Toroidal plasma rotation induced by the dynamic ergodic divertor in the TEXTOR tokamak

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m/n=3/1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m/n=2/1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer.     

Improved confinement due to open ergodic field lines imposed by the dynamic ergodic divertor in TEXTOR

The ergodization of the magnetic field lines imposed by the dynamic ergodic diverter (DED) in TEXTOR can lead both to confinement improvement and to confinement deterioration. The cases of substantial improvement are in resonant ways related to particular conditions in which magnetic flux tubes starting at the X points of induced islands are connected with the wall. This opening process is connected with a characteristic modification of the heat deposition pattern at the divertor target plate and leads to a substantial increase and steepening of the core plasma density and pressure. The improvement is tentatively attributed to a modification of the electric potential in the plasma carried by the open field lines. The confinement improvement bases on a spontaneous density built up due to the application of the DED and is primarily a particle confinement improvement.     

Influence of the static Dynamic Ergodic Divertor on edge turbulence properties in TEXTOR

Systematic measurements on the edge turbulence and turbulent transport have been made by Langmuir probe arrays on TEXTOR under various static Dynamic Ergodic Divertor (DED) configurations. Common features are observed. With the DED, in the ergodic zone the local turbulent flux reverses sign from radially outwards to inwards. The turbulence properties are profoundly modified by energy redistribution in frequency spectra and suppression of large scale eddies. The fluctuation poloidal phase velocity changes direction from electron to ion diamagnetic drift, consistent with the observed reversal of the Er x B flow. In the laminar region, the turbulence is found to react to an observed reduced flow shear.     

Change of the magnetic-field topology by an ergodic divertor and the effect on the plasma structure and transport

The magnetic-field perturbation produced by the dynamic ergodic divertor in TEXTOR changes the topology of the magnetic field in the plasma edge, creating an open chaotic system. The perturbation spectrum contains only a few dominant harmonics and therefore it can be described by an analytical model. The modeling is performed in the vacuum approximation without assuming a backreaction of the plasma and does not rely on any experimentally obtained parameters. It is shown that this vacuum approximation predicts in many details the experimentally observed plasma structure. Several experiments have been performed to prove that the plasma edge behavior is defined mostly by the magnetic topology of the perturbed volume. The change in the transport can be explained with the knowledge of only the magnetic structures; i.e., the ergodic pattern dominates the plasma properties.     

Remark on the continuity of the density of states of ergodic finite difference operators

We give an elementary proof that for a large class ofd-dimensional finite difference operators including tight-binding models for electron propagation and models for harmonic phonons with random masses or couplings, the integrated density of states is a continuous function of the energy.     

Ising model in the high density limit

It is proved that the free energy per spin in the thermodynamic limit of an Ising model on a lattice with coordination numberz approaches the classical Curie-Weiss free energy in the limitz→∞. The infinite spacial dimension limit of nearest neighbour lattice models is a special case of this result.     

Influence of the inverse sheath on divertor plasma performance in tokamak edge plasma simulations

Recently, it was shown that strong electron thermionic emission from material walls could result in the formation of an “inverse sheath,” which prevents the flow of cold ions to the wall.^[1–3] Such regimes look very favourably from the point of view of plasma–material interactions at the edge of magnetic fusion devices, where the problem of the erosion of plasma-facing components under ion irradiation is one of the key issues for the development of future magnetic fusion reactors. However, it is not clear whether such regimes are compatible with edge plasma parameters and heat removal requirements in fusion reactors. To address the issue of practicality of the “inverse sheath” regime for edge tokamak plasma conditions, we perform a set of numerical simulations with 2D edge plasma transport code UEDGE^[4] for a DIII-D-like geometry and magnetic configuration. To describe both “standard” and “inverse sheath” conditions within the framework of the UEDGE code (which does not consider the sheath region per se), at the material surfaces, we apply effective boundary conditions that emulate both “standard” and “inverse sheath” regimes. We demonstrate that, for the same input parameters, spatial distributions of edge plasma parameters corresponding to detached divertor and “inverse sheath” regimes are similar, with only a few minor differences. We discuss the compatibility of “inverse sheath” regimes with core plasma parameters.     

