A study on the ion temperature gradient driven turbulence in tokamak plasmas

The continuous growth of the energy worldwide consumption is one of the most important challenges to our civilization. New kinds of energy resources are without doubt needed. Nuclear fusion promises to supply large amounts of energy, with minimal environmental impact. This has motivated at least sixty years of research in which substantial progress has been achieved, but without breakthrough result. Nuclear fusion can occur at temperatures of the order of 150 million degrees Celsius (thermonuclear fusion). At these temperatures atoms are completely ionized, the fuel is then in the state of matter called a plasma, a gas of ions and electrons. The most promising approach towards the goal of using thermonuclear fusion for large scale energy production is to confine the plasma using magnetic fields. The tokamak is the device that produces the best results concerning plasma magnetic confinement to date. One of the main tasks of fusion research is the understanding of plasma confinement. The energy confinement must be sufficiently good such that a large amount of reactions take place, this in order to make the process economically convinient. This translates in the necessity of minimizing the heat fluxes out of the plasma. The heat fluxes observed experimentally in tokamak plasmas are much higher than those that can be ascribed to collisions. This so called anomalous transport is largely controlled by the destabilization of low frequency drift wave fluctuations, resulting in turbulence in the plasma on small scales compared to the tokamak size. The drift waves are collective modes of plasma oscillations that propagate through the plasma, arising as a result of the independent dynamics of ions and electrons in the presence of gradients of quantities describing the plasma (temperature, density, etc.). In this thesis, physical phenomena connected with the global description of turbulence in tokamak plasma have been analysed. Quasi-local simulations of electrostatic Ion Temperature Gradient (ITG) modes instabilities, i.e. electrostatic microinstabilities driven in the plasma by the presence of an ion temperature gradient, have been performed. Quasi-local refers to the case in which background quantities are assumed constant throughout the simulation domain, but inhomogeneities in the profiles of the turbulent quantities are taken into account. The work consists of two main parts. In the first part of the thesis, the electrostatic linear ITG modes growth rate (γ) spectrum is numerically calculated. It is observed that γ as a function of the poloidal wave vector (kΘ) is given by a double-humped curve. In particular, it is observed that modes with high value of kΘ have a maximum amplitude at a position that is shifted away from the low field side. The physical mechanism responsible for this behaviour is clarified through the use of a fluid model. It is shown that the shift of the mode away from the low field side reduces the effective drift frequency which allows for the instability to develop. Numerical tests using the gyro-kinetic model confirm this physical mechanism. The second part of the thesis is dedicated to the study of Turbulence Spreading (TS), i.e. the turbulent transport of turbulence. Gyro-kinetic simulations predict that, when increasing the size of the reactor, the heat conduction coefficient ($\chi$) undergoes a scaling transition from Bohm (\chi\propto\chi_B, with \chi_B the Bohm diffusion coefficient) to gyro-Bohm (\chi\propto\rho_*\chi_B, with \rho_* the normalized Larmor radius \rho_*=\rho/R where $\rho$ is the ion Larmor radius and $R$ is the tokamak size). This transition is ascribed to non-local phenomena. Non-local refers to situations in which the fluxes do not depend just on the local gradients. In the literature, TS has been proposed as the mechanism responsible for this transition. Up to now, TS has been analytically described applying an ad hoc conservation equation for the evolution of the local intensity of the turbulence, defined as the squared modulus of the electrostatic potential. The conservation equation is given in the form of a Fisher-Kolmogorov (FK) equation with inhomogeneous diffusion coefficient. Although physically motivated, the FK equation proposed to describe TS is not derived from first principles. No explicit expression for the transport flux of turbulence exists, and this flux can therefore not be directly calculated in numerical simulations of plasma turbulence. In this thesis, a conservation equation is derived for the radially dependent entropy in toroidal geometry using the local approximation of the gyro-kinetic equation. This naturally leads to an operative definition for the turbulence intensity. The treatement provides an operative tool for both analytic as well as numeric studies of the radial propagation of turbulence in tokamak plasmas. In fact, explicit expressions for the turbulence intensity and the turbulence intensity flux, that allow direct numerical evaluation, are derived. A carefully designed numerical experiment is used to determine the turbulence diffusion coefficient for the first time. This is found to be smaller than the heat conduction coefficient, and a spreading length is found to be of the order of the turbulence correlation length. The results show that turbulence spreading can play a role in the non-local flux gradient relation, or in the scaling of transport coefficients with the normalized Larmor radius, only over length scale of the order of the turbulence correlation length. Finally, the turbulence convection through the drift connected with the magnetic field inhomogeneities is investigated. The convective flux integrates to zero under the flux surface average unless there is an up-down (in the poloidal plane) asymmetry in the tubulence intensity. The latter asymmetry can be generated through a radial inhomogeneity or plasma rotation. It is shown that the turbulence convection can lead to a spreading of the order of the correlation length under some cicumstances.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Bayreuth

Year

2015

Author dc:creator

• Migliano, Pierluigi

Contributors dc:contributor

• Peeters, Arthur G.

Repository record source_url

https://epub.uni-bayreuth.de/id/eprint/2167/

OAI identifier oai:identifier

oai:epub.uni-bayreuth.de:2167