Decay of enhanced density and damping of plasma flows after the electrode biasing termination on the CASTOR tokamak

Electrode biasing is a standard tool for modification of both edge and global plasma parameters on the CASTOR tokamak (R=0.4 m,a=85 mm,B _T=1.3 T,I _p1≈9 kA,q _a≈10). During a steady state phase of a discharge, a polarization voltage is applied on an electrode immersed into the edge plasma. This voltage causes radial currents that create radial electric field and, due to theE×B drift, they cause an enhanced rotation. Then, as a consequence, the interaction with walls decreases and particle confinement and density increase. Recently, the decay of plasma density and plasma flows after the termination of the biasing period was investigated on the CASTOR tokamak. These observations are linked to processes and mechanisms that control generation of radial electric fields in plasmas and damping ofE×B sheared flows and that therefore represent a key issue for understanding the transition to improved confinements modes. In the contribution, measured time scales of the transition to the ohmic regime after the biasing termination will be shown. Further, possible consequences of these measured scales for the valuation and explanation of important processes in the plasma will be discussed.     

The Role of Radial Electric Fields in the Tokamaks TEXTOR-94, CASTOR, and T-10

Radial electric fields (E _r) and their role in the establishment of edge transport barriers and improved confinement have been studied in the tokamaks TEXTOR-94 and CASTOR, where E _r is externally applied to the plasma in a controlled way using a biased electrode, as well as in the tokamak T-10 where an edge transport barrier (H-mode) is obtained during electron-cyclotron resonance heating (ECRH) of the plasma.The physics of radial currents was studied and the radial conductivity in the edge of TEXTOR-94 (R = 1.75 m, a = 0.46 m) was found to be dominated by recycling (ion-neutral collisions) at the last closed flux surface (LCFS) and by parallel viscosity inside the LCFS. From a performance point of view (edge engineering), such electrode biasing was shown to induce a particle transport barrier, a reduction of particle transport, and a concomitant increase in energy confinement. An H-mode-like behaviour can be induced both with positive and negative electric fields. Positive as well as negative electric fields were shown to strongly affect the exhaust of hydrogen, helium, and impurities, not only in the H-mode-like regime.The impact of sheared radial electric fields on turbulent structures and flows at the plasma edge is investigated on the CASTOR tokamak (R = 0.4 m, a = 0.085 m). A non-intrusive biasing scheme that we call "separatrix biasing" is applied whereby the electrode is located in the scrape-off layer (SOL) with its tip just touching the LCFS. There is evidence of strongly sheared radial electric field and E×B flow, resulting in the formation of a transport barrier at the separatrix. Advanced probe diagnosis of the edge region has shown that the E×B shear rate that arises during separatrix biasing is larger than for standard edge plasma biasing. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates ( 5×10⁶ s^-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements.During ECRH in the tokamak T-10 (R = 1.5 m, a = 0.3 m), a regime of improved confinement is obtained with features resembling those in the H-mode in other tokamaks. Using a heavy ion beam probe, a narrow potential well is observed near the limiter together with the typical features of the L-H transition. The time evolution of the plasma profiles during L-H and H-L transitions is clearly correlated with that of the density profile and the formation of a transport barrier near the limiter. The edge electric field is initially positive after the onset of ECRH. It changes its sign during the L-H transition and grows till a steady condition is reached. Similar to the biasing experiments in TEXTOR-94 and CASTOR, the experimentally observed transport barrier is a barrier for particles.     

Direct Measurements of E×B Flow and Its Impact on Edge Turbulence in the CASTOR Tokamak Using an Optimized Gundestrup Probe

New experimental evidence of the correlation between edge sheared E×B flow and reduction of turbulence has been measured in the CASTOR tokamak (R = 0.4 m, a = 0.085 m, B _T = 1 T). A biasing electrode is placed at the separatrix in a configuration which has demonstrated strongly sheared electric fields and consequent improvement of the global particle confinement. A set of movable electrostatic probes (rake, Langmuir, Gundestrup, and rotating Mach) provide redundant, simultaneous measurements of poloidal flow, toroidal flow, electron temperature, density, and radial electric field with high temporal resolution and at the same poloidal location. Particular effort has been made in the optimization of the Gundestrup probe collector geometry in order to reduce the relative uncertainty of Mach number measurements in plasmas with weak flow (M , M < 0.1). The measurements from the rake, Gundestrup, and rotating Mach probes give three independent radial profiles of E×B shear in ohmic and biased modes. Good agreement is obtained both for the profile shape and its absolute magnitude. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates (5×10⁶ s^-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements. In addition, we compare the measured E×B ion mass flow with the phase velocity of fluctuations moving poloidally across the Gundestrup collectors. Given the poloidal separation of the collecting plates and the sampling frequency (5 MHz), the maximum detectable phase velocity turns out to be rather modest compared to the measured bulk poloidal flow speed. Therefore the two quantities are only compared when the poloidal speed is low; in that case, they show similar behaviour in response to the applied bias.     

