Beta-limiting MHD phenomena in toroidal systems

Equilibrium effects, neoclassical tearing modes, and resistive wall modes are discussed as phenomena limiting attainable plasma pressure, with emphasis on the current progress in theoretical studies at the Kurchatov Institute. The review is based on the results presented at the 11th International Congress on Plasma Physics (Sydney, 2002).     

Some problems of axisymmetric toroidal equilibria in orthogonal flux coordinates

Formulations of axisymmetric equilibrium problems are presented in orthogonal flux coordinates with boundary conditions that do not assume fixation of the boundary shape for both levitron-type traps with a plasma-embedded conductor and conductor-free configurations, including a tokamak. Illustrative examples of numerical solutions of these problems are presented. For traps with a conductor, it is demonstrated how the geometry of the equilibrium with an isodynamic magnetic surface can be found using flux coordinates.     

MHD plasma stability in alternative toroidal systems and the local dispersion relation

The local dispersion relation obtained for an inhomogeneous anisotropic high-pressure plasma in the Chew-Goldberger-Low approximation is used to qualitatively study small-scale MHD plasma instabilities in alternative magnetic configurations in which the plasma compressibility plays a significant stabilizing role. It is established that it is important to satisfy the Bernstein-Kadomtsev condition in order to reduce the growth rate of the quasi-flute oscillations. Moderate plasma anisotropy is shown not to have a substantial destabilizing effect on the MHD plasma stability under the Bernstein-Kadomtsev condition in alternative systems. The situation in which the electron compressibility vanishes while the ion compressibility is nonzero is discussed; it is shown that, in this situation, the Bernstein-Kadomtsev condition becomes more stringent as the longitudinal wavenumber increases.     

Tearing instability of a force-free magnetic configuration in a collisionless plasma

The equilibrium and stability of a sheared force-free magnetic field in a collisionless plasma are investigated, and the main features of charged particle motion in such a field are analyzed. A steady solution is derived to the Vlasov-Maxwell equations for the charged particle distribution function that describes different equilibrium configurations. The tearing instability of the magnetic field configurations is studied both analytically and by particle-in-cell simulations.     

Choice of coordinates on a toroidal magnetic surface

Construction of global angular coordinates on an arbitrarily shaped toroidal surface is considered. It is shown that global orthogonal, isothermal, and semigeodesic geometric coordinates can always be introduced on a toroidal surface. Such coordinates can be rather efficient in solving problems of plasma equilibrium and stability in a magnetic field. At the same time, it is impossible to introduce global geodesic coordinates and coordinates based on curvature lines. It is proposed to use a magnetic analogy to search for transformations of global angular geometric coordinates that simplify the expression for the length element on an arbitrary toroidal surface. An algorithm for the computation of such coordinates is offered. With this approach, a “virtual” magnetic field such that its force lines, as well as the lines orthogonal to them, are closed is searched for on the toroidal surface. These lines comprise a geometric coordinate grid on an actual magnetic surface formed by the actual magnetic field.     

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U₀. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2v_T/R (where v_T is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ? of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.     

Construction of a toroidal model for the magainin pore

Magainins are natural peptides that selectively kill bacteria at concentrations that are harmless to animal cells. Due to a positive charge and distinct hydrophobic moment, magainins in the alpha-helical conformation interact favorably with bacterial membrane lipids. These interactions lead to the formation of large openings in the membrane and to the cell's death. The openings (toroidal pores) are supramolecular structures consisting of lipid and peptide molecules. A computer model of the pore in a bacterial membrane was constructed (see Figure) for the study of the molecular basis for magainin selectivity and specificity. Details of the construction and the preliminary equilibration of the pore model are given in this paper.     

Formation of plasma and gaseous toroidal vortices in air

The mechanism for the formation of high-temperature (plasma) vortices and low-temperature vortex rings produced by ejecting pulsed subsonic plasma/gas jets into air was investigated experimentally. A toroidal vortex forms due to the interaction between a pulsed jet with the flow induced by this jet in the ambient medium. By analyzing the experimental data and conservation laws, an equation is derived that allows one to determine the initial propagation velocity of the vortex as a function of the characteristics of the vortex generator and the ambient medium. The results obtained by solving this equation agree well with the experimental data.     

Three-dimensional MHD simulations of forced magnetic reconnection

Results are presented from MHD simulations of three-dimensional flows of a high-conductivity plasma in the vicinity of a null point of a magnetic field. The excitation of an electric current at the boundary of the computation region results in self-consistent plasma flows and change in the structure of the magnetic field. Generally, in the vicinity of a null point, an MHD singularity arises that manifests itself in the formation of locally plane current sheets. It is shown that the current sheet can be oriented either along the separatrix surface of a magnetic configuration or perpendicular to it, except for axisymmetric configurations (or close to them), when the excitation of an electric current in the direction orthogonal to the separatrix surface does not lead to the formation of a current sheet.     

