in the TVD and DAMAVAND tokamaks. It is shown that the ion temperature increases during a major disruption by a factor of 1.5–2. The ions are accelerated predominantly across the magnetic field near the rational magnetic surfaces. Results on the ion acceleration along the magnetic field indicate that disruptions are accompanied by the generation of longitudinal electric fields that are aligned in opposite directions at the plasma periphery and near the plasma axis.     

Study of charged particle motion in fields of different configurations for developing the concept of plasma separation of spent nuclear fuel

The concept of plasma separation of spent nuclear fuel in a plane perpendicular to the magnetic field in an electric potential of special configuration is developed. A specific feature of the proposed approach consists in using an accelerating potential for reducing energy and angular spread of plasma ions at the entrance to the separator chamber and a potential well for the spatial separation of ions with different masses. The trajectories of ions of the substance imitating spent nuclear fuel are calculated. The calculations are performed for azimuthal and axial magnetic fields and model electric field configurations corresponding to different geometries of the separator chamber. It is shown that, using magnetic fields with a characteristic strength of 1 kG and electric potentials of up to 1 kV inside a region with a linear size less than 100 cm, it is possible to separate ions of spent nuclear fuel with energies from 0.2 to 3 eV. The calculations were performed for a collisionless mode in the single-particle approximation. Possible variants of the experimental facility for plasma separation of spent nuclear fuel are proposed.     

Current density in a model of a human body with a conductive implant exposed to ELF electric and magnetic fields

A numerical model of a human body with an intramedullary nail in the femur was built to evaluate the effects of the implant on the current density distribution in extremely low frequency electric and magnetic fields. The intramedullary nail was chosen because it is one of the longest high conductive implants used in the human body. As such it is expected to alter the electric and magnetic fields significantly. The exposure was a simultaneous combination of inferior to superior electric field and posterior to anterior magnetic field both alternating at 50 Hz with the values corresponding to the ICNIRP reference levels: 5000 V m^?1 for electric field and 100 µT for magnetic flux density. The calculated current density distribution inside the model was compared to the ICNIRP basic restrictions for general public (2 mA m^?2). The results show that the implant significantly increases the current density up to 9.5 mA m^?2 in the region where it is in contact with soft tissue in the model with the implant in comparison to 0.9 mA m^?2 in the model without the implant. As demonstrated the ICNIRP basic restrictions are exceeded in a limited volume of the tissue in spite of the compliance with the ICNIRP reference levels for general public, meaning that the existing safety limits do not necessarily protect implanted persons to the same extent as they protect people without implants. Bioelectromagnetics 30:591–599, 2009. © 2009 Wiley‐Liss, Inc.     

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.     

Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

A theoretical analysis of electric and magnetic fields of the heart, based solely upon the scalar multipole expansion, is carried out in order to gain an insight into the interrelation of the data contained in electro- and magnetocardiological measurements. The usual multipole expansion is applied for the electric field, however corresp[nding equivalent multipoles are formulated as idealized generators, having not only flow sources, but also vortex sources of the field. Furthermore, the magnetic field in a homogeneous infinite volume conductor is expressed as a sum of two series, the first being the usual multipole expansion of the nonvortex component of the magnetic field, and the second being a sequence of magnetic fields set up by the aforementioned electric multipole generators reduced to axial form. The former term is uniquely defined by the electric multipole components, but the latter reflects properties of the cardiogenerator that can be revealed only by means of magnetic measurements. Features of the electric and magnetic multipole components as integral characteristics of the cardiogenerator are discussed and concepts of the magnetic centre and magnetic axis of the cardiogenerator are proposed. The analysis is illustrated by examples of simple generator configurations.     

Measurement of magnetically induced electric fields in conductive media near a 60 Hz current-carrying wire.

Electric fields induced in a conductive body by the magnetic field of a current-carrying wire were analyzed theoretically and experimentally to assess the dosimetric importance of highly nonuniform, field-exposure conditions. Experimentation revealed that a 60-Hz magnetic field was inversely proportional to the radius of a wire bundle carrying 100 A within a 0.5-m2 test area. A miniaturized electric field probe was used to measure the electric fields induced in 5-cm-deep, saline-filled models. In the theoretical analysis, numerical estimates of induced fields were made by a spreadsheet method. The theoretical calculations and the measured values of induced electric fields were generally in good agreement. The induced fields were in a plane perpendicular to a vertically incident magnetic field; the maximally induced fields were in areas nearest the wire bundle. The strength of the induced field increased with model size: from 96 microV/cm in a 10 x 10 cm model to 176 microV/cm in a 40 x 40 cm model. The strength of the field induced in a 20 x 20 cm model decreased with increasing model-to-wire spacing: from 132 microV/cm for a 1-cm spacing (2-mT maximum, incident field) to 50 microV/cm for a 6-cm spacing (0.33-mT maximum). The results indicate that increases in local values of nonuniformly incident fields produce relatively small increases in induced electric fields. This finding may be important in dosimetric consideration of circumstances, such as use of electric blankets, in which fields of low average strength are accompanied by intense local fields.