Zonal flows and their high-frequency counterpart, the geodesic acoustic modes (GAMs) are considered as a possible mechanism of the plasma turbulence self-regulation. In the T-10 tokamak GAMs have been studied by the heavy ion beam probing and multipin Langmuir probes. The wide range of the regimes with Ohmic, on-axis and off-axis electron cyclotron resonance heating (ECRH) were studied (B t = 1.5-2.4 T, I p = 140-300 kA, ne = (0.6-6.0) × 10 19 m −3 , P EC < 1.2 MW). It was shown that GAM has radially homogeneous structure and poloidal m = 0 for potential perturbations. The local theory predicts that f GAM ∼ √ T /m i /R, that means the frequency increases with the decrease of the minor radius. In contrast, the radial distribution of experimental frequency of the plasma potential and density oscillations, associated to GAM, is almost uniform over the whole plasma radius, suggesting the features of the nonlocal (global) eigenmodes. The GAM amplitude in the plasma potential also tends to be uniform along the radius. GAMs are more pronounced during ECRH, when the typical frequencies are seen in the narrow band from 22 to 27 kHz for the main peak and 25-30 kHz for the higher frequency satellite. GAM characteristics and the range of GAM existence are presented as functions of T e , density, magnetic field and P EC .

Heavy ion beam probing (HIBP) is a unique diagnostics to study the core plasma potential and turbulence. Advanced HIBPs operate in the T-10 tokamak and TJ-II flexible heliac with fine focused (<1 cm) and intense (100 µA) beams. They provide measurements in the wide density interval n e = (0.3-5) × 10 19 m −3 , in a wide range of Ohmic and electron cyclotron resonance heated (ECRH) discharges with various currents at T-10, and in the wide range of magnetic configurations with ECR and neutral beam injection (NBI) heating at TJ-II. Time evolution of the radial profiles and/or local values of plasma parameters from high field side (HFS) to low field side (LFS), −1 < ρ < 1, is observed in TJ-II by 125 keV Cs + ions in a single shot, while LFS (+0.2 < ρ < 1) is observed in T-10 by 300 keV Tl + ions. Multi-slit energy analyzers provide simultaneously data on the plasma potential ϕ (by the beam extra energy), plasma density n e (by the beam current), poloidal magnetic field B pol (by the beam toroidal shift), poloidal electric filed E pol that allows one to derive the electrostatic turbulent particle flux Γ E×B . The cross-phase of density oscillations produces the phase velocity of their poloidal propagation or rotation; also it gives the poloidal mode number. Dual HIBP, consisting of two identical HIBPs located ¼ torus apart provide the long-range correlations of core plasma parameters. Low-noise high-gain electronics allows us to study broadband turbulence and quasi-coherent modes like geodesic acoustic modes and Alfvén eigenmodes.

New experimental observations of the plasma potential using the heavy ion beam probe diagnostic are presented together with a theoretical description of the formation of the electric field E r in the T-10 circular tokamak (B 0 = 1.5-2.5 T, R = 1.5 m, a = 0.3 m). Ohmically heated (OH) deuterium plasmas with main plasma parameters ne = (0.6-4.7) × 10 19 m −3 , T e (0) < 1.3 keV, T i (0) < 0.6 keV are characterized by a negative potential ϕ(ρ) with maximum negative values of ϕ(6 cm) = −1400 V with respect to the wall. The potential profile monotonically increases towards the plasma edge. A density rise due to gas puff is accompanied by a plasma potential that becomes increasingly negative. When the density approaches values in the range ne = (2.5-3.5) × 10 19 m −3 , the value of the plasma potential saturates, while the energy confinement time still increases up to a saturation value that is obtained at a slightly higher density. With auxiliary heating by electron cyclotron resonance heating (ECRH) up to 1.2 MW, T e (0) increases (up to 3 keV) and the absolute value of the plasma potential decreases. In some cases the plasma potential changes its sign and becomes positive at the edge. The radial profile of E r and its dependence on n e and T i are qualitatively explained by a neoclassical model in the core, and a turbulent dynamic model (Braginskij magnetohydrodynamic equations) in the edge.

New findings in study of geodesic acoustic modes (GAMs) on the T-10 tokamak since the last IAEA FEC 2014 are described. The broadband fluctuations of potential φ and electron density ne in Ohmic and ECRH regimes are analyzed with Heavy Ion Beam Probing along with fluctuations of poloidal magnetic field Bpol. At the edge, at ρ  >  0.8, the dominated GAM peak with frequency 17 kHz in potential fluctuations, and noticeable peak of quasi-coherent density and potential fluctuations with frequency 40–100 kHz and HFHM ~30 kHz are observed. During ECRH of high density ~ 4  ×  1019 m−3 plasmas, the level of broadband fluctuations decreases, but the energy confinement degrades and the GAM amplitude on φ rises. The bi-spectral analysis of φ and ne fluctuations demonstrates the existence of statistically significant auto- and cross-bicoherence at the GAM frequency that points out to three-wave interaction between GAM and broadband electrostatic turbulence, while the cross-bicoherence for φ, ne and Bpol indicates three-wave interaction between GAM and broadband electromagnetic turbulence. These three-wave interactions may be explained by quadratic character of nonlinear GAM generation, e.g. owing to Reynolds stress.