Effect of the transverse magnetic field on turbulence and parameters of a plasma column in the L-2M stellarator

The influence of magnetic configurations with magnetic hills or wells on the parameters of a plasma column and turbulence characteristics were studied in experiments in which the plasma was created and heated by a microwave beam at the second harmonic of the electron cyclotron frequency. Calculations show that, for 〈β〉=(1.5?2)×10^?, a configuration with a magnetic well takes place and the Mercier criterion for stability of the ideal MHD modes is satisfied. It is shown that the compensation of the Shafranov shift of the plasma column by a transverse (vertical) field (B _v /B ₀ =5×10^?3) leads to a configuration with a magnetic hill in which the Mercier stability criterion is violated in the central region of the plasma column. It is experimentally shown that the stored plasma energy in the magnetic-hill configuration is reduced by one-half in comparison with the magnetic-well configuration. In the case of a magnetic hill, the energy of fluctuations increases both in the plasma core and near the separatrix, and the quasi-regular components of the wavelet spectra grow. When the Shafranov shift is compensated only partially (B _v/B ₀～3×10^?3) and the system is near the instability threshold, the stored plasma energy and the central electron temperature are somewhat higher, and the radiation power of fast electrons from non-Maxwellian tails at the second harmonic of the electron gyrofrequency decreases. It is found that the wavelet spectra of fluctuations change, the coherence coefficient for spectral components increases, and the radial electric field near the separatrix decreases.     

Effect of electron-cyclotron resonance heating conditions on the local parameters of short-wavelength plasma turbulence in the L-2M stellarator

Changes in the energy spectra of short-wavelength (k _s ≈ 35 cm^?1) plasma density fluctuations in the local region of the plasma column (r/a = 0.5–0.6) of the L-2M stellarator were studied by the method of collective scattering of 150-GHz radiation. The plasma was heated at the second harmonic of the electron gyrofrequency, the microwave heating power being in the range of 90–170 kW. A sector limiter was introduced in the peripheral plasma (r/a ≥ 0.8), and the Shafranov shift of the magnetic axis was varied by varying the vertical magnetic field. The results of measurements were averaged over 9–16 discharges. It is found that an increase in the heating power and/or the introduction of the sector limiter in the plasma lead to an increase in the energy of density fluctuations, which correlates with a decrease in the plasma energy lifetime. In the spectra of fluctuations, a broad spectral band in the range of 3–50 kHz was observed in which the spectral density was one order of magnitude higher than in the rest of the spectrum. Analysis of the Fourier spectra showed that the introduction of the sector limiter in the plasma resulted in an increase in both the spectral density of fluctuations in the range of 3–50 kHz and the fraction of quasi-coherent structures in turbulent density fluctuations.     

Study of the fine structure of the plasma current sheath and magnetic fields in the axial region of the PF-1000 facility

Results of measurements of magnetic fields in the plasma pinching region during the compression of the deuterium plasma current sheath (PCS) at the PF-1000 plasma focus facility are presented. The fine structure of the PCS (shock wave-magnetic piston) and its variations in the course of plasma compression toward the facility axis are studied using magnetic probes and laser interferometry. The radial distributions of the plasma density and current in the PCS are compared. It is shown that, in the shock wave region, the electron density of the compressed plasma is on the order of ～10¹⁸ cm^?3, whereas the PCS current is almost entirely concentrated in the magnetic piston region—a plasma layer with an electron density of less than 10¹⁵ cm^?3. Efficient transportation of the current by the PCS into the axial region of the facility in discharges with a high neutron yield (Y _n > 10¹¹ neutrons/shot) is detected. It is shown that the total neutron yield is well described by the dependence Y _n ≈ (1.5–3) × 10¹⁰ I _p ⁴ , where I _p is the pinch current (in MA) flowing within the region r ≤ 13 mm.     

