This paper presents the latest results on confinement studies in the TJ-II stellarator. The inherently strong plasma–wall interaction of TJ-II has been successfully reduced after lithium coating by vacuum evaporation. Besides H retention and low Z, Li was chosen because there exists a reactor-oriented interest in this element, thus giving special relevance to the investigation of its properties. The Li-coating has led to important changes in plasma performance. Particularly, the effective density limit in NBI plasmas has been extended reaching central values of 8 × 1019 m−3 and T e ≈ 250–300 eV, with peaked density, rather flat T e profiles and higher ion temperatures. Due to the achieved density control, a second type of transition has been added to the low density ones previously observed in ECRH plasmas: higher density transitions characterized by the fall in Hα emission, the onset of steep density gradient and the reduction in the turbulence; which are characteristics of transition to the H mode. Confinement studies in ECH plasmas indicate that lowest order magnetic resonances, even in a low shear environment, locally reduce the effective electron heat diffusivities, while Alfven eigenmodes destabilized in NBI plasmas can influence fast ion confinement.

First plasmas have been successfully achieved in the TJ-II stellarator using electron cyclotron resonance heating (f = 53.2 GHz, P ECRH = 250 kW). Initial experiments have explored the TJ-II flexibility in a wide range of plasma volumes, different rotational transform and magnetic well values. In this paper, the main results of this campaign are presented and, in particular, the influence of plasma wall interaction phenomena on TJ-II operation is discussed briefly.

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation (KdV7). A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation we obtain other solutions by some ansatzes different from the Cole-Hopf transformation.

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