Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

The role of the bootstrap and polarization currents for the stability of neoclassical tearing modes is investigated employing both a drift kinetic and a gyrokinetic approach. The adiabatic response of the ions around the island separatrix implies, for island widths below or around the ion thermal banana width, density flattening for islands rotating at the ion diamagnetic frequency, while for islands rotating at the electron diamagnetic frequency the density is unperturbed and the only contribution to the neoclassical drive arises from electron temperature flattening. As for the polarization current, the full inclusion of finite orbit width effects in the calculation of the potential developing in a rotating island leads to a smoothing of the discontinuous derivatives exhibited by the analytic potential on which the polarization term used in the modeling is based. This leads to a reduction of the polarization-current contribution with respect to the analytic estimate, in line with other studies. Other contributions to the perpendicular ion current, related to the response of the particles around the island separatrix, are found to compete or even dominate the polarization-current term for realistic island rotation frequencies.     

Suppression of the neoclassical tearing modes in tokamaks under anomalous transverse transport conditions when the magnetic well effect predominates over the bootstrap drive

A study is made of the suppression of neoclassical tearing modes in tokamaks under anomalous transverse transport conditions when the magnetic well effect predominates over the bootstrap drive. It is stressed that the corresponding effect, which is called the compound suppression effect, depends strongly on the profiles of the electron and ion temperature perturbations. Account is taken of the fact that the temperature profile can be established as a result of the competition between anomalous transverse heat transport, on the one hand, and longitudinal collisional heat transport, longitudinal heat convection, longitudinal inertial transport, and transport due to the rotation of magnetic islands, on the other hand. The role of geodesic effects is discussed. The cases of competition just mentioned are described by the model sets of reduced transport equations, which are called, respectively, collisional, convective, inertial, and rotational plasmophysical models. The magnetic well is calculated with allowance for geodesic effects. It is shown that, for strong anomalous heat transport conditions, the contribution of the magnetic well to the generalized Rutherford equation for the island width W is independent of W not only in the collisional model (which has been investigated earlier) but also in the convective and inertial models and depends very weakly (logarithmically) on W in the rotational model. It is this weak dependence that gives rise to the compound effect, which is the subject of the present study. A criterion for the stabilization of neoclassical tearing modes by the compound effect at an arbitrary level of the transverse heat transport by electrons and ions is derived and is analyzed for two cases: when the electron heat transport and ion heat transport are both strong, and when the electron heat transport is strong and the ion heat transport is weak.     

Analytical solutions for global geodesic acoustic modes in tokamak plasmas

Analytical solutions for global geodesic acoustic modes in the plasma of a tokamak with circular concentric magnetic surfaces are obtained. In the framework of ideal magnetohydrodynamics, an integral equation for eigenvalues (dispersion relation) taking into account toroidal coupling between electrostatic perturbations and electromagnetic perturbations with the poloidal mode number |m| = 2 is derived. In the absence of such coupling, the dispersion relation yields only the standard continuous spectrum. The existence of a global geodesic acoustic mode is analyzed for equilibria with both on-axis and off-axis maxima of the local geodesic acoustic frequency. The analytical results are compared with results of numerical calculations.     

A possible interpretation of the zebra pattern in solar radiation

The nature of the zebra pattern in continual type-IV solar radio bursts is discussed. It is shown that, when a weakly relativistic monoenergetic proton beam propagates in a highly nonisothermal plasma, the energy of the slow beam mode can be negative and explosive instability can develop due to the interaction of the slow and fast beam modes with ion sound. Due to weak spatial dispersion, ion sound generation is accompanied by cascade merging, which leads to stabilization of explosive instability. The zebra pattern forms due to the scattering of fast protons by ion sound harmonics. The efficiency of the new mechanism is compared with that of previously discussed mechanisms.     

