Model magnetic field configurations with islands

Helical perturbations of the tokamak magnetic field can give rise to magnetic islands in the vicinity of the rational magnetic surfaces at which the pitch of the magnetic field lines coincides with that of the perturbation. The widely known relationship between the magnetic island width and the perturbation amplitude is valid under the assumptions that the island width is small in comparison to the radius of the rational surface and that the perturbation amplitude is constant in the radial direction. The latter assumption indicates that the island width is small in comparison to the radial size of the region where the perturbation current is localized. The calculations carried out for four model magnetic field configurations show that the geometry of the magnetic islands depends on the extent to which the perturbation current is localize and that the width of the magnetic islands is smaller than that calculated from the familiar relationship. The larger the perturbation amplitude, the greater this difference: it may be as large as 25% for the strong perturbations arising during disruptions. The calculations are based on the solution of the geometric problem of constructing the lines of the magnetic field determined by the given distributions of the initial current and perturbation current; the equilibrium equation is not considered. The question of the direction of the perturbation current within the island relative to the direction of the initial unperturbed current is discussed. The perturbation current flowing in an island is directed opposite to the initial current with a radially decreasing density; for this reason, such an island can naturally be called a “negative” island. Together with the formation of negative islands, the formation of “positive” ones is also considered. The latter are shown to form under the following conditions: the perturbation current density should be higher than the density of the current that produces the unperturbed field and the perturbation current itself should be localized in a sufficiently narrow radial layer. The positive islands are smaller in size than negative ones.     

Influence of the magnetic fields on frog sciatic nerve

The constant magnetic field (1000–7120 gauss) was applied to previously stimulated frog sciatic nerve. The following was observed : a) There is no instantaneous effect of either parallel or perpendicular magnetic field on compound action potential amplitude. b) Parallel magnetic field of 1000–7120 gauss does not change the amplitude of compound action potential significantly with time. c) When perpendicular magnetic field was applied to the nerve, an increase in the amplitude of compound action potential was observed, which can mean that the nerve exhibits some sort of magnetic anisotropy.     

Effects of non-uniform static magnetic fields on the rate of myosin phosphorylation

The effect on myosin phosphorylation from exposure to a magnetic field generated by an array of four permanent magnets was investigated. Two lateral positions in the non-uniform field over the array were explored, each at four vertical distances over the surface of the device. The rate of myosin phosphorylation was found to depend on the position laterally over the array as well as the distance from the device surface. The square magnet array was comprised of axially magnetized, cylindrical NdFeB permanent magnets arranged with poles of alternating polarity in a plane (MagnaBloc trade mark therapeutic device). Detailed dosimetry of the magnet array was compiled: the magnetic flux density averaged over the exposure volume spanned the range 0.7-86 mT for the eight different exposure positions. The corresponding range for the absolute field gradient was 0.4-20 T/m. Comparing the dosimetry to the experimental outcome, our results imply that magnetic field amplitude alone is not sufficient to describe the influence of the field in this preparation.     

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.     

Modeling of antibiotics production in magneto three-phase airlift fermenter

A mathematical model is developed to describe the performance of a three-phase airlift reactor utilizing a transverse magnetic field. The model is based on the complete mixing model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase airlift reactor with P. chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At relatively high magnetic field intensities a certain discrepancy in the model solution was observed when the model over estimates the product concentration.     

A Lorentz model for weak magnetic field bioeffects: Part I—Thermal noise is an essential component of AC/DC effects on bound ion trajectory

We have previously employed the Lorentz–Langevin model to describe the effects of weak exogenous magnetic fields via the classical Lorentz force on a charged ion bound in a harmonic oscillator potential, in the presence of thermal noise forces. Previous analyses predicted that µT‐range fields give rise to a rotation of the oscillator orientation at the Larmor frequency and bioeffects were based upon the assumption that the classical trajectory of the bound charge itself could modulate a biochemical process. Here, it is shown that the thermal component of the motion follows the Larmor trajectory. The results show that the Larmor frequency is independent of the thermal noise strength, and the motion retains the form of a coherent oscillator throughout the binding lifetime, rather than devolving into a random walk. Thermal equilibration results in a continual increase in the vibrational amplitude of the rotating oscillator towards the steady‐state amplitude, but does not affect the Larmor orbit. Thus, thermal noise contributes to, rather than inhibits, the effect of the magnetic field upon reactivity. Expressions are derived for the ensemble average of position and the velocity of the thermal component of the oscillator motion. The projection of position and velocity onto a Cartesian axis measures the nonuniformity of the Larmor trajectory and is illustrated for AC and combined AC/DC magnetic fields, suggesting a means of interpreting resonance phenomena. It is noted that the specific location and height of resonances are dependent upon binding lifetime and initial AC phase. Bioelectromagnetics 30:462–475, 2009. © 2009 Wiley‐Liss, Inc.     

Magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions

The feasibility of magnetic field perturbations as a tool for controlling enzyme-regulated and oscillatory biochemical reactions is studied. Our approach is based on recent experimental results that revealed magnetic field effects on the in vitro activity of enzyme systems in accordance with the radical pair mechanism. A minimum model consisting of two coupled enzyme-regulated reactions is discussed that combines, in a self-consistent manner, magnetic field-sensitive enzyme kinetics with non-linear dynamical principles. Furthermore, a simple detector mechanism is described that is capable of responding to an oscillatory input. Results reveal that moderate-strength magnetic fields (B=1-100 mT) may effectively alter the dynamics of the system. In particular, a response behavior is observed that depends on: (1) the combination of static and time-varying magnetic fields; (2) the field amplitude; and (3) the field frequency in a non-linear fashion. The specific response behavior is critically determined by the biochemical boundary conditions as defined by the kinetic properties of the system. We propose an experimental implementation of the results based on the oscillatory peroxidase-oxidase reaction controlled by the enzyme horseradish peroxidase.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Antibiotics production in a fluidized bed reactor utilizing a transverse magnetic field

A mathematical model is developed to describe the performance of a three-phase fluidized bed reactor utilizing a transverse magnetic field. The model is based on the axially dispersed plug flow model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase fluidized bed reactor with Penicillium chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At low and relatively high magnetic field intensities certain discrepancy in the model solution is observed when the model over estimates the product concentration.     

Effect of various physical factors on oscillations of light-dispersion in water and aqueous biopolymer solutions

Study of the dependence of light scattering fluctuation on temperature, mechanic perturbation and magnetic field in water and water hemoglobin and DNA solution has shown that an increase in temperature results in the decline of long-term fluctuation amplitude and in the increase of short-term fluctuation amplitude. Mechanical mixing removes long-term fluctuations and over 10 hours are spent for their recovery. Regular fluctuations appear when the constant magnetic field above 240 A/m is applied; the fluctuations are retained for many hours after the removal of the field (when the field is off). It was supposed that maintenance of long-range correlation of molecular rotation-translation fluctuation by the effect of long-range forces and external fields underlies the mechanism of long-term light scattering fluctuations.     

Influence of 50 Hz-1 mT magnetic field on human median nerve

In this study, human median nerve was exposed to power frequency magnetic fields in order to provide clarification for possibly changeable nerve conduction mechanism. The nerve was exposed to 50 Hz magnetic field by utilizing a special Helmholtz applicator. The experiments were carried out with six healthy human-volunteers. Median motor distal amplitude/proximal amplitude ratios were recorded from adult human median nerve pre-exposure, during, and post-exposure to a 50 Hz, 1 mT magnetic field. The result of 18 measurements shows that median motor distal amplitude/proximal amplitude ratio significantly decreases in pre-exposure state as compare to post exposure of which. The results of this study may be useful for some nerve rehabilitation, excitation, and stimulation in more effective/safe physical therapy. Additionally, 50 Hz, 1 mT sinusoidal magnetic field should not be recognizing as safe for conduction mechanism on a nerve. These mechanisms would be cleared by new advanced engineering models in other future works.     

Dependence of effects of weak combined low-frequency variable and constant magnetic fields on the intensity of asexual reproduction of planarians Dugesia tigrina on the magnitude of the variable field

It was shown that the stimulating effect of weak combined magnetic fields (constant component 42 microT, frequency of the variable component 3.7 Hz) on the division of planarians depends on the amplitude of the variable component of the field. The effect is particularly pronounced at 40 (the main maximum), 120, 160, and 640 nT. Narrow ranges of effective amplitudes alternate in some cases with equally narrow ranges in which the system does not respond to he treatment. In the range of super weak amplitudes of the variable field (0.1 and 1 nT), the stimulating effect is poorly pronounced. The data obtained indicate the presence of narrow amplitude windows in the response of the biological systems to weak and super weak magnetic fields. In a special series of experiments, it was shown that the effect of fields on planarians is partially mediated via aqueous medium preliminarily treated with weak magnetic fields. It is noteworthy that in experiments with water treated with weak magnetic fields, there were no pronounced maxima and minima in the magnitude of the effect in the range of amplitude of the variable magnetic field from 40 to 320 nT.     

Analysis of the structure of magnetic fields that induced inhibition of stimulated neurite outgrowth

The important experiments showing nonlinear amplitude dependences of the neurite outgrowth in pheochromocytoma nerve cells due to ELF magnetic field exposure had been carried out in a nonuniform ac magnetic field. The nonuniformity entailed larger than expected variances in magnetic field magnitudes associated with specific levels of biological effects, thereby evoking a question about validity of the interpretations formulated for the case of a uniform field. In this work, we calculate the relative value of nonuniformity and deviations in ac magnetic field. It is shown that these factors do not affect the main conclusion in the original papers about the form of the amplitude dependence of the observed biological effect.     

