Excitation of the turbulence in the range of drift wave frequency and zonal flow in magnetized plasmas is analyzed. Nonlinear stabilization effect on zonal flow drive is introduced, and the steady state solution is obtained. The condition for the onset of turbulent transport is obtained and partition ratio of fluctuation energy into turbulence and zonal flows is derived. The turbulent transport coefficient, which includes the effect of zonal flow, is also obtained. Analytic result and direct numerical simulation show a good agreement.
As the finalization of the hydrogen experiment towards the deuterium phase, the exploration of the best performance of the hydrogen plasma was intensively performed in the Large Helical Device (LHD). High ion and electron temperatures, Ti, Te, of more than 6 keV were simultaneously achieved by superimposing the high power electron cyclotron resonance heating (ECH) on the neutral beam injection (NBI) heated plasma. Although flattening of the ion temperature profile in the core region was observed during the discharges, one could avoid the degradation by increasing the electron density. Another key parameter to present plasma performance is an averaged beta value . The high regime around 4 % was extended to an order of magnitude lower than the earlier collisional regime. Impurity behaviour in hydrogen discharges with NBI heating was also classified with the wide range of edge plasma parameters. Existence of no impurity accumulation regime where the high performance plasma is maintained with high power heating > 10 MW was identified. Wide parameter scan experiments suggest that the toroidal rotation and the turbulence are the candidates for expelling impurities from the core region.
Remarkable progress in the physical parameters of net-current free plasmas has been made in the Large Helical Device (LHD) since the last Fusion Energy Conference in Chengdu, 2006 (O.Motojima et al., Nucl. Fusion 47 (2007. The beta value reached 5 % and a high beta state beyond 4.5% from the diamagnetic measurement has been maintained for longer than 100 times the energy confinement time. The density and temperature regimes also have been extended. The central density has exceeded 1.0×10 21 m -3 due to the formation of an Internal Diffusion Barrier (IDB). The ion temperature has reached 6.8 keV at the density of 2×10 19 m -3 , which is associated with the suppression of ion heat conduction loss. Although these parameters have been obtained in separated discharges, each fusion-reactor relevant parameter has elucidated the potential of net-current free heliotron plasmas. Diversified studies in recent LHD experiments are reviewed in this paper.
A statistical model for the bifurcation of the radial electric field Er is analyzed in view of describing L-H transitions of tokamak plasmas. Noise in microfluctuations is shown to lead to random changes of Er if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of Er are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Because of the suppression of turbulence by shear in Er, the limit deviates from Maxwell's rule.
The role of zonal flows ͑ZFs͒ in the formation of an internal transport barrier in a toroidal helical plasma is analyzed. The turbulent transport coefficient is shown to be suppressed when the plasma state changes from the branch of a weak negative radial electric field to the strong positive one. This new transition of turbulent transport is caused by the change of the damping rate of the ZFs. It is clearly demonstrated, theoretically and experimentally, that the damping rate of the ZFs governs the global confinement of toroidal plasmas. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2435310͔The turbulence-driven transport and the structural formation in confined plasmas are one of the principal issues of modern plasma physics.1 In particular, the transport barriers in toroidal plasmas 2 have attracted attention, in which the turbulent transport coefficient shows a steep gradient at a particular radius after the onset of the transition. 3-5 One thread of thought to explain transport barriers is the structural transition in the profile of the radial electric field, E r , and suppression of turbulence by its gradient through the sheared advection of fluctuations. 3,[6][7][8][9] For the study of turbulent structural transitions, toroidal helical plasmas provide unique opportunities: That is, the bifurcation of the radial electric field is influenced by the neoclassical ripple transport, 10 and the resultant electric field interface ͑by which the radial domains with positive E r and negative E r are separated͒ was predicted to induce the internal transport barrier. The E r interface was found on the compact helical system ͑CHS͒, 11 and the improvement of the electron confinement was found inside of the E r interface 12 ͓hereafter called the electron internal transport barrier ͑e-ITB͔͒. Observations on Wendelstein 7AS ͑W7AS͒, 13 LHD, 14 and other experiments followed. 5,15 The appearance and location of the E r interface were analyzed. [16][17][18] However, the essential issue of e-ITB formation has been unexplained, i.e., the turbulent transport coefficient was found to be suppressed not only near the interface but also in the whole region of strong positive E r ͑where the gradient dE r /dr is not strong enough to suppress turbulent transport͒. Therefore the fundamental problem remains unresolved. In this article, we study the role of zonal flows ͑ZFs͒ ͑Ref. 19͒ in the formation of an e-ITB. The turbulent transport coefficient, in which the screening influence of ZFs is included, is shown to be suppressed when the plasma state changes from the branch of weak negative E r to that of strong positive E r . This new transition of turbulent transport is induced by the change of the damping rate of the ZFs, which is strongly influenced by the neoclassical ripple transport. The analytic theory is explained first. Then the transport analysis is shown. Finally, the experimental verification based on the CHS plasmas is demonstrated. This is the first report to clarify that the collisional damping rate of the ZFs gover...
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