Experimental measurements and modelling of the structure of the radial electric field in RFX

The experimental determination of the radial electric fieldE _r and the associatedE ×B drift velocity at the edge of RFX is presented and possible mechanisms responsible for its generation are discussed.E _r measurements by means of an array of Langmuir probes and those deduced from Doppler spectroscopy of impurity lines agree fairly well. In particular the rotation velocity of the plasma edge has been determined from the Doppler shift of a C III emission line. The observation of other ions characterised by different radial positions, such as B IV and C V, has allowed an estimate of the velocity shear. Typical values of plasma rotation at the edge are around 10 km/s while the velocity shear is of the order of (10⁵−10⁶)s⁻¹ in the spontaneous layer, a few cm thick, usually observed in standard discharges. Plasma rotation has been artificially modified by both positive and negative edge biasing and the associated increase or decrease of the fluid velocity is well in agreement with the radial electric field change. The modification ofE _r during edge biasing and Pulsed Poloidal Current Drive (PPCD) are also reported and interpreted within a momentum balance model. Analytical and self-consistent Monte Carlo models at the plasma edge suggest that impurities have a relevant role in the generation of the radial electric field, due to their relatively large Larmor radius. Presented at the Workshop on Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June 2000.     

The quadratic Lagrangians in General Relativity

The solutions of the General Relativity equations with quadratic LagrangiansR _iklmR^iklm, R_ikR^ik, R² are studied. It is shown that nontrivial Euclidian (atr ) solution of the theory equations does not exist whenT0 (T is a trace of the energy-momentum tensor of matter). The Schwarzschild solution is not an external part of a total solution whenT0. Under conditionT=R=0 LagrangiansR _iklmR^iklm, R_ikR^ik lead to the identical field equations, so there exist the only quadratic Lagrangian and the only field equations. This equation has a solution with an external part being a standard Schwarzschild solution for the statical spherically symmetric case.     

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

On the phase transitions for the electronic excitations in semiconductors

A model Hamiltonian for a system of interacting electrons, holes and Wannier excitons is derived. This system of electronic excitations is assumed to be in a quasi-equilibrium state. With the aid of Bogolubov's variational principal the thermodynamic potential is calculated. Using the most general mean-field Hamiltonian as a trial Hamiltonian, a set of coupled integral equations is obtained for the self-energies. These equations are solved numerically for equal effective masses of the electrons and holes. Below a critical temperature ofk _B T _c0.65E _ex ^b whereE _ex ^b is the exciton binding energy, we find a first order phase transition from an exciton rich phase into a degenerate electron-hole phase. The mechanical and thermal stability of both phases is proven. Below a critical temperaturek _B T _c0.11E _ex ^b the exciton system becomes degenerate (Bose-Einstein condensation). A complete phase diagram of these three phases is given.This is a project of the Sonderforschungsbereich Frankfurt/Darmstadt, financed by special funds of the Deutsche Forschungsgemeinschaft     

Statistical Mechanical Theory of Bimolecular Reaction. Derivation of the Arrhenius Law. Characterization of a Catalyst

A statistical mechanical theory is developed for gas-phase bimolecular (binary) reactions: AB ⇌ A + B. Based on the activated-complex hypotheses, and expression for the association rate constant k_a is derived: k_a = k*_{AB* → AB} (QAB*/q_A+B), where k*_{AB* →AB} is the rate constant for the transition from the activated state AB* to the molecular state AB, and qx is the equilibrium occupation probability for state X. The three states (AB, AB*, A + B) are defined by three regions of the energyseparation plane for the relative motion of the reactant pair (A, B). If the interatomic potential has a critical barrier ϵ_c at separation r_c and an attractive well with depth ϵ_b (ϵ_c, ϵ_b > k_BT) computations of the q_AB*/q_{A +B} generate an Arrhenius-Boltzmann factor exp (—ϵ_c/k_BT). The virtual rate constant k*_{AB* →AB} is calculated by assuming that the reactant pair reaching the activated state AB* with the separation r < r_c and the energy E > _c moves on to the molecular state AB only if it loses part of its radial kinetic energy with the aid of third body (catalyst or collision) and is trapped by the potential well. With no catalysts present, this constant is approximately given by k*_{AB* →AB} =πd′²v′ R′⁻³, where v′ is the thermal center-of-mass speed, and d′ and R′ are respectively the collision-sphere radius and the mean distance between AB* and any molecule (A, B, AB or AB*). For binary dissociation, the rate constant k_d is given by k_d = k*_{AB* →A+B} q_AB*/q_AB), which generates exp [—(ϵ_c + ϵ_b)/k_BT]. A catalyst for binary reaction is assumed to act as a mediator, facilitating the energy exchange between the radial and rotational modes of motion. Additionally for association only, it also acts as a confinement agent, preventing the pair from flying away from each other. Connections with the collision theory and the activated complex theory are discussed critically.     

Parameter optimization of F?P HgCdTe and InSb bistable devices

The parameter optimization of HgCdTe and InSb infrared bistable devices of both transmission and reflection types is studied with computer numerical calculation. The results point that the steady state behavior of the devices changs quasi-periodically with the sample thickness L; the output modulation amplitude I_T is almost inversely proportional to R_B; and the switching power grows nonlinearly with increasing R_F, but I_T is hardly affected by R_F. These conclusions may be useful in guiding the design of such infrared devices.     