Origin of tokamak density limit scalings

The onset criterion for radiation driven islands [P. H. Rebut and M. Hugon, Plasma Physics and Controlled Nuclear Fusion Research 1984: Proc. 10th Int. Conf. London, 1984, (IAEA, Vienna, 1985), Vol. 2] in combination with a simple cylindrical model of tokamak current channel behavior is consistent with the empirical scaling of the tokamak density limit [M. Greenwald, Nucl. Fusion 28, 2199 (1988)]. Many other unexplained phenomena at the density limit are consistent with this novel physics mechanism.     

Self-Similarity of Edge Plasma Fluctuations in TEXTOR

In TEXTOR the long-range time dependence of edge plasma fluctuations has been investigated. The results indicate that the tail of the autocorrelation function decays as a power law for time lags longer than the local decorrelation time. The frequency spectra of the fluctuations show similar features to those obtained in "sandpile" models. Using rescaled range (R/S) analysis techniques the self-similarity parameters have been estimated for the potential fluctuation data detected by Langmuir probes. The results show that the Hurst exponents are well above 0.5 over the self-similarity range at all the measured radial locations. All these facts reveal the self-similar character of the electrostatic fluctuations at the plasma edge of TEXTOR, consistent with plasma transport as characterized by self-organized criticality (SOC). Furthermore, we have analyzed in this respect discharges in which an edge transport barrier was created by means of edge biasing, hitherto limited to floating potential measurements in the scrape off layer outside the barrier region. The results show a decrease of fluctuating amplitudes, a reduction of decorrelation time of local turbulence and, surprisingly, a concomitant increase of the Hurst exponent. This result implies that the mechanisms governing the decorrelation of local turbulence may differ from those governing the decorrelation of SOC transport events.     

Synergy of anomalous transport and radiation in the density limit

The critical plasma density n(cr) above which the edge anomalous transport in tokamaks is dominated by drift resistive ballooning instability is found analytically. In this transport regime, the drastic increase of particle losses and drop of the edge temperature provoke a strong increase in impurity radiation, and thermal equilibrium does not exist if the density is ramped up above the ultimate limit n(max). Because of the nonlinear character of impurity radiation, this density limit n(max) is very close to n(cr) and practically does not change with the ion effective charge. The importance of the synergy between the anomalous transport and impurity radiation for the density limit phenomenon is confirmed by the results of numerical simulations.     

Ground-state density of the pauli operator in the large field limit

The ground-state density of the Pauli operator in the case of a nonconstant magnetic field with constant direction is studied. It is shown that in the large field limit, the naturally rescaled ground-state density function is bounded from above by the megnetic field, and under some additional conditions, the limit density function is equal to the magnetic field. A restatement of this result yields an estimate on the density of complex orthogonal polynomials with respect to a fairly general weight function. We also prove a special case of the paramagnetic inequality.Part of this research was conducted during the U.S.-Sweden Workshop on Spectral Methods sponsored by the NSF under grant INT-9217529. Partial support by NSF grant PHY90-19433 A02 is also acknowledged.     

Study on divertor plasma behavior through sweeping strike point in new lower divertor on EAST

A series of L-mode discharges have been conducted in the new ‘corner slot’ divertor on the Experimental Advanced Superconducting Tokamak (EAST) to study the divertor plasma behavior through sweeping strike point. The plasma control system controls the strike point sweeping from the horizontal target to the vertical target through poloidal field coils, with keeping the main plasma stability. The surface temperature of the divertor target cools down as the strike point moves away, indicating that sweeping strike point mitigates the heat load. To avoid the negative effect of probe tip damage, a method based on sweeping strike point is used to get the normalized profile and study the decay length of particle and heat flux on the divertor target λ_js, λ_q. In the discharges with high radio-frequency (RF) heating power, electron temperature T_e is lower and λ_js is larger when the strike point locates on the horizontal target compared to the vertical target, probably due to the corner effect. In the Ohmic discharges, λ_js, λ_q are much larger compared to the discharges with high RF heating power, which may be attributed to lower edge T_e.     

Trapped fermions with density imbalance in the Bose-Einstein condensate limit

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms.     

Global energy balance and density limit on CASTOR tokamak

Total radiative power losses have been measured by a pyroelectric detector on the CASTOR tokamak in a broad range of plasma parameters. It has been shown that while for the low density operation (n _e <10 ¹⁹ m ^–3 ) the most important channel of energy losses is a thermal conductivity, the high density regimes are radiation dominated. Using a simple analytic energy balance model, the connection between such a high level of radiation and shrinking of the current channel resulting in an enhanced MHD activity is discussed.The authors would like to thank Dr. R. Klíma for many helpful and stimulating discussions.