Reconstruction of the q and p profiles in ITER from external and internal measurements

A method is developed for calculating uncertainties in reconstructing the equilibrium profiles of the safety factor q and plasma pressure p in the ITER device from external magnetic measurements and from motional Stark effect line polarization (MSE-LP) and motional Stark effect line shift (MSE-LS) signals from excited NBI atoms inside the plasma core. It is shown that, with MSE-LP signals, as well as with MSE-LS signals (the use of which was recently proposed by Nova Photonics, Inc.), it is possible to substantially improve the reconstruction of the profiles that determine the plasma magnetic configuration.     

Reaction of turbulence at the edge and in the center of the plasma column to pulsed impurity injection caused by the sputtering of the wall coating in L-2M stellarator

Impurity injection into plasma caused by the sputtering of the wall coating in the L-2M stellarator during auxiliary electron cyclotron resonance heating leads to a change in the level of plasma density fluctuations with frequencies above 0.25 MHz: suppression of long-wavelength (k _⊥ = 2 cm^–1) density fluctuations in the edge plasma, intensification of short-wavelength (k _⊥ = 30 cm^–1) and long-wavelength (k _⊥ = 1 cm^–1) fluctuations at the midradius of the plasma column, and intensification of short-wavelength fluctuations (k _⊥ = 20 cm^–1) in the plasma center (including the gyroresonance region). At the same time, the level of fluctuations with frequencies below 0.25 MHz remains unchanged. In the edge plasma, a decrease in the plasma potential and suppression of its fluctuations is observed during impurity injection, which also causes an increase in MHD activity.     

Capillary operators

The goal of this work is an examination of capillary exchange models as mathematical operators. The concentration function relations for the Krogh cylinder of a single capillary, basic to many organ models, are studied via the theory of operators on the Lebesgue normed spacesL _p[0,∞], (1<-p<-∞). A discussion is included of theL _p -normsvis-à-vis the coefficient of variation currently used in finding capillary parameters and evaluating parameter searches. The capillary model determines two operators on the space of locally integrable functions: O _K (relating extravascular concentration to intravascular) and K _{a, k} (relating intravascular concentration to input), wherek is the ratio of permeabilitysurface area (PS) to extravascular volume, and α is the ratio of PS to flow. These operators are shown to induce contractive (‖O _K ‖ _p <-1, ‖K _{a, k} ‖ _p <-1), isotone, linear operators onL _p . The uniform convergence relation $$K_{a,k} = \mathop {\lim _{(p)} }\limits_{N \to \infty } \left( {\sum\limits_{n = 0}^N {P_n (a)O_k^n } } \right)$$ (as operators onL _p) is derived, whereP _n (a) is the Poisson probabilitye ^?a a ⁿ /n!. For the important special cases ofp=∞, 1, 2 the norms are found (‖O_k‖=‖K_a,k‖_p=1). Consideration is also given to the norms and operators when the functions involved are limited to a finite interval of time.     

Geometric properties of magnetic field lines on toroidal magnetic surfaces in the context of plasma equilibrium

An analysis of plasma equilibrium in a magnetic confinement system includes studies of how the shape of the magnetic surfaces is distorted with varying magnitude and profile of the plasma pressure. Such studies allow one, in particular, to determine the maximum β value consistent with equilibrium, β_eq, i.e., the maximum plasma pressure above which the equilibrium in a confinement system under analysis is impossible. Since the magnetic field lines form magnetic surfaces, their global relationship with equilibrium is obvious. Here, special attention is paid to a local relationship between equilibrium and geometric properties of the magnetic field lines.     

ThepH dependence of the equilibrium constantK Hyd for the hydrolysis of the Lys15-Ala16 reactive-site peptide bond in bovine pancreatic trypsin inhibitor (aprotinin)

ThepH dependence of the equilibrium constant K_Hyd for the hydrolysis of the Lys¹⁵-Ala¹⁶ reactive-site peptide bond of the bovine pancreatic trypsin inhibitor (aprotinin) was investigated over thepH range 2.3–6.5. Solutions of aprotinin, modified aprotinin with the Lys¹⁵-Ala¹⁶ peptide bond cleaved and mixtures of both species were incubated with 10 mol% porcine β-trypsin. The state of equilibrium was determined by analytical cation-exchange HPLC. The K_Hyd values obtained did not exactly obey the simple equation of Dobry et al. (1952), which had to be used in an extended form with two additional parameters for a satisfactory fit. ThepH-independent equilibrium constant is 0.90 and thepK values of the Lys¹⁵ carboxyl group and of the Ala¹⁶ amino group are 3.10 and 8.22, respectively. ThepK of an additional group is apparently perturbed by the peptide-bond hydrolysis. It is 4.60 in the native and 4.40 in the modified aprotinin.     