Coulomb systems seen as critical systems: Ideal conductor boundaries

When a classical Coulomb system has macroscopic conducting behavior, its grand potential has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system: the massless Gaussian field. Here, the Coulomb system is assumed to be confined, by walls made of an ideal conductor material; this choice corresponds to simple (Dirichlet) boundary conditions for the Gaussian field. For ad-dimensional (d2) Coulomb system confined in a slab of thicknessW, the grand potential (in units ofk _B T) per unit area has the universal term (d/2)(d)/2^dd/2W^d–1. For a two-dimensional Coulomb system confined, in a disk of radiusR, the grand potential (in units ofk _B T) has the universal term (1/6) lnR. These results, of general validity, are checked on two-dimensional solvable models.Laboratoire Associé au Centre National de la Recherche Scientifique-URA 63.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Nuclear spin relaxation of Xe in liquid Te

By the method of time differential perturbed angular distribution following a nuclear reaction, the relaxation rateT _r ^–1 of the 8 msI =10⁺ isomer of¹³²Xe has been measured in liquid Te. Between 670 °K (supercooled liquid) and 1,000 °K the rate decreases from about 720/s by about a factor of two. From existing experimental material it is concluded thatT _r ^–1 is mainly due to quadrupolar interaction (T _r ^–1 T _Q ^–1 ). Its magnitude is discussed considering the metallic and the noble gas limit as models for the Xe-Te-interactions. The temperature dependenceT _Q(T) apparently does not correlate with the diffusion constant of Te in contrast to a simplified theoretical treatment. — The nuclearg value of the isomer has been determined to be g=(–)0.195(5) thus confirming the configuration (vh_11/2)².     

Efficiency of plasma biasing by movable localized limiter in tokamak ISTTOK

The correlation between the efficiency of plasma biasing and the position of a localized limiter has been investigated. It has been found that two distinct zones of limiter position can be distinguished in ISTTOK plasma: Far-zone at r _lim > 7.2 cm, and Close-zone at r _lim < 7.2 cm. The strongest modifications of edge plasma potential take place for both positive and negative limiter biasing when it is positioned inside Close-zone. The transition between zones is correlated with effective screening of the wall by the limiter, being more efficient as it is immersed deeper into the plasma. The indicative difference between zones can be a difference of non-ambipolar fluxes flowed onto short-circuited limiter: mostly positive (ion) inside Far-zone, and mostly negative (electron) inside Close-zone.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Zero differential resistance in a double quantum well at high filling factors

The differential resistance r _xx in a GaAs double quantum well with two occupied size-quantization subbands have been studied at temperatures T = 1.6–4.2 K in magnetic fields B < 0.5 T. It has been found that differential resistance r _xx vanishes at the maxima of magneto-intersubband oscillations with an increase in the direct current I _dc. It has been shown that the discovered r _xx ≈ 0 state appears under the condition 2R _c E _H/ħω_c < 1/2, where R _c is the cyclotron radius of electrons at the Fermi level, E _H is the Hall electric field induced by the current I _dc, and ω_c is the cyclotron frequency.     

Direct and reverse energy transport in systems of monomers and imperfect traps: Monte Carlo simulations

A Monte Carlo simulation of the concentration dependence of the fluorescence quantum yield _M and emission anisotropyr _M of a system containing dye molecules in the form of monomers M and clusters T (statistical pairs and trimers) playing the role of the imperfect traps for nonradiative excitation energy transfer (NET) has been carried out. The simulation has been made for determined values of Förster critical distancesR ₀ ^MM andR ₀ ^MT and for several values ofR ₀ ^TM andR ₀ ^TT , assuming that the energy may be transferred from M^* to T as well as from T^* to M (reverse nonradiative energy transfer, RNET). It was shown that the RNET process in the range of high concentrations may strongly change the values ofr _M as well as those of _M. For emission anisotropyr _M an effect of repolarization was observed which decreases rapidly with increasingR ₀ ^TM andR ₀ ^TT . A very good agreement between the simulation results of _M and the theoretical model with no adjustable parameters was found. In the model, the RNET process and influence of correlation between active molecules on energy migration among monomers were taken into account.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Temperature dependence of electron magnetic resonance and magnetization in NiO nanorods

For NiO nanorods of 5 nm diameter prepared by sol-gel technique, variations of the magnetization M with temperature T (5-370 K) and magnetic field H up to 55 kOe are reported. Also, temperature variations of the EMR (electron magnetic resonance) parameters (intensity I₀, linewidth ΔH and resonance field H_r) of an observed line due to uncompensated spins are followed for The M vs. H and T variations yield a blocking above which the data fits modified Langevin function with magnetic moment μ_p?1240 μ_B/particle. For the EMR line, I₀ decreases rapidly for T<T_B, and the line broadens and shifts to lower H with lowering T, following the lineshift δH_r=(ΔH)ⁿ with n?2.8. This is close to the value of n=3 expected for randomly oriented particles.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).