Drift stabilization of internal resistive-wall modes in tokamaks

The problem of drift stabilization of the internal resistive-wall modes (RWMs) in tokamaks is theoretically investigated. The basic assumption of the model is that, when the drift effects are neglected, these modes are unstable in the absence of a conducting wall and stable in the presence of a close-fitting perfectly conducting wall. In the former case, the instability condition is expressed as Δ′_∞>0, where Δ′_∞ is the matching parameter calculated under the assumption that the wall is removed to infinity. In the latter case, one has Δ _W ^′ <0, where Δ _W ^′ is the external matching parameter of tearing modes calculated assuming a perfectly conducting wall at the plasma boundary. In the case with a resistive wall, the relevant parameter can be either Δ′_∞ or Δ _W ^′ , depending on whether the value of the dimensionless parameter ωτ_s/2m is small or large, respectively (here ω is the mode frequency, τ_s is the resistive time constant of the wall, and m is the poloidal mode number). In the presence of drift effects, the mode frequency ω is approximately equal to the electron drift frequency, ω≈ω_*e. The value of the parameter ω_*eτ_s/2m, which therefore determines the behavior of internal RWMs, is estimated for several existing tokamaks, namely, AUG (ASDEX-Upgrade), DIII-D, JET, TFTR, and JT-60U, as well as for the projected ITER-FEAT. It is shown that, although drift effects do not stabilize internal RWMs in current devices, they should be efficient in suppressing these modes in reactor-grade tokamaks.     

Geodesic acoustic modes in noncircular cross section tokamaks

The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.     

On the dispersion of geodesic acoustic modes

The problem of dispersion of geodesic acoustic modes is revisited with two different methods for the solution of the kinetic equation. The dispersive corrections to the mode frequency are calculated by including the m = 2 poloidal harmonics. Our obtained results agree with some earlier results but differ in various ways with other previous works. Limitations and advantages of different approaches are discussed.     

Nonlinear damping of zonal flows

The modulatonal instability theory for the generation of large-scale (zonal) modes by drift modes has been extended to the second order including the effects of finite amplitude zonal flows, ? _q . The nonlinear (second-order) sidebands are included in the perturbative expansion to derive the nonlinear equation for the evolution of ? _q . It is shown that effects of finite ? _q reduce the growth rate of zonal flow with a possibility of oscillatory regimes at a later stage.     

Chemostat-cultivated Escherichia coli at high dilution rate: multiple steady states and drift

The representation of metabolic network reaction kinetics in a scaled, polynomial form can allow for the prediction of multiple steady states. The polynomial formalism is used to study chemostat-cultured Escherichia coli which has been observed to exhibit two multiple steady states under ammonium ion-limited growth conditions: a high cell density-low ammonium ion concentration steady state and a low cell density-high ammonium ion concentration steady state. Additionally, the low-cell-density steady state has been observed to drift to the high-cell-density steady state. Inspection of the steady-state rate expressions for the ammonium ion transport/assimilation network (in polynomial form) suggests that at low ammonium ion concentrations, two steady states are possible. One corresponds to heavy use of the glutamine synthetase-glutamate synthase (GLNS-GS) branch and the second to heavy use of the glutamate dehydrogenase (GDH) branch. Realization of the predicted intracellular steady states is also found to be dependent on the parameters of the transport process. Moreover, the two steady states differ in where their energy intensity lies. To explain the drift, GLNS, which is inducible under low ammonium ion concentrations, is suggested to be a "memory element." A chemostat-based model is developed to illustrate that perturbations in dilution rate can lead to drift between the two steady states provided that the disturbance in dilution rate is sufficiently large and/or long in duration.     

Eigenmode Decomposition of the Near-Field Enhancement in Localized Surface Plasmon Resonances of Metallic Nanoparticles

I present a direct and intuitive eigenmode method that evaluates the near-field enhancement around the surface of metallic nanoparticles of arbitrary shape. The method is based on the boundary integral equation (BIE) in the electrostatic limit. Besides the nanoparticle polarizability and the far-field response, the near-field enhancement around nanoparticles can be also conveniently expressed as an eigenmode sum of resonant terms. Moreover, the spatial configuration of the near-field enhancement depends explicitly on the eigenfunctions of both the BIE integral operator and of its adjoint. It has also established a direct physical meaning of the two types of eigenfunctions. While it is well known that the eigenfunctions of the BIE operator are electric charge modes, it is less known and used that the eigenfunctions of the adjoint represent the electric potential generated by the charge modes. For the enhanced spectroscopies, the present method allows an easy identification of hot spots which are located in the regions with maximum charge densities and/or regions with fast variations of the electric potential generated by the charge modes on the surface. This study also clarifies the similarities and the differences between the far-field and the near-field behavior of plasmonic systems. Finally, the analysis of concrete examples like the nearly touching dimer, the prolate spheroid, and the nanorod illustrate some modalities to improve the near-field enhancement.     

