Status and prospects of controlled thermonuclear fusion

Of all approaches to controlled thermonuclear fusion the tokamak experiments have been most successful. Over the last decade particularly three large devices have achieved plasma density,n, temperature,T, and energy confinement time, _E, in ranges necessary for a fusion reactor plasma. Such maximum values have, however, been obtained not yet simultaneously but only in separate pulses, although the crucial triple product,nT _E, has also been improved by several orders of magnitude. The high temperatures sufficient in a fusion reactor can be produced by injection of neutral atoms or by absorption of radio frequency waves in the ion cyclotron frequency range. The plasma confinement ( _E1s) is still not understood and is handled through empirical scaling laws. Particle densities have usually been on the low side (n5×10¹⁹ m^–3) because increased fuelling rates can easily lead to violent current disruptions. Progress in obtaining peaked density profiles with pellet injection has led to high density plasmas without disruptions. Serious unsolved problems concern the spoiling of the fusion rates by (nonhydrogenic) impurities, the plasma parameter control over longer periods of time and indeed the plasma heating by fusion alpha-particles (ignition, burning). The most urgent technological question refers to the lifetime of the first wall which is in direct contact with the plasma. An important step towards ignition has been made by the recent JET/DT experiments in which, for the first time, the actual reactor fuel component tritium has been used to produce neutrons. The next generation tokamak ITER is, at present, being planned and designed in a world-wide collaborative effort. It should be operating before the year 2010 and is intended to investigate an ignited plasma burning for several minutes.     

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.     

Study of the plasma potential evolution during ECRH in the T-10 tokamak and TJ-II stellarator

Comparison of the plasma electric potential evolution in the T-10 tokamak and TJ-II stellarator was performed. The core potential was measured by the heavy-ion beam probing and the edge potential was measured by Langmuir probe. The intrinsic potentials in both devices are different in sign, positive in TJ-II low-density discharge and negative in T-10 higher-density discharges, but during ECRH they evolve similarly: the potential becomes more positive, and increase of ECRH power leads to stronger rise of core potential. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Tarragona, Spain, July 3–4, 2005.     

Quantization of Spherically Symmetric Solution of SU(3) Yang-Mills Theory

A recent investigation of the SU(3) Yang-Millsfield equations found several classical solutions whichexhibited a type of confinement due to gauge fieldswhich increased without bound as r . This increase of the gauge fields gave thesesolutions an infinite field energy, raising questionsabout their physical significance. In this paper weapply some ideas of Heisenberg about the quantization of strongly interacting nonlinear fields to thisclassical solution and find that at large r thisquantization procedure softens the unphysical behaviorof the classical solution, while the interestingshort-distance behavior is maintained. This quantizationprocedure may provide a general method for approximatingthe quantum corrections to certain classical fieldconfigurations.     

Potential Confinement of a High Density Plasma in the GAMMA 10 Tandem Mirror

Potential confinement was demonstrated experimentally under various electron cyclotron resonance heating (ECRH) scenarios. The particle confinement time and the plasma confining potential increased with ECRH power. The plug potential formation by means of only _ce ECRH was studied by Monte-Carlo simulation. Potential confinement experiments have advanced in higher density region up to 4×10¹² cm^-3. The higher density plasma was obtained by high frequency ICRF heating and recently installed neutral beam injector in the central cell. Studies of scaling relation of the potential confinement with respect to the plasma density have started with the high density plasma.     

Electronic structure of hydrogen-like impurities in nearly-free-electron metals

Recent developments in our understanding of the electronic structure of hydrogen and its isotopes in simple metals is reviewed. The role of nonlinear electron density distribution in the interpretation of the electronic properties of hydrogen-like impurities is emphasized. Calculated Knight shifts and hyperfine fields at + site and electric field gradients at cubic host nuclear sites due to interstitial + are compared with recent experimental data. The feasibility of using positive muon as a probe of defect structure is discussed. Future experiments and theoretical investigations aimed at a deeper understanding of the electronic properties of + are suggested.Work supported by the National Science Foundation and the U. S. Department of Energy.     

New Possibilities of Radioastronomical Diagnostics of the Jovian Magnetosphere Using the Observed Polarization of its Decameter Radio Emission

We discuss possibilities of diagnostics of the Jovian magnetosphere based on the results of measurements of the polarization characteristics of the decameter radio emission. It is shown that the essentially elliptical polarization of that radiation and its generation at frequencies near the local electron gyrofrequency opens new possibilities for radioastronomical diagnostics of the Jovian magnetosphere. The plasma distribution can be studied not only along the radiation path but also in the transverse direction, i.e., over latitudes. Moreover, since the relative position of the source and observer during a decameter noise storm is rather stable, it is possible to perform tomography of the magnetosphere (its diagnostics at different longitudes) using the planet rotation. We present the examples of diagnostics of different regions in the Jovian magnetosphere, such as sources of decameter radio emission, i.e., lower-magnetosphere regions located at a distance of about 1.5-2 R_J from the center of the planet, and the Io plasma torus located at a distance of about 6R_J from the center of the planet. It is pointed out that the number density of the magnetospheric plasma outside the Io magnetic flux tube is small (n 1 cm^-3 at the height of the gyroresonance level f_Be 30 MHz) while it is higher inside this flux tube at the same height: n 3 cm^-3. We estimate the variations in the number density of the plasma along the Io magnetic flux tube (n B, 1-1.8), determine the rate at which the integral plasma density varies over latitudes (d( n dz)/dh 2· 10³ cm^-3), and find the average number density of the plasma in the region where the radiation crosses the Io torus ( n 2· 10³ cm^-3).     