Dissociation constants of phenothiazine drugs incorporated in phosphatidylcholine bilayer of small unilamellar vesicles as determined by carbon-13 nuclear magnetic resonance spectrometric titration

The dissociation constants (pK_ms) of the phenothiazine drugs promazine, chlorpromazine, and triflupromazine, incorporated in the phosphatidylcholine (PC) bilayer of small unilamellar vesicles (SUV), were investigated by a ¹³C nuclear magnetic resonance (NMR) titration method employing their N-¹³CH₃ (ionizable group) labelled derivatives. Use of the labelled drugs enabled direct observations of the ionization equilibrium of the N-dimethyl group. A second derivative spectrophotometric study proved that 95-98% of the phenothiazine species in the sample solutions (200 μM phenothiazine in the presence of 27 mM PC SUV) were incorporated into the PC bilayer, which simplified the calculation of pK_m values by allowing that the phenothiazines in the aqueous phase could be neglected. The pK_m values were calculated from the chemical shift dependence of the N-dimethyl ¹³C NMR signal on the pH value of sample solutions. The pK_m values obtained were smaller than those measured in aqueous solutions by about one unit. The existence of cholesterol (30 mol%) in the PC bilayer showed little effect on the pK_m values, suggesting that cholesterol in the bilayer does not largely affect the interfacial region where the N-dimethyl group of the incorporated phenothiazines is located. The results offered clear evidence for the pK_m decrease and provided their precise values.     

Medium-β free-boundary equilibria of a quasi-isodynamic stellarator

Free-boundary MHD equilibria with magnetic surfaces in the vacuum region surrounding the plasma [E. Strumberger, Nucl. Fusion 37, 19 (1997); M. Drevlak, D. Monticello, and A. Reiman, Nucl. Fusion 45, 731 (2005)] are obtained for a quasi-isodynamic stellarator [A. A. Subbotin, M. I. Mikhailov, V. D. Shafranov et al., Nucl. Fusion 46, 921 (2006); M. I. Mikhailov, J. Nuhrenberg, and V. D. Shafranov, Plasma Phys. Rep. 35, 529 (2009)].     

Plasma equilibrium in axisymmetric open divertor configurations

The equilibrium of a plasma with isotropic pressure in a periodic divertor configuration with a poloidal magnetic field is calculated. The issue of how the plasma equilibrium changes as the parameter β≡8πp/B ² increases is considered for a fairly representative class of pressure profiles p(ψ) (where ψ is the flux coordinate). It is shown that the plasma can be in equilibrium up to β values (in terms of the vacuum magnetic field at the divertor axis) on the order of unity.     

Study of the azimuthal magnetic fields and scaling laws at the KPF-4-Phoenix facility

Results are presented from magnetic probe measurements in the pinching region formed during the compression of the plasma current sheath (PCS) in a discharge in deuterium at the KPF-4-Phoenix plasma focus facility. The fine structure (shock front-magnetic piston) of the PCS and its time evolution in the course of plasma compression toward the facility axis was studied by means of magnetic probes. It is shown that the fraction of the current transported into the axial region by the PCS does not exceed 65% of the total discharge current. The integral neutron yield Y _n is well described by the formula Y _n ≈ (1.5–3) × 10¹⁰ I _p ⁴ , where I _p (in MA) is the pinch current flowing in the region r ≤ 22 mm.     

