M. V. A. P. Heller

SCRAPE-OFF LAYER INTERMITTENCY IN THE CASTOR TOKAMAK

Spatial–temporal intermittency of floating potential and ion saturation current fluctuations is analyzed by using data obtained from two probes arrays in the scrape-off layer of the CASTOR tokamak [Proceedings of the 1996 International Conference on Plasma Physics (Nagoya) (International Atomic Energy Agency, Vienna, 1997), Vol. I, p. 322]. For these ion saturation current fluctuations with non-Gaussian probability density functions, a conditional averaging analysis shows coherent structures with correlation lengths and lifetimes larger for larger amplitude conditions. Nevertheless, there is no evidence of such large structures in the potential fluctuations. Furthermore, wavelet transforms are used to analyze these nonstationary fluctuations and obtain details not observed with the Fourier technique. So, examining wavelet power and coherence spectra, strong intermittency is found for both kinds of fluctuations, in a time scale two orders of magnitude higher than that observed in the conditional analysis. ...

Recurrence in plasma edge turbulence

Common statistics of turbulent electrostatic fluctuations observed at the plasma edge and scrape-off layer are analyzed in three tokamak devices that have different configurations. The statistics of experimental data collected using fixed sampling time is the same than the statistics of the time for which the oscillation return to a specified reference interval of values. This observation, in addition to the finding of power-scaling laws for some average quantities with respect to either the sampling time or the size of the reference interval, suggests that turbulence on tokamaks have recurrent characteristics, typical of a recurrent chaotic low-dimensional system. Furthermore, the first Poincare recurrence time and other dynamical tools are used to simulate the mentioned fluctuation statistical properties.

Edge turbulence spectrum alterations driven by resonant fields

An ergodic magnetic structure is generated in the TBR-1 Tokamak boundary to handle heat flux and minimize impurity generation. In this work, the effect of this structure on the plasma edge turbulence is investigated. Thus, spectral alterations driven by perturbing magnetic fields created by resonant helical windings are observed in the small Tokamak TBR-1. The investigated oscillations are detected with an array of Langmuir and magnetic probes. Spectral and bispectral analyses revealed significant changes induced by the resonant helical windings, mainly in the MHD frequency band. Thus, whereas the known Mimov oscillation amplitude reduction is observed, the density and potential oscillation spectra are slightly affected. However, the bispectral analysis shows a clear reduction of the wave-wave mode coupling in the MHD frequency range, while the high frequency turbulent coupling is steadily reduced

Control of chaotic magnetic fields in tokamaks

Chaotic magnetic field lines play an important role in plasma confinement by tokamaks. They can either be generated in the plasma as a result of natural instabilities or artifficially produced by external conductors, like resonant helical windings and ergodic magnetic limiters. This is a review of works carried out at the Universidade de Sao Paulo and Universidade Federal do Parana on theoretical and experimental aspects of generation and control of chaotic magnetic field lines in tokamaks.

Temperature fluctuations and plasma edge turbulence in the Brazilian tokamak TBR

To investigate the tokamak turbulence, a set of Langmuir probes and a triple probe have been designed and used in the TBR [J. Fusion Energy 12, 529 (1993)] to measure average and fluctuating values of density, potential, and temperature of the plasma edge. The obtained results showed a significant influence of the temperature fluctuations in the transport parameters. Namely, taking into account this influence, the density and plasma potential power spectra were obtained, and the turbulence parameters reevaluated. Furthermore, the computed cross‐power‐spectra showed appreciable linear correlation, and the cross‐bispectra showed a quadratic mode coupling between temperature fluctuations and other quantities. Significant bicoherence between these fluctuations was observed. Finally, for a fluctuation monitored at two probe points, no preferential direction for energy cascading was detected.

Experimental analysis of mode coupling and plasma turbulence induced by magnetic fields

Wavelet spectrum and bispectrum techniques are applied to study the development of temporal turbulence induced by a confinement toroidal magnetic field in a toroidal magnetoplasma created by radio frequency waves. For low magnetic fields the plasma is roughly uniform and the analyzed electrostatic linear frequency spectra are essentially determined by the driven radio frequencies. However, by increasing the toroidal magnetic field, gradients in the plasma radial profiles and broader frequency spectra are observed. Thus, spectral components with frequencies higher than those injected in the plasma are excited. Moreover, this variation of magnetic field also induces nonlinear phase coupling between low frequency coherent peaks and continuous high frequency spectral components.

Correlation between Plasma Edge Electrostatic and Magnetic Oscillations in the Brazilian Tokamak TBR

Measurements of poloidal and radial magnetic field, density, potential, and temperature fluctuations were simultaneously performed at the plasma edge of the TBR tokamak using a especially constructed probe system. Direct cross spectral and bispectral analyses of these fluctuations showed evidences of both linear and nonlinear coupling between electrostatic and magnetic oscillations. Resonances created by external perturbing magnetic fields slightly reduced the linear coupling and almost entirely suppressed the quadratic coupling.

Electrostatic turbulence driven by high magnetohydrodynamic activity in Tokamak Chauffage Alfvén Brésilien

In Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao et al., Plasma Phys. Controlled Fusion 43, 1181 (2001)], high magnetohydrodynamic (MHD) activity may appear spontaneously or during discharges with a voltage biased electrode inserted at the plasma edge. The turbulent electrostatic fluctuations, measured by Langmuir probes, are modulated by Mirnov oscillations presenting a dominant peak with a common frequency around 10kHz. We report the occurrence of phase locking of the turbulent potential fluctuations driven by MHD activity at this frequency. Using wavelet cross-spectral analysis, we characterized the phase and frequency synchronization in the plasma edge region. We introduced an order parameter to characterize the radial dependence of the phase-locking intensity.

Periodic driving of plasma turbulence

Tools to characterize three important characteristics of turbulence are proposed: Structures-within-structures, intermittent amplitude bursting, and turbulence complexity. These tools are applied to show that the injection of a rf wave into the plasma confined on the Tokamak Chauffage Alfven Bresilien (TCABR) [R. M. O. Galvao, V. Bellintani, Jr., R. D. Bengtson et al., Plasma Phys. Controlled Fusion 43, A299 (2001)] decreases plasma edge turbulence, although not completely destroy it, by destroying the only two types of time structures found in the data. Both structures present multiscaling spectra, with infinitely many possible scalings. So, according to this analysis, complexity of this turbulence is mainly due to the multiscaling character of the oscillations.

Low-dimensional dynamics in observables from complex and higher-dimensional systems

We analyze fluctuating observables of high-dimensional systems as the New York Stock Market S&P 500 index, the amino-acid sequence in the M. genitalium DNA, the maximum temperature of the San Francisco Bay area, and the toroidal magneto plasma potential. The probability measures of these fluctuations are obtained by the statistical analysis of a rescaling combination of the first Poincare return time of a low-dimensional chaotic system. This result indicates that it is possible to use a measure of a low-dimensional chaotic attractor to describe a measure of these complex systems. Moreover, within this description we determine scaling power laws for average measurements of the analyzed fluctuations.