On the toroidal condensed state of closed circular DNA

The influence of double helix torsional elasticity on the compaction and structure of circular DNA compact form is studied theoretically in the case when the compact (globular) form has torus shape. For closed circular DNA the topological invariant, the linking number, yields a strict connection between conformation of the double helix considered as unifilar homopolymer and elastic energy of torsional twisting. The contribution of torsional elasticity to the free energy of the toruslike globule is calculated. This contribution is shown to be proportional to the square of superhelical density. Allowance of the torsional elasticity decreases the equilibrium radius of the toruslike globule formed by circular DNA. Closure of linear DNA into a ring widens the stability range of the relatively short DNA compact form and tightens it for long DNA.     

Thermodynamic equilibria of cholesterol-detergent-water.

Cholesterol monomer is incorporated into alkyl sulfate micelles with a unitary free energy of -10.3 kcal/mol. This experimental free energy is in good agreement with that predicted by our previous determination of the hydrophobicity of the sterol suggesting that the partitioning is primarily hydrophobic with little or no contribution to the free energy from head group interactions in this system. The intrinsic hydrophobicity of cholesterol is shown to be insufficient for effective partitioning of the sterol between micelles (or bilayers) and its own self-associated form. This finding strongly supports a model of phospholipid-cholesterol interaction involving significant free energy contributions from head group effects such as alterations in hydrogen bonds or hydration. Since these head group contributions are not observed in the cholesterol-alkyl sulfate system, one concludes that there is a high degree of specificity of interaction between the sterol OH and polar moieties of other amphiphilic molecules.     

Association-dissociation equilibria of Octopus hemocyanin

The equilibria between the native (decameric) Octopus hemocyanin and its subunits were studied by analytical sedimentation. Equilibrium is obtained slowly, but the reaction is thermodynamically reversible. The mass action law for a monomer-decamer reaction is obeyed. The reassociated hemocyanin is virtually identical in its sedimentation behavior and oxygen binding with the native protein. The association-dissociation equilibria are mediated by cations; Mg2+, Ca2+, Na+, and H+ are all effective in stabilizing the decameric form at appropriate concentrations. About three to four cations per monomer must be bound for association to occur. Under some conditions, dimers of the subunits can be observed, but formation of this dimer does not depend on cation concentration, and it does not appear to be an obligate intermediate in the association to decamer.     

Modeling of the parametric dependence of the edge toroidal rotation

Modeling of the edge toroidal rotation and its dependence on the edge plasma parameters is performed by means of the B2SOPS5.0 transport code for ohmic shots both for MAST and ASDEX Upgrade configurations. The impact of plasma current, toroidal magnetic field, plasma density, and temperature is investigated. The connection between the toroidal rotation and edge radial electric field is also studied. The results of the simulation are consistent with the parametric dependence predicted analytically. Published in Russian in Fizika Plazmy, 2008, Vol. 34, No. 9, pp. 791–797. The text was submitted by the authors in English.     

Recent examples of novel secondary metabolites

Modern trends in the detection, isolation and characterization of leads for novel therapeutic compounds are reviewed. Some current biological test systems (immunological, chemical, enzymic, receptor,etc.) and examples of their successful application are highlighted including the structures of selected novel and prospective metabolites. Dedicated to Dr. Z. Vaněk on the occasion of his 70th birthday     

"研究性学习"设计二例

结合《双子叶植物气孔类型观察》和《空气中细菌污染的监测》活动项目,探索生物科技活动中研究性学习的方法和途径。指出在开展活动中,要注意增强学生多方面才能,树立环境意识,培养持之以恒精神和不畏挫折工作态度。     

Two definitions of stability of equilibria

In classical physics the stability of an equilibrium requires that any, even infinitesimal, displacement from the configuration of equilibrium results in forces which tend to restore the original equilibrium configuration. In case of several stable equilibrium configurations, the height of the threshold, which must be exceeded by the deviarion from the stable equilibrium in order to bring the configuration into another stable equilibrium is taken as a measure of stability of the first configuration. In quantum mechanics, and in the recent work of I. Baianu, S. Comorosan and M. Marinescu (Bull. Math. Biophysics,30, 625–635, 1968;31, 59–70, 1969;32, 539–561, 1970) on organismic supercategories, preference is given to take, as ameasure of the degree of stability of a configuration, or of a “state”, the length of time during which the system remains in that configuration. It is shown that under rather general conditions the two criteria are equivalent.     

Adiabatic separation of motions and reduced MHD equations

A variational method for separating fast and slow motions in quasi-Lagrangian continuous media is proposed, which makes it possible to discard fast stable collective degrees of freedom and to derive simpler (reduced) nonlinear equations describing the adiabatic dynamics of quasi-Lagrangian systems. The method is applied to derive an improved version of the reduced Kadomtsev-Pogutse-Strauss MHD equations that describe the dynamics of a tokamak plasma with steady-state sheared flows, as well as adiabatic equations for two-dimensional modeling of MHD plasma convection near the threshold for flute instability in systems like compact tori. __________ Translated from Fizika Plazmy, Vol. 26, No. 6, 2000, pp. 566–576. Original Russian Text Copyright ￠ 2000 by Pastukhov.