Neoclassical offset toroidal velocity and auxiliary ion heating in tokamaks

In conditions of ideal axisymmetry, for a magnetized plasma in a generic bounded domain, necessarily toroidal, the uniform absorption of external energy (e.g., RF or any isotropic auxiliary heating) cannot give rise to net forces or torques. Experimental evidence on contemporary tokamaks shows that the near central absorption of RF heating power (ICH and ECH) and current drive in presence of MHD activity drives a bulk plasma rotation in the co-I _p direction, opposite to the initial one. Also the appearance of classical or neoclassical tearing modes provides a nonlinear magnetic braking that tends to clamp the rotation profile at the q-rational surfaces. The physical origin of the torque associated with P _RF absorption could be due the effects of asymmetry in the equilibrium configuration or in power deposition, but here we point out also an effect of the response of the so-called neoclassical offset velocity to the power dependent heat flow increment. The neoclassical toroidal viscosity due to internal magnetic kink or tearing modes tends to relax the plasma rotation to this asymptotic speed, which in absence of auxiliary heating is of the order of the ion diamagnetic velocity. It can be shown by kinetic and fluid calculations, that the absorption of auxiliary power by ions modifies this offset proportionally to the injected power thereby forcing the plasma rotation in a direction opposite to the initial, to large values. The problem is discussed in the frame of the theoretical models of neoclassical toroidal viscosity.     

Study of the termination phase of plasma production and the formation of magnetic flux breakthroughs during wire array implosion

The phenomenon of magnetic flux breakthrough into a wire array during its implosion was studied experimentally at the Angara-5-1 facility. It is shown that breakthroughs develop in the final stage of plasma production from the wire material and occur near the initial wire position. The spatial distributions of the azimuthal magnetic field within tungsten, molybdenum, copper, and aluminum wire arrays were studied using magnetic probes. The distributions of the azimuthal magnetic field B _φ(z, t) along the array height in different stages of implosion were measured, and the characteristic dimensions of regions with a nonuniform magnetic field that appear during magnetic flux breakthroughs at the outer boundary of the wire array plasma were determined. The dimensions of these regions are compared with those of the regions with depressed plasma radiation observed in frame and time-integrated X-ray images. The dynamics of the distribution B _φ(z, t) in regions with a nonuniform magnetic field during breakthroughs of the azimuthal magnetic flux is compared with that of the spatial distribution of pinch radiation in the frame X-ray images in different stages of implosion. The experimental data on the characteristics of spatially nonuniform breakthroughs of the magnetic flux into the wire array are analyzed using the plasma rainstorm model proposed by V.V. Aleksandrov et al. (JETP 97, 745 (2003)). The plasma density in the region of magnetic flux breakthrough is estimated.     

Local surface equilibrium equations for currentless magnetic configurations

Invariant local surface equilibrium equations are derived that interrelate the absolute value of the magnetic field B, the absolute value of the gradient of the magnetic flux |?Φ|, the local shear s, and the plasma pressure on nested equilibrium magnetic surfaces in currentless configurations. Examples of applying these equations to analysis of symmetric and isodynamic equilibria are considered.     

Cooperativity in viral fusion

A simple model for membrane fusion mediated by vial spike glycoproteins is presented. The viral proteins are considered to be allosteric proteins that undergo concerted conformational transitions when they bind the ligand. The ligand in this case is H⁺. The effect of the conformational transition is to bring membranes together and induce their fusion. An equation is derived for the dependence of fusion rates on ligand concentration, for a given dissociation constant (K _d), equilibrium constant for the conformational change (L), and number of cooperating subunits (n). Curves generated by this equation provide a reasonable fit to data on the rates of fusion of Vesicular Stomatitis virus with cells for a pK _d of 6.3,L=1000 andn=6.     

Cardiac chemical constant. Part I: Derivation of the characteristic phenomenological equation

A physiochemical parameter is derived and defined as the cardiac chemical equilibrium dissociation constant (K_D), K_D is based upon a phenomenological model in which the cardiac muscle chemical reaction kinetics describe the interconversion between long and short unils (i.e. the individual sarcomere is fully extended or fully contracted). K_D is defined as the ratio of the number of units in the long state to the number of units in the short state. The mathematical development proceeds through four stages: derivation of the governing differential equation during cardiac systole; simplification of the differential equation to describe the cardiac model; determination of the upper and lower limits and average value of Nt (the total number of units in a hypothetical mid-wall circumferential fibre); definition and calculation of the cardiac chemical constant (K_D). K_D is shown to describe a series of equilibrium points throughout cardiac systole. This requires that each mechanical equilibrium state (a series of static, steady-state intervals over time) is also associated with its own specific chemical equilibrium state.     