Homogenität,Kovarianz und Relativität

Zusammenfassung Es werden zwei Begriffe: Homogenität des Raumzeitkontinuums und Kovarianz der Gleichungen, wie sie in der Relativitätstheorie gebraucht werden, definiert und erläutert. Es wird gezeigt, doss die beiden Begriffe wesentlich verschieden sind und in Form nichtäquivalenter mathematischer Bedingungen ihren Ausdruck finden. Trotzdem werden beide Begriffe sowohl von Einstein, als auch in der Literatur über Relativitätstheorie mit einem und demselben Wort Relativität bezeichnet. Der Missgebrauch des Wortes Relativität bedeutet nicht nur einen terminologischen Fehler, sondern spricht auch von einem ungenügenden Verständnis der Grundidee der Relativitätstheorie, besonders der sog. allgemeinen Relativitätstheorie. Versteht man unter Relativität Homogenität des Raumes, so ist in der sog. allgemeinen Relativitätstheorie überhaupt keine Relativität vorhanden. Versteht man dagegen unter Relativität Kovarianz der Gleichungen, so steckt in jener Theorie nicht mehr Relativität, wie z. B. in den unrelativistischen Bewegungsgleichungen, welche ebensogut eine allgemein-kovariante Formulierung gestatten (Lagrangesche Gleichungen 2-ter Art). Die Bezeichnung allgemeine Relativitätstheorie ist daher irrefuhrend. Die geniale Theorie Einsteins ist eine reine Gravitationstheorie. , No 4, . 131, 1955. (RhilosophischeFragen No 4, S. 131, Moskau 1955. Ins Deutsche über setzt vom Verfasser).     

Experimental investigation of the nonlinear properties of the surface helical instability in germanium

The results of an experimental investigation of the parameters of the surface helical instability (SHI) in germanium are presented. The dependence of the amplitude of the current oscillations of the helical wave and frequency on the electric E and magnetic B fields with E and B significantly exceeding the threshold values E_t and B_t are presented for the case of nonequilibrium (for temperatures T < 343°K) and equilibrium (T 343°K) plasma. It is shown that for small supercriticality (_E = (E-E_t)/Et 1, = ( -_t)/_t 1) > the square of the amplitude of the current oscillations and the frequency shift are proportional to the supercriticality, i.e., the regime for excitation of SHI is soft.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–21, May, 1981.     

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.     

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.     

Edge Turbulence During Limiter Biasing Experiments in the TJ-II Stellarator

The influence of limiter biasing on plasma confinement, turbulence and plasma flows has been investigated in the TJ-II stellarator. Experimental results show that it is possible to modify global particle confinement and edge plasma parameters with both positive and negative biasing. Significant and minor modifications in the structure of plasma fluctuations have been observed during the transition to improved confinement regimes induced by limiter biasing. These results show evidence of electric field induced improved confinement via multiple mechanisms. The investigation of the relaxation of plasma potential and electric fields shows evidence of two different characteristic decay times.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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Semi-classical asymptotics in solid state physics

This article studies the Schrödinger equation for an electron in a lattice of ions with an external magnetic field. In a suitable physical scaling the ionic potential becomes rapidly oscillating, and one can build asymptotic solutions for the limit of zero magnetic field by multiple scale methods from homogenization. For the time-dependent Schrödinger equation this construction yields wave packets which follow the trajectories of the semiclassical model. For the time-independent equation one gets asymptotic eigenfunctions (or quasimodes) for the energy levels predicted by Onsager's relation.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Relativistic scattering theory for long-range potentials of the nonelectrostatic type

We define a modified free-time evolution for the Dirac equation with long-range potentials (1/|x|), where is the Dirac matrix, and prove a strong asymptotic completeness of the corresponding wave operators. Our methods also work for the magnetic fields ·A(x).     

Determination of rf electric field strengths in deuterium from satellite structure of Balmer lines

In a linear magnetoplasma withn _e5×10¹⁸ m^–3 microwaves with frequencyf=34.8 GHz and powerP100 kW were focussed with a quasi-optical horn-lens system. The profiles of the deuterium lines D, D, and D were recorded from the focus. The profiles show a satellite structure which is generated by the rf electric field. Beside the first order satellites which can be resolved from the main line, even second order satellites were detectable. Comparing the satellites' intensities with theory it is possible to determine the electric field strength in the focus. Due to a sensitive dependence of the satellites' intensities upon the polarization direction one can also determine an unknown polarization direction.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

Electric quadrupole interaction at181Ta in RNi5 compounds

The time differential perturbed angular correlation measurements in PrNi₅, NdNi₅, GdNi₅, DyNi₅ and ErNi₅ rare-earth intermetallics with¹⁸¹Ta as probe nuclei have revealed that these impurity nuclei experience a non-axial electric quadrupole interaction. In all the cases, except in GdNi₅, the interaction frequency has a single value in the range 15–20 MHz with asymmetry parameter 0.98. In GdNi₅, however, there are two interaction frequencies (13.61 MHz and 26.89 MHz), the former being the dominant one (90%) with 0.35 and the latter (10%) with 0.98. It is concluded that in all cases the probe nuclei experiencing the highly asymmetric electric field gradient (efg) occupy the unique Ni(3g) site. Annealing studies have shown that in the case of GdNi₅ the interaction gets highly damped, while there is negligible effect in the other cases. The temperature variation of the efg in all cases seems to follow the empiricalT ^3/2 relation.     

Piron's axioms for quantum mechanics: A reply to Foulis and Randall

In their paper A note on Misunderstandings of Piron's Axioms for Quantum Mechanics, Foulis and Randall undertake a reply to our critique of Piron's question-proposition system (qp-s) which appeared in previous issues of this journal. In the present paper, we want briefly to refute the points of criticism raised by Foulis and Randall (FR). We argue that the misunderstandings are not ours, and we prove it.