Spectroscopic Investigation of Local Mechanical Impedance of Living Cells

We studied nanoscale mechanical properties of PC12 living cells with a Force Feedback Microscope using two experimental approaches. The first one consists in measuring the local mechanical impedance of the cell membrane while simultaneously mapping the cell morphology at constant force. As the interaction force is increased, we observe the appearance of the sub-membrane cytoskeleton. We compare our findings with the outcome of other techniques. The second experimental approach consists in a spectroscopic investigation of the cell while varying the tip indentation into the membrane and consequently the applied force. At variance with conventional dynamic Atomic Force Microscopy techniques, here it is not mandatory to work at the first oscillation eigenmode of the cantilever: the excitation frequency of the tip can be chosen arbitrary leading then to new spectroscopic AFM techniques. We found in this way that the mechanical response of the PC12 cell membrane is found to be frequency dependent in the 1 kHz - 10 kHz range. In particular, we observe that the damping coefficient consistently decreases when the excitation frequency is increased.     

Global modes of flute instability of a rotating cylindrical plasma

The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of one-fluid magnetohydrodynamics. The dispersion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azimuthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the displacement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated.     

Stability of hybrid modes of a single-component electron plasma containing an admixture of background gas ions

The spectrum of eigenmodes of a waveguide completely filled with a cold electron plasma containing a small admixture of ions produced due to electron-impact ionization of background gas atoms is calculated numerically. The calculations were performed within the entire range of allowable values of the radial electric and longitudinal magnetic fields for both magnetized and unmagnetized ions by using the earlier derived nonlocal dispersion relation [Plasma Phys. Rep. 36, 563 (2010)]. The spectrum consists of three families of electron modes with frequencies equal to the Doppler-shifted upper and lower hybrid frequencies and modified ion cyclotron (MIC) modes. When the Doppler shift caused by electron rotation in the crossed electric and magnetic fields compensates for the hybrid frequency, the electron modes become low-frequency modes and interact with the ion modes. For m = 1, only the lower hybrid modes can be low-frequency ones, whereas at m ≥ 2, both lower and upper hybrid modes can be low-frequency ones. The spectrum of modes having the azimuthal number m = 2 is thoroughly analyzed. It is shown that, in this case, the lower hybrid modes behave similar to the m = 1 modes. The dispersion curves of the upper hybrid modes intersect with all harmonics of the MIC frequency (positive, negative, and zero) and are unstable in the vicinities of the intersections. The maximum value of the instability growth rate is several times higher than the ion plasma frequency. The MIC modes are unstable within a wide range of the field strengths, and their growth rates are two orders of magnitude slower. Instabilities are caused by the relative motion of electrons and ions (the transverse current) and the anisotropy of the ion distribution function.     

随机漂移亚群体等位基因频率分布的假定及在DNA指纹数据中的应用

研究影响计算两ＤＮＡ指纹偶然匹配率的亚群体结构,首次提出随机漂移各亚群体单个位点等位基因频率服朋参数为（ｐ１（１－θ）／θ,ｐ２（１－θ）／θ,…ｐｍ（１－θ）／θ）的Ｄｉｒｉｃｈｌｅｔ分布的假定（ｐ１,ｐ２,…,ｐｍ为随机漂移初始频率,θ为近交系数）,证明依分布产生亚群体,其结构、性质与群体遗传理论、样本理论一致;将该分布应用于ＤＮＡ指纹数据,得到了其它方法的类似结论。     

Ponderomotive force of the low-frequency field and modulational instability of drift waves

A study is made of the processes that occur in an inhomogeneous nonisothermal plasma in a strong external magnetic field and whose characteristic frequencies are lower than the ion Langmuir frequency but higher than the collision frequency. An expression for the ponderomotive force of the low-frequency field is derived. The excitation of a long-wavelength low-frequency drift wave during the development of the modulational instability of a drift pump wave is investigated. The growth rates of the instability are obtained, and the conditions for its onset are determined. The possible relation of the modulational instability to the formation of structures in the plasma is discussed.     

Progress in theory of instabilities in a rotating plasma

A review is given of the basic results of modern theory of instabilities in a rotating plasma. Both axisymmetric and nonaxisymmetric perturbations are considered. Main attention is given to the magnetorotational instability (MRI), discovered earlier by Velikhov, and the rotational-convective instability (RCI) discussed in a number of papers of astrophysical trend. For qualitative explanation of the results, a local approach is used which, with equilibrium plasma pressure gradient and/or nonsymmetry of perturbations, requires operation with nonlocal azimuthal perturbed magnetic field. The gravity and effects of pressure anisotropy are taken into account. In addition to hydrodynamic, the electrodynamic approach is formulated. The drift effects are considered. Analyzed are the ideal instabilities and those depending on the dissipative effects: viscosity and heat conductivity. The MRI is considered at presence of the charged dust particles. Besides the local approach, the nonlocal approach is formulated for the plasma model with a steplike profile of angular rotation frequency. Alongside with perturbations which frequencies are small compared to the ion cyclotron frequency, the perturbations are analyzed with frequencies larger than the ion cyclotron frequency. The latter corresponds to the Hall regime and subregime of nonmagnetized plasma.     