Effect of the magnetic field structure on the intensity of electron cyclotron emission from the plasma of the L-2M stellarator

Results are presented from experimental studies of the influence of the stellarator magnetic field structure on the plasma behavior in electron-cyclotron resonance regimes with a high heating power per electron. The magnetic field structure was changed by varying the induction current I _p from ?14 to +14 kA. The plasma electrons were heated at the second harmonic of the electron gyrofrequency by an X-mode microwave beam with a power of P ～ 200 kW, the average plasma density being in the range n _e = (0.5–2) × 10¹³ cm^?3. At I _p = 0, the rotational transform varies from $\rlap{--} \iota $ (0) = 0.2 on the magnetic axis to 0.8 at the plasma boundary. At a positive current of I _p = 13.5 kA, the rotational transform was $\rlap{--} \iota $ (0) = 0.8 on the axis and $\rlap{--} \iota $ (a _p) = 0.9 at the plasma boundary. Experiments with a positive current have shown that the radiative temperature first increases with current. When the current increases to I _p = 11–14 kA, strong modulation appears in the electron cyclotron emission signals received from all the plasma radii, the emission spectrum changes, and the emission intensity decreases. At a negative current of I _p = ?(6.5–13.5) kA, the rotational transform vanishes at r/a _p = 0.4–0.6. In this regime, the number of suprathermal electrons is reduced substantially and the emission intensity decreases at both low and high plasma densities.     

Production of gluconic acid from glucose by Aspergillus niger: growth and non-growth conditions

Batch fermentation of glucose to gluconic acid was conducted using Aspergillus niger under growth and non-growth conditions using pure oxygen and air as a source of oxygen for the fermentation in 2 and 5 l stirred tank reactors (batch reactor). Production of gluconic acid under growth conditions was conducted in a 5 l batch reactor. Production and growth rates were higher during the period of supplying pure oxygen than that during supplying air, and the substrate consumption rate was almost constant. For the production of gluconic acid under non-growth conditions, conducted in the 2 l batch reactor, the effect of the pure oxygen flow rate and the biomass concentration on the gluconic acid production was investigated and an empirical equation suggested to show the dependence of the production rate r_p on the biomass concentration C_x and oxygen flow rate Q, at constant operating conditions (30 °C, 300 rpm and pH 5.5). Biomass concentration had a positive effect on the production rate r_p, and the effect of Q on r_p was positive at high biomass concentrations.     

Solvent isotope effects on α-glucosidase

The solvent kinetic isotope effects (SKIE) on the yeast α-glucosidase-catalyzed hydrolysis of p-nitrophenyl and methyl-d-glucopyranoside were measured at 25 °C. With p-nitrophenyl-d-glucopyranoside (pNPG), the dependence of k_cat/K_m on pH (pD) revealed an unusually large (for glycohydrolases) solvent isotope effect on the pL-independent second-order rate constant, ^DOD(k_cat/K_m), of 1.9 (±0.3). The two pK_as characterizing the pH profile were increased in D₂O. The shift in pK_a2 of 0.6 units is typical of acids of comparable acidity (pK_a=6.5), but the increase in pK_a1 (=5.7) of 0.1 unit in going from H₂O to D₂O is unusually small. The initial velocities show substrate inhibition (K_is/K_m～200) with a small solvent isotope effect on the inhibition constant [^DODK_is=1.1 (±0.2)]. The solvent equilibrium isotope effects on the K_is for the competitive inhibitors d-glucose and α-methyl d-glucoside are somewhat higher [^DODK_i=1.5 (±0.1)]. Methyl glucoside is much less reactive than pNPG, with k_cat 230 times lower and k_cat/K_m 5×10⁴ times lower. The solvent isotope effect on k_cat for this substrate [=1.11 (±0. 02)] is lower than that for pNPG [=1.67 (±0.07)], consistent with more extensive proton transfer in the transition state for the deglucosylation step than for the glucosylation step.