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It has been shown [Maccio, Phys. Plasmas 8, 895 (2001)] that a uniform radial electric field can stabilize the toroidal ion temperature gradient mode in tokamak plasmas. In this paper, using the ballooning transform, the mechanism leading to stabilization is further clarified. However, the stabilizing effect depends on the choice of the background distribution function. It is shown that if the electric field is connected with a toroidal plasma rotation the stabilizing effect becomes ineffective. Consequently, in many current experiments this effect should not play a role. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Profile consistency is a long-standing mystery of transport in thermonuclear fusion plasmas. This phenomenon is critically tested by studying the system response to off-axis fueling or heating. The present paper investigates the potential of a recently proposed probabilistic transport model to simulate this phenomenon, and it is found that most of the observed phenomenology can be reproduced, at least qualitatively. In particular, the observed differences between tokamaks and stellarators under off-axis heating may find an explanation in this framework. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Changes in the poloidal magnetic field around a tokamak magnetic surface due to different values of triangularity and ellipticity are analyzed in this paper. The treatment here presented allows the determination of the poloidal magnetic field from knowledge of the toroidal current density. Different profiles of these currents are studied. Improvements in the analytic forms of the magnetic surfaces have also been found. The treatment has been performed using a recent published system of coordinates. Suitable analytic equations have been used for the elliptic magnetic surfaces with triangularity and Shafranov shift. [ABSTRACT FROM AUTHOR]

The formation of coherent structures by two-dimensional interchange turbulence in the scrape-off layer (SOL) of tokamak plasmas and their subsequent contribution to anomalous plasma transport has been studied in recent years using electron continuity and current balance equations. In this paper, it is demonstrated that the inclusion of electron energy equation in the simulations changes the nature of coherent structures in a significant manner and gives results which are in better agreement with experiments. Specifically, it is observed that radial potential gradients are established which give a poloidal elongation and movement to the structures. Only during the radial transport events do the structures get significantly extended in the radial direction giving radial velocities of order 1 km/s. Sometimes detachment of density structures from the main plasma is observed. These detached structures either decay into the background plasma or are transported out from the SOL. The simulated particle flux and its statistical properties also are discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The effect on a tokamak of applying a nonaxisymmetric magnetic perturbation δB is computed. An equilibrium with scalar pressure p yields zero net radial current, and therefore zero torque. Thus, the usual approach, which assumes scalar pressure, is not self-consistent, and masks the close connection that exists between that radial current and the in-surface currents, which provide shielding or amplification of δB. Here, the pressure anisotropy, p∥,p⊥≠p, and from this, both the radial and in-surface currents, are analytically computed. The surface average of the radial current recovers earlier expressions for ripple transport, while the in-surface currents provide an expression for the amount of self-consistent shielding the plasma provides. [ABSTRACT FROM AUTHOR]

It is demonstrated that the pitch angle integrals in the transport fluxes in the ν regime calculated in K. C. Shang [Phys. Plasmas 10, 1443 (2003)] are divergent as the trapped-circulating boundary is approached. Here, ν is the collision frequency. The origin of this divergence results from the logarithmic dependence in the bounce averaged radial drift velocity. A collisional boundary layer analysis is developed to remove the singularity. The resultant pitch angle integrals now include not only the original physics of the ν regime but also the boundary layer physics. The transport fluxes, caused by the particles inside the boundary layer, scale as ν. [ABSTRACT FROM AUTHOR]

Plasma edge turbulence in Tokamak Chauffage Alfvén Brésilien (TCABR) [R. M. O. Galvão et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences. [ABSTRACT FROM AUTHOR]