Excitation of a magnetospheric MHD cavity by Kelvin-Helmholtz instability

The Kelvin-Helmholtz instability is investigated analytically by using a one-dimensional nonuniform model of the Earth’s magnetosphere and the adjacent solar wind region. Its properties are shown to be essentially governed by the presence of an MHD cavity that arises in the magnetosphere because of the non-uniformity of the latter and also because of the jump in the parameters of the medium at the magnetopause (the outer boundary of the magnetosphere). System oscillations constitute a discrete spectrum of eigenmodes, which are determined by the wave vector k _t along the tangential discontinuity and also by the mode number n = 0, 1, 2, …, playing the role of the wavenumber along a coordinate normal to the magnetopause. Analytic expressions are obtained for the frequency and instability growth rate of each eigenmode and for the functions describing its spatial structure. All these quantities depend parametrically on the solar wind velocity V _W , or more precisely, on the Doppler frequency shift ω _W = k _t · V _W . For each eigenmode, there is a lower instability threshold depending on the parameter ω _W and a sharp maximum in the growth rate at the eigenfrequency of the magnetospheric cavity. For ω _W values below the threshold, the properties of an eigenmode are highly sensitive to the type of solar wind nonuniformity. Three cases are considered: a uniform solar wind and solar winds in which the speed of sound increases or decreases away from the magnetopause.     

Possible fundamental unity of magnetobiological "resonances"

Organisms exposed to a combination of weak, parallel directed static and alternate magnetic fields show a distinct response when the frequency of the alternate component is formally equal to the cyclotron frequencies for Ca2+ or other biologically important ions. It is impossible to explain the observable phenomenon through a magnetoinduced drift of the ions, as the Lorentz's force is too small to change ionic movements. In similar conditions, a resonance-like response arises when the alternate field is tuned to the Larmor frequency for nuclear-spin magnetic moments. The mechanism of these phenomena is also still unclear. In the report, the arguments are presented to treat both types of effects in a single context for which the existence of ion magnetic dipoles is postulated.     

Swarming behaviour of the mosquito Culex pipiens quinquefasciatus: a quantitative analysis

ABSTRACT. Analysis of video recordings of Culex pipiens quinquefasciatus Say swarms showed that the overall swarming patterns of males and virgin females are similar, even though the short-term characteristics of their flight, such as speed and turning angle, differ. This suggests they have the same response to the visual cue of the swarm 'marker'. The swarming pattern of an individual consists of elliptical loops which, in the short-term, define an area smaller than the swarm as a whole. The foci of these ellipses drift gradually with respect to the marker; individuals do not seem to have preferred positions within the swarm, but drift at random. Male mosquitoes identify and locate females by the sound of their wing-beats. Diffuse sound at the wing-beat frequency of female C.p. quinquefasciatus (500–600 Hz) caused males within the swarm to slow down significantly. Their turning behaviour remained unchanged, so the ellipses decreased in size. The swarm as a whole collapsed into a smaller volume, centred over the marker. Apparently, the response of males to sound consists of at least two parts: initially they alter their flight speed, and then alter their turning behaviour once they have located the source of the sound.     

RF absorption involving biological macromolecules

The fundamental intramolecular frequency of a globular protein can be obtained from the measurements of acoustic velocities of bulk protein matter. This lowest frequency for common size molecules is shown to be above several hundred GHz. All modes below this frequency would then be intermolecular modes or bulk modes of the molecule and surrounding matter or tissue. The lowest frequency modes of an extended DNA double helix are also shown to be bulk modes because of interaction with water. Only DNA modes, whose frequency is well above 4 GHz, can be intrahelical modes, that is, confined to the helix rather than in the helix plus surroundings. Near 4 GHz, they are heavily damped and, therefore, not able to resonantly absorb. Modes that absorb radio frequency (RF) below this frequency are bulk modes of the supporting matter. Bulk modes rapidly thermalize all absorbed energy. The implication of these findings for the possibility of athermal RF effects is considered. The applicability of these findings for other biological molecules is discussed.