The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus
necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Braginskii-type fluid simulations, and check this against a first-principles theoretical model. The analysis of the numerical simulations indicates that the probability distribution function of the intermittent process contains strong exponential tails, as predicted by the analytical theory.
Hybrid inflation models are especially interesting as they lead to a spike in the density power spectrum on small scales, compared to the CMB, while also satisfying current bounds on tensor modes. Here we study hybrid inflation with $N$ waterfall fie
lds sharing a global $SO(N)$ symmetry. The inclusion of many waterfall fields has the obvious advantage of avoiding topologically stable defects for $N>3$. We find that it also has another advantage: it is easier to engineer models that can simultaneously (i) be compatible with constraints on the primordial spectral index, which tends to otherwise disfavor hybrid models, and (ii) produce a spike on astrophysically large length scales. The latter may have significant consequences, possibly seeding the formation of astrophysically large black holes. We calculate correlation functions of the time-delay, a measure of density perturbations, produced by the waterfall fields, as a convergent power series in both $1/N$ and the fields correlation function $Delta(x)$. We show that for large $N$, the two-point function is $<delta t({bf x}),delta t({bf 0})>,proptoDelta^2(|{bf x}|)/N$ and the three-point function is $<delta t({bf x}),delta t({bf y}),delta t({bf 0})>,proptoDelta(|{bf x}-{bf y}|)Delta(|{bf x}|)Delta(|{bf y}|)/N^2$. In accordance with the central limit theorem, the density perturbations on the scale of the spike are Gaussian for large $N$ and non-Gaussian for small $N$.