A Tokamak à Configuration Variable (TCV) [G. Tonetti, A. Heym, F. Hofmann et al., in Proceedings of the 16th Symposium on Fusion Technology, London, U.K., edited by R. Hemsworth (North-Holland, Amsterdam, 1991), p. 587] plasma with high power density (up to 8 MW/m3) core deposited electron cyclotron resonance heating at significant plasma densities (<=7×1019 m-3) is analyzed for the electron thermal transport. The discharge distinguishes itself as it has four distinct high confinement mode (H-mode) phases. An Ohmic H-mode with type III edge localized modes (ELMs), which turns into a type I ELMy H-mode when the ECRH is switched on. The ELMs then vanish, which gives rise to a quasistationary ELM-free H-mode. This ELM-free phase can be divided into two, one without magnetohydrodynamics (MHD) and one with. The MHD mode in the latter case causes the confinement to drop by ∼15%. For all four phases both large-scale trapped electron (TEM) and ion temperature gradient (ITG) modes and small-scale electron temperature gradient (ETG) modes are analyzed. The analytical TEM formulas have difficulty in explaining both the magnitude and the radial profile of the electron thermal flux. Collisionality governs the drive of the TEM, which for the discharge in question implies it can be driven by either the temperature or density gradient. The TEM response function is derived and it is shown to be relatively small and to have sharp resonances in its energy dependence. The ETG turbulence, predicted by the Institute for Fusion Studies electron gyrofluid code, is on the other hand driven solely by the electron temperature gradient. Both trapped and passing electrons add to the ETG instability and turbulent thermal flux. For easy comparison of the results of the above approaches and also with the Weiland model, a dimensionless error measure, the so-called average relative variance is introduced. According to this method the ETG model explains 70% of the variation in the electron heat diffusivity whereas the predictive capabilities of the TEM-ITG models are poor. These results for TCV support the conclusion that the ETG model is able to explain a wide range of anomalous electron transport data, in addition to existing evidence from ASDEX [F. Ryter, F. Leuterer, G. Pereverzev, H.-U. Fahrbach, J. Stober, W. Suttrop, and the ASDEX Upgrade Team, Phys. Rev. Lett. 86, 2325 (2001)], Tore Supra [G. T. Hoang, W. Horton, C. Bourdelle, B. Hu, X. Garbet, and M. Ottaviani, Phys. Plasmas 10, 405 (2003)] and the Frascati Tokamak Upgrade [A. Jacchia, F. D. Luca, S. Cirant, C. Sozzi, G. Bracco, A. Brushi, P. Buratti, S. Podda, and O. Tudisco, Nucl. Fusion 42, 1116 (2002)]. [ABSTRACT FROM AUTHOR]

A simple map [A. Punjabi, A. Verma, and A. Boozer, Phys. Rev. Lett. 69, 3322 (1992)] is the simplest map that has the topology of divertor tokamaks [A. Punjabi, H. Ali, T. Evans, and A. Boozer, Phys. Lett. A 364, 140 (2007)]. Here, action-angle coordinates, the safety factor, and the equilibrium generating function for the simple map are calculated analytically. The simple map in action-angle coordinates is derived from canonical transformations. This map cannot be integrated across the separatrix surface because of the singularity in the safety factor there. The stochastic broadening of the ideal separatrix surface in action-angle representation is calculated by adding a perturbation to the simple map equilibrium generating function. This perturbation represents the spatial noise and field errors typical of the DIII-D [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)] tokamak. The stationary Fourier modes of the perturbation have poloidal and toroidal mode numbers (m,n,)={(3,1),(4,1),(6,2),(7,2),(8,2),(9,3),(10,3),(11,3)} with amplitude δ=0.8×10-5. Near the X-point, about 0.12% of toroidal magnetic flux inside the separatrix, and about 0.06% of the poloidal flux inside the separatrix is lost. When the distance from the O-point to the X-point is 1 m, the width of stochastic layer near the X-point is about 1.4 cm. The average value of the action on the last good surface is 0.19072 compared to the action value of 3/5π on the separatrix. The average width of stochastic layer in action coordinate is 2.7×10-4, while the average area of the stochastic layer in action-angle phase space is 1.69017×10-3. On average, about 0.14% of action or toroidal flux inside the ideal separatrix is lost due to broadening. Roughly five times more toroidal flux is lost in the simple map than in DIII-D for the same perturbation [A. Punjabi, H. Ali, A. Boozer, and T. Evans, Bull. Amer. Phys. Soc. 52, 124 (2007)]. [ABSTRACT FROM AUTHOR]

A model for field error penetration is developed that includes nonresonant as well as the usual resonant field error effects. The nonresonant components cause a neoclassical toroidal viscous torque that tries to keep the plasma rotating at a rate comparable to the ion diamagnetic frequency. The new theory is used to examine resonant error-field penetration threshold scaling in ohmic tokamak plasmas. Compared to previous theoretical results, the plasma is found to be less susceptible to error-field penetration and locking, by a factor that depends on the nonresonant error-field amplitude. [ABSTRACT FROM AUTHOR]