不同时变磁场对神经纤维的诱导刺激作用的仿真研究

利用神经纤维的无源电缆模型描述神经纤维在磁刺激下的阈下行为,通过数字仿真得出了神经纤维在不同频率的磁刺激感应电场作用下阈下膜电位的时间特征包括波形和幅度,发现高频的感应电场诱导作用下得到的膜电位幅值小于低频电场的性质。同时采用积分变换频域分析的方法,得出了在不同空间分布的感应电场诱导刺激作用下神经纤维的响应特性,发现和低频比较,高频的空间分布函数频率成分的感应电场诱导得到的膜电位幅值较低。计算出在刺激线圈中采用典型刺激电流作用下在神经纤维响应得到的膜电位的特征。从时空两域阐述神经纤维对不同时变磁场诱导作用下的阈下响应行为,对磁刺激仪中刺激线圈的刺激电流的选择和线圈尺寸的设计都具有指导意义。     

A new study of bacterial motion: superconducting quantum interference device microscopy of magnetotactic bacteria.

The recently developed "microscope" based on a high-Tc dc SQUID (superconducting quantum interference device) is used to detect the magnetic fields produced by the motion of magnetotactic bacteria, which have permanent dipole moments. The bacteria, in growth medium at room temperature, can be brought to within 15 micron of a SQUID at liquid nitrogen temperature. Measurements are performed on both motile and nonmotile bacteria. In the nonmotile case, we obtain the power spectrum of the magnetic field noise produced by the rotational Brownian motion of the ensemble of bacteria. Furthermore, we measure the time-dependent field produced by the ensemble in response to an applied uniform magnetic field. In the motile case, we obtain the magnetic field power spectra produced by the swimming bacteria. Combined, these measurements determine the average rotational drag coefficient, magnetic moment, and the frequency and amplitude of the vibrational and rotational modes of the bacteria in a unified set of measurements. In addition, the microscope can easily resolve the motion of a single bacterium. This technique can be extended to any cell to which a magnetic tag can be attached.     

What is the time scale of magnetic field interaction in biological systems?

An experimental test constraining the intrinsic time scale of a primary physical mechanism that detects extremely-low-frequency (ELF) magnetic fields in biological systems is proposed. The suggested test postulates that a transductive mechanism operating on time scales much shorter than the period of an applied magnetic field cannot obtain any information about the exposure conditions other than the absolute magnitude of the field. By generating field exposures that differ in their vector properties but are equivalent in their time-varying absolute amplitude, it is possible to differentiate between two broad classes of mechanisms: 1) those with intrinsic time scales comparable with or longer than those of the external influence, and 2) those that are much faster than the period of the applied field. The hypothesis assumes an experimental model proven to respond to magnetic fields and sensitive to a change of about a factor of two in one of the field parameters (AC, DC amplitude or frequency). The case of general linearly polarized fields is discussed, and an analytical solution for the case of perpendicular AC/DC fields is given. Bioelectromagnetics 18:244–249, 1997 © 1997 Wiley-Liss, Inc.     

Effect of static magnetic fields on bioelectric properties of the Br and N1 neurons of snail Helix pomatia

The effects of 2.7 mT and 10 mT static magnetic fields were investigated on two identified neurons with different bioelectric properties of the snail Helix pomatia. Membrane resting potential, amplitude, spiking frequency, and duration of action potential were measured. The two neurons of H. pomatia, parabolic burster Br and silent N₁, showed different responses to a static magnetic field. The magnetic field of 2.7 mT intensity caused changes in the amplitude and duration of action potential of the Br neuron, whereas the 10 mT magnetic field changed the resting potential, amplitude spike, firing frequency, and duration of action potential of the Br neuron. Bioelectric parameters measured on the N₁ neuron did not change significantly in these magnetic fields.     

Nifedipine is an antagonist to cyclotron resonance enhancement of Ca incorporation in human lymphocytes

The incorporation of 45Ca in mixed human lymphocytes was measured following one-hour exposures of the cells to combined steady and periodic magnetic fields designed to probe for cyclotron resonance response in calcium incorporation. Measurements were made as a function of magnetic field frequency, up to 30 Hz, and as a function of magnetic field amplitude, up to 1.5 x 10(-4) Trms. The amplitude measurements demonstrated that the relative 45Ca uptake at resonance follows different mechanisms of interaction above and below 0.2 x 10(-4) Trms. After adjusting the magnetic field configuration for maximum incorporation, we then determined the effects of the calcium influx blocker nifedipine on 45Ca incorporation, with and without simultaneous exposure to this specific magnetic field combination. The presence of nifedipine in both unexposed and exposed cell suspensions resulted in decreased 45Ca uptake, presumably through the slow inward calcium channels. Evidence was found suggesting that nifedipine acts antagonistically to the 45Ca cyclotron resonance tuning signal.     

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

Determination of the resonant harmonics of the error field from dynamic magnetic measurements in a tokamak

The possibility is discussed of determining the amplitude and phase of a static resonant error field in a tokamak by means of dynamic magnetic measurements. The method proposed assumes measuring the plasma response to a varying external helical magnetic field with a small (a few gauss) amplitude. The case is considered in which the plasma is probed by square pulses with a duration much longer than the time of the transition process. The plasma response is assumed to be linear, with a proportionality coefficient being dependent on the plasma state. The analysis is carried out in a standard cylindrical approximation. The model is based on Maxwell’s equations and Ohm’s law and is thus capable of accounting for the interaction of large-scale modes with the conducting wall of the vacuum chamber. The method can be applied to existing tokamaks.