Measurements in the LHD, L2-M, and TJ-II stellarators show that plasma density fluctuations have non-Gaussian distributions with heavy tails and sharper vertices. Non-Gaussian probability densities of stochastic plasma processes indicate non-Brownian character of the motion (diffusion) of particles. The role of rare events related to stochastic plasma processes with larger spatial and temporal scale becomes important. It is shown that the first-order differences of fluctuation samples are stochastic and their probability distribution is a mixture of Gaussians with different scales. Subordinated Lèvy process can be used to describe the turbulent transport process.

Previous investigations of small-scale density fluctuation by means of correlation reflectometry in T-10 tokamak revealed the existence of several density fluctuation types and strong radial and poloidal variation of their amplitudes and correlation properties. This paper is focused on the new measurements of the 3D spatial distributions of the amplitudes, the radial correlation lengths and the long range correlations along the field lines for the different turbulence types. The properties of the density fluctuations were systematically studied with the improved reflectometers, data analyzing and acquisition hardware. The density fluctuations were measured by heterodyne correlation reflectometry using ordinary mode. New T-10 antenna set have horn antennae arrays at four places distributed toroidally and poloidally over tokamak torus. The experiments confirmed previously found strong poloidal amplitude asymmetry of the broad band and the quasi-coherent oscillations and the uniform poloidal distribution of stochastic low frequency fluctuations. The presence of those turbulence types was also proved by the measurements of perturbation properties using heavy ion beam probe diagnostic. The radial correlation measurements were performed at four poloidal angles to understand the poloidal dependence of the radial correlation length for the different fluctuation types. The significant decrease of the radial correlation lengths towards the high magnetic field side was observed for quasi-coherent and stochastic low frequency turbulence types. The long range correlations along the field lines were measured by the reflectometers in two cross-section separated by 1/4 of the torus. The reflectometers have the same frequency thus provide reflection from the same magnetic surface. Reflection radii are chosen by the frequency variation of the launched wave from shot to shot in a series of reproducible discharges. The measurements were carried out at the low and the high magnetic field side with two currents and simultaneous reverse of the direction of the toroidal magnetic field and the plasma current. Resonance radii were also calculated using 3D tracing of the magnetic field line and demonstrate good agreement with experiments. These results allow to propose the new approach for the current profile measurements in tokamaks.

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Electric field Ε or electric potential j plays a key role in the transport and turbulence of toroidal plasmas. It is believed that mean radial E r suppresses the turbulence eddies via E×B shear, while oscillatory E r (zonal flows and geodesic acoustic modes, GAM) presents the mechanism of the turbulence self-regulation. Various aspects of the electron cyclotron resonance heating (ECRH), e.g. variation of power P ECRH value and deposition effect on the static and oscillatory components of potential were studied in two machines of similar size by heavy ion beam probe (HIBP), operating now on the T-10 tokamak and TJ-II stellarator. HIBP measures in a wide density range n e =(0.3-5)×10 19 m −3 and in various magnetic configurations in Ohmic and ECRH plasmas on T-10, and in ECRH and NBI-heated plasmas on TJ-II. With ECRH, the potential evolves towards the positive direction. This extra potential Δj increases with P ECRH increase, while Δj decreases with plasma density raise. ECRH excites the broadband electrostatic oscillations in low-density TJ-II plasma, while in high-density T-10 plasma, this effect is opposite. In T-10 GAM frequency f GAM increases with P ECRH in accordance with theoretical dependence on electron temperature ( f GAM ∼T e 1 2 / ), and GAM amplitude increases with P ECRH . ECRH affects to NBI-excited Alfvén eigenmodes (AEs): the steady frequency AEs transform to the chirping modes. In the low-density TJ-II plasmas, strong ECRH produces suprathermal (ST) electrons, exciting the electrostatic ST-modes. Dual HIBP measures the stable long-range potential correlations in TJ-II, resembling spatially localized low-frequency zonal flows in the core of ECRH plasmas. Finally, various aspects of the ECRH effects on the mean potential, broadband electrostatic turbulence, and on quasicoherent modes, including GAMs, AEs and ST-modes, are summarized.

In the T-10 tokamak, the local fluctuations of poloidal electric fieldẼ pol and densityñ e were simultaneously measured by heavy ion beam probe (HIBP) with 5-slit energy analyzer that allow us to estimate the turbulent particle flux and E × B rotation velocity in the gradient zone of plasma column (r/a = 0.8). It was shown that at the Ohmic heating (OH) stage of discharge, the outward flux is in the range of 2 × 10 19 m −2 s −1 , increasing at the ECRH stage by a factor of 1.5. At OH stage, the poloidal rotation velocity is about 4.5 km/s.

2D poloidal contour plots of plasma potential, plasma density, and their fluctuations have been measured in low density plasmas sustained by Electron Cyclotron Resonance Heating using a heavy ion beam probe (HIBP) system in the TJ-II stellarator. A HIBP has been used in the new energy scanning mode to obtain the measurements for a 2D poloidal cross section of the stellarator. The 2D map for the absolute plasma potential shows a local maximum in the plasma core as expected in low density plasma scenarios. Fluctuations in the HIBP secondary ion current, as a proxy of plasma density fluctuations, appear both in positive and negative density gradient regions, with a normalized level of density fluctuations higher in the negative density gradient region. The TJ-II innovative experimental setup developed using a dual HIBP diagnostic paves the way for model validation on core plasma potential asymmetries and particle transport and fluctuations under positive and negative density gradient scenarios.

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The structure of fluctuations and turbulent transport have been investigated in the plasma boundary region of the L2-M stellarator. Normalized fluctuation levels are in the range (3-20)% and fluctuations are dominated by frequencies below 300 kHz. In the edge plasma region located inside the last closed magnetic flux surface the radial coherence of fluctuations is due to high-frequency fluctuations (>100 kHz). The poloidal coherence is dominated by low frequencies. Linear coupling of resistive interchange modes is considered a candidate to explain the existence of highly radially correlated fluctuations in the high-frequency range.