The resilience to chaotic perturbations of one-parameter one-degree-of-freedom Hamiltonian dynamics is shown to increase when its corresponding separatrix vanishes due to a saddle-node bifurcation. This is first highlighted for the magnetic chaos related to quasisingle helicity (QSH) states of the reversed field pinch. It provides a rationale for the confinement improvement of helical structures experimentally found for QSH plasmas; such a feature would not be expected from the classical resonance overlap picture as the separatrix disappearance occurs when the amplitude of the dominant mode increases.

The reversed field pinch (RFP) is a configuration for magnetic confinement akin to the tokamak, but its toroidal field has an amplitude comparable to the poloidal one, and reverses in the outer region. Recent progress in experiments and theory open a path beyond the standard paradigm that a bath of magnetic turbulence is intrinsic to the RFP. In RFX, the largest present RFP experiment, the existence of plasma states with a hot helical core has been proven by soft x-ray tomography. Such states have been seen transiently in several RFPs, but also permanently in discharges in RFX. This last fact makes these states germane to the stationary single-helicity (SH) states displayed by three-dimensional visco-resistive MHD simulations. These simulations also display multiple-helicity (MH) states whose features, in particular magnetic chaos, are analogous to the traditional turbulent state of RFP plasmas. The numerical MH states bifurcate to SH ones when the product (viscosity×resistivity) is increased. The SH states correspond to an integrable magnetic field with good flux surfaces, a feature favourable to good confinement. SH states are not Taylor states, but they may be viewed as the nonlinear state of a resistive kink mode stabilized by the toroidal field reversal.

The stochastic diffusion process has been carefully analysed for the Reverse Field Pinch ͑RFP͒ equilibrium configuration. Three different approaches to the problem have been used, i.e. the direct calculation of the stochastic diffusion coefficient (D st ) from the radial evolution of an ensemble of field lines, an indirect determination using a Gaussian-fit to the field line probability distribution function and finally the relationship of D st with the maximum Lyapunov exponent of the system. Different perturbation spectra have been also considered and compared and the quasi-linear approximation has been tested.

This paper reports experimental results showing that coherent helical structures are formed in the reversed field pinch (RFP) self-organizing plasma core as a result of transitions to states where the n-spectrum of the m=1 modes is dominated by a single (1,nmax) geometrical helicity. These states are dubbed quasi-single helicity (QSH) states. Their magnetic and thermal properties measured in the reverse field experiment (RFX) [G. Rostagni, Fusion Eng. Des. 25, 301 (1995)] device are described. The present theoretical understanding of QSH states is discussed and some recent theoretical results are presented. The role of aspect ratio is discussed. These results represent a significant step to open a path beyond the standard paradigm that a bath of magnetohydrodynamic (MHD) modes is intrinsic to the RFP.