A slab model is developed to study the excitation of lower hybrid instability triggered by the injection of a transverse neutral beam in a tokamak with magnetic shear. The lower hybrid mode is evanescent in the inner and outer region while propagating waves in the intermediate region. The neutral beam, on getting fully ionized in the plasma, resonantly couples with the lower hybrid wave in the intermediate region, driving the mode unstable. The theory of this process reveals that the growth rate scales as one third power of beam density, and increases significantly with the sheared magnetic field due to modification in the parallel wave number and the mode structure. [ABSTRACT FROM AUTHOR]

Collisional diffusion is analyzed for plasma tokamaks with different ellipticities and triangularities. Improved nonlinear equations for the families of magnetic surfaces are used here. Dimensionless average velocities are calculated as a function of the inductive electric field, elongation, triangularity, and Shafranov shift. Confinement has been found to depend significantly on triangularity. [ABSTRACT FROM AUTHOR]

Tokamak equilibrium has been analyzed with the magnetohydrodynamics nonlinear momentum equation in the low vorticity case. A large simplification in the analysis is obtained in this case compared with previous general treatments for rotating plasmas in tokamaks. Now pressure is not conserved around magnetic surfaces, however, other generalized functions have been found, which are conserved on each magnetic surface. A generalized Grad–Shafranov-type equation has been also derived for this case. How to determine the gradient of these new conserved functions on each magnetic surface from their value at one point of the corresponding surface is also shown. [ABSTRACT FROM AUTHOR]

Configurations with nearby multiple resonant surfaces have broad spectra of linearly unstable coupled tearing modes with dominant high poloidal mode numbers m. This was recently shown for the case of multiple q=1 resonances [Bierwage et al., Phys. Rev. Lett. 94 65001 (2005)]. In the present work, similar behavior is found for double tearing modes (DTM) on resonant surfaces with q>=1. A detailed analysis of linear instability characteristics of DTMs with various mode numbers m is performed using numerical simulations. The mode structures and dispersion relations for linearly unstable modes are calculated. Comparisons between low- and higher-m modes are carried out, and the roles of the inter-resonance distance and of the magnetic Reynolds number SHp are investigated. High-m modes are found to be destabilized when the distance between the resonant surfaces is small. They dominate over low-m modes in a wide range of SHp, including regimes relevant for tokamak operation. These results may be readily applied to configurations with more than two resonant surfaces. [ABSTRACT FROM AUTHOR]

Plasma rotation is shown to remove the impossibility of the existence of “normal” equilibrium in a tokamak with reversed current. The mathematical procedure of how to overcome the peculiarities, which appear in the equilibrium equations due to current reversal, is suggested. An example of normal tokamak equilibrium with a reversed current is constructed. [ABSTRACT FROM AUTHOR]

