| This work will look at two areas. The first area is the calculation and analysis of a plasma conductivity tensor which includes the effects of magnetic field geometry more completely than any previous calculation. The second area is the creation of a test which will differentiate between data from a chaotic system and data from colored random noise.; We examine the effect of complicated magnetic geometries and collisions on the propagation and absorption of radio frequency waves in a plasma. This is accomplished by calculating a conductivity tensor for the plasma using the method of integration along characteristics. Previous theories treated only the lowest order effects of linear parallel gradients and treated collision in an arbitrary manner. The physics of plasma response is described in terms of the physics of the characteristic trajectories and the plasma distributions. Methods for calculating the relative importance of each effect based on the plasma and magnetic parameters are derived. One dimensional calculations of wave propagation and absorption in a tokamak are performed using the All Orders Reduced Spectral Algorithm (AORSA1D) code. The results of these calculations demonstrate a clear change in power absorption due to the proper treatment of collisions and higher order effects of linear parallel gradients.; A method is developed for distinguishing between data from a chaotic system with a strange attractor and data from colored random noise. For both types of data the apparent dimension, as measured by the correlation dimension, is finite and non-integer for some length scales, and so an additional test is needed to distinguish them. To this end we have developed the variance growth test, which looks for the increase of the variance, as measured by the root mean squared deviation, of a data set as a function of the set length. For strange attractor data the variance saturates once the data length exceeds one return time. In contrast, the variance of colored random noise increases with increasing set length indefinitely. Application of the method to the Bargatze data set shows that the auroral lower index or AL index behaves like a deterministic dynamical system. |
