Two approaches to self-organization in plasma: Kinetic theory treatment for the dynamo problem and sandpile automaton model for pedestal formation in magnetically confined plasma.

摘要

The dissertation consists of two parts, both of which relate to the topic of the self-organization in plasma. Self-organization in plasma is a process of spontaneous formation of ordered structures at scales much larger than the turbulent correlation scale. Examples of such structures could be a mean magnetic field in interstellar or in interplanetary space, accretion disks around dense objects, zonal fields and zonal flows in fusion plasmas, steep gradient profiles in tokamaks etc.; Part I of the dissertation addresses the fundamental problem of magnetic field generation (dynamo action). The novelty of our work is that, applying a quasilinear theory to the kinetic Alfven wave (KAW) turbulence, we demonstrate the possibility of the ‘fast dynamo’, i.e. a dynamo action which does not depend on plasma resistivity, which is extremely small in most of the relevant plasmas in space and in laboratories. Instead, the irreversibility of the dynamo action is provided by the Landau damping of the kinetic Alfven waves on plasma electrons.; Whereas Part I explicitly exploite microscopic properties of the plasma instability, the opposite methodology is applied in Part II to the problem of L → H transition and pedestal formation in magnetically confined plasmas. There a generic dynamical model, known as a sandpile cellular automaton is applied. This model is independent of the particular kind of underlying turbulence and incorporates the key features of a confined plasma, namely, collisional diffusion, shear induced bistability of turbulent transport and a local MHD limit on the gradient. One chapter of Part II describes the general phenomenology of the pedestal formation. Another chapter is concerned with an effect of the diffusion. Diffusion changes the character of the edge discharge events and can lead to hysteresis in the L → H → L transition.