The effect of parametric ion cyclotron turbulence on the heating of cold and suprathermal ions in the edge of a tokamak plasma during injection of high radio frequency (rf) power in the ion cyclotron resonance frequency range is studied. The maximum turbulent heating rates for cold edge ions and suprathermal edge ions are calculated analytically for ion cyclotron turbulence driven by rf heating at the plasma edge. It is demonstrated that the maximum turbulent ion-heating rate for suprathermal ions is insufficient to explain the observed heating of edge ions. Therefore, the excitation of ion cyclotron turbulence by rf heating systems in the plasma edge is unlikely to be responsible for the experimentally observed large population of suprathermal ions in the edge of tokamak plasmas. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Transport theory for potato orbits in the region near the magnetic axis in an axisymmetric torus such as tokamaks and spherical tori is extended to the situation where the toroidal flow speed is of the order of the sonic speed as observed in National Spherical Torus Experiment [E. J. Synakowski, M. G. Bell, R. E. Bell et al., Nucl. Fusion 43, 1653 (2003)]. It is found that transport fluxes such as ion radial heat flux, and bootstrap current density are modified by a factor of the order of the square of the toroidal Mach number. The consequences of the orbit squeezing are also presented. The theory is developed for parabolic (in radius r) plasma profiles. A method to apply the results of the theory for the transport modeling is discussed. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The memory effect, due to postafterglow survival of some species which affect subsequent breakdown, was analyzed from the behavior of memory curves. In early afterglow, up to several tens of a millisecond, the memory effect in nitrogen is a consequence of the presence of positive ions formed by the collision between metastable molecules and highly vibrationally excited molecules remaining from the previous discharge. In late afterglow, the memory effect is due to N(4S) atoms created during the previous discharge and in early afterglow. When the atom density is reduced enough the breakdown is initiated by cosmic rays which always exists. In late afterglow in nitrogen the memory effect is very sensitive on cathode material. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The influence of a slow ion beam on an ion-acoustic wave is studied theoretically and experimentally. A kinetic dispersion relation of an ion-beam–plasma system predicts a critical value of the ion-beam density above which the ion-acoustic wave is transformed into the fast mode of the ion beam. Below the critical value, the ion-acoustic wave propagates without transforming into the fast mode of space charge waves for any beam velocity. A dispersion relation based on a fluid model does not provide such a critical value for the ion-beam density. Experimentally, the ion-beam density is controlled carefully to test the presence of the critical density at which the change in topology of dispersion roots appears. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Experiments carried out on the Frascati Tokamak Upgrade (FTU) [B. Angelini et al., Nucl. Fusion 43, 1632 (2003)] with the injection of deuterium pellets in ohmic, high density plasmas show that a remarkable enhancement of the energy confinement time is achieved when the pellet penetrates deeply in the plasma core. Here a study of pellet effects on the electrostatic turbulence is carried out with the gyrokinetic codes Kinezero [C. Bourdelle et al., Nucl. Fusion 42, 892 (2002)] and GS2 [M. Kotschenreuther, G. Rewoldt, and M. W. Tang, Comput. Phys. Commun. 88, 128 (1995)]. The analysis shows that the collisionality of FTU plasmas is high enough to detrap the electrons. The low wavelength unstable modes remaining are then pure ion temperature gradient modes that are stabilized by more peaked density profiles. In the postpellet phase the density peaking stabilizes also strongly the high wavelength electron temperature gradient modes. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A two-dimensional hydrodynamic simulation code CAP has been developed in order to investigate the dynamics of hydrogenic pellet ablation in magnetized plasmas throughout their temporal evolution. One of the properties of the code is that it treats the solid-to-gas phase change at the pellet surface without imposing artificial boundary conditions there, as done in previous ablation models. The simulation includes multispecies atomic processes, mainly molecular dissociation and thermal ionization in the ablation flow beyond the pellet, with a kinetic heat flux model. It was found that ionization causes the formation of a quasistationary shock front in the supersonic region of the ablation flow, followed by a “second” sonic surface farther out. Anisotropic heating, due to the directionality of the magnetic field, contributes to a nonuniform ablation (recoil) pressure distribution over the pellet surface. Since the shear stress can exceed the yield strength of the solid for a sufficiently high heat flux, the solid pellet can be fluidized and flattened into a “pancake” shape while the pellet is ablating and losing mass. The effect of pellet deformation can shorten the pellet lifetime almost 3× from that assuming the pellet remains rigid and stationary during ablation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Measurements of toroidal flow velocities in the midplane of the inner and outer scrape-off layers (SOL) of Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] plasmas are made using a high-resolution spectrograph. Doppler shifts of the line emissions from either He[sup +] at 468.6 nm or neutral deuterium at 656.1 nm from two local gas puffs are observed along radially separated, toroidally viewing chords to obtain the radial profiles of the toroidal ion and neutral flow velocities and of the temperatures in the midplane of the inner and outer SOL’s. In these experiments, the ion vertical drift due to the toroidal magnetic field gradient (ion B×∇B drift) is directed towards the lower X-point, and an outer SOL plasma flow with a velocity in the range of 5–10 km/s in the direction of the plasma current is observed at the midplane far above the divertor plates. Plasma flow in a similar direction with similar velocities is observed in the inner SOL midplane. This observation suggests a toroidal rotation of the edge plasma in a co-current direction, consistent with an E[sub r]×B[sub θ] motion that would arise from a radially outward electric field. Interestingly, the neutral atoms in these views are observed to flow in the opposite directions in the inner and outer SOL’s, i.e., the neutrals flow in the plasma current direction in the inner SOL and in a direction opposite to the plasma current in the outer SOL. Also, the neutrals move much slower (velocities ∼2–4 km/s) in the outer SOL compared to the inner SOL (velocities ∼4–10 km/s). Temperatures determined from the Doppler broadening of the spectral lines are found to be in the range of ∼15–25 eV for the He[sup +] ions in the inner and outer SOL’s. Much lower temperatures of ≤2–5 eV are indicated for the deuterium atoms in both SOL’s. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]