Interaction renormalization and the plasma staircase

Abstract

We resolve an existing question concerning dynamical and structural stability of the E {\times} B staircases in magnetically confined fusion plasma. The problem has stirred considerable interest in the literature due to a unique combination of its scientific and practical aspects. Here, we report a new approach to the problem by combining the paradigmatic Hasegawa-Wakatani model of electrostatic drift-wave turbulence with an idea of interaction renormalization, imported from quantum field theory. It is shown based on the Schrödinger-Newton equation with renormalized interaction constant that the plasma staircase is robust and stable as soon as the nonadiabaticity parameter, δ, goes above a certain critical value, and is unstable otherwise. This critical value is an exact result of the interaction model and is found to be δc = π. For δ < δc , the unstable system expands in the radial direction, resulting in a radial second moment that grows with time t as t^(2/3). The results obtained bear important implications with regard to the implementation of arrays of semipermeable transport barriers in tokamaks, suggesting a threshold condition for their generation.