An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom

We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is implemented both for isoenergetically nondegenerate and for degenerate Hamiltonians. For the spiral mean frequency vector, we find numerically that the iterations of the transformation on nondegenerate Hamiltonians tend to degenerate ones on the critical surface. As a consequence, isoenergetically degenerate and nondegenerate Hamiltonians belong to the same universality class, and thus the corresponding critical invariant tori have the same type of scaling properties. We numerically investigate the structure of the attracting set on the critical surface and find that it is a strange nonchaotic attractor. We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure

Quasilinear transport modelling at low magnetic shear

Accurate and computationally inexpensive transport models are vital for routine and robust predictions of tokamak turbulent transport. To this end, the QuaLiKiz [Bourdelle et al., Phys. Plasmas 14, 112501 (2007)] quasilinear gyrokinetic transport model has been recently developed. QuaLiKiz flux predictions have been validated by non-linear simulations over a wide range in parameter space. However, a discrepancy is found at low magnetic shear, where the quasilinear fluxes are significantly larger than the non-linear predictions. This discrepancy is found to stem from two distinct sources: the turbulence correlation length in the mixing length rule and an increase in the ratio between the quasilinear and non-linear transport weights, correlated with increased non-linear frequency broadening. Significantly closer agreement between the quasilinear and non-linear predictions is achieved through the development of an improved mixing length rule, whose assumptions are validated by non-linear simulations. (C) 2012 American Institute of Physics