The transport of impurities in fusion reactor plasmas has been the object of many theoretical, computational, and experimental investigations. These impurities can be charged particles created from plasma-wall interactions in tokamaks, for example. The transport of such impurities raise a number of key issues in both physical and technological levels. In ITER the particle transport (not just impurities) may generate heat loads of $5 - 10 MW/m^2$ that can damage the tokamak inner wall. Chaotic magnetic field lines have been proposed to uniformize heat and particle loadings. However, experimental results show that these loadings are not really uniform, but that the deposition pattern has a self-similar organization, a fractal pattern indeed. Magnetic field line models using non-integrable Hamiltonian systems are able to show that these fractal patterns are ultimately related to the chaotic saddle. In this work, we shall pursue another pathway to describe chaotic impurity transport in toroidal plasmas, by including electrostatic fluctuations in the model equations.

The magnetic confinement of toroidal plasmas is strongly affected by a large number of instabilities. Among them, one of the most important is represented by drift instabilities, occurring when there are steep density gradients in the plasma column. For low frequencies, drift waves are electrostatic, in the sense that the electric field points along the propagation direction. The electrostatic field associated with the drift wave, combined with the dominant magnetic field, produces an ExB drift in particle motion. The advection of passive particles is due to the ExB drift motion, can be described in a Hamiltonian form.

In this work, we investigate the transport of chaotic impurities in a fusion plasma with toroidal geometry. We use realistic tokamak profiles for electric and magnetic fields as well as toroidal rotation effects, and consider also the effects of electrostatic fluctuations due to drift instabilities on particle motion. We show that the chaotic transport in the outer plasma region is influenced by fractal structures that are described in topological and metric point of views. Furthermore, we demonstrate the existence of a hierarchical structure of islands around islands in the phase space, which effectively traps the particles.