Theory of drift wave turbulence

Toroidal ion temperature gradient (ITG) driven drift mode turbulence has been analyzed analytically and numerically. By using weak nonlinearity arguments and random phase approximation, dynamic and wave kinetic equations are derived. It is found that three different nonlinearities, namely E x B, convective and diamagnetic nonlinearities, play important role in the turbulent spectral transfer. The power spectra of the weak ITG-mode turbulence are obtained analytically for \k\ much greater than 1 and \k\ < 1 ranges in the wave number space. It is shown that forward energy cascading due to convective and diamagnetic nonlinearities will balance the inverse energy cascading due to E x B nonlinearity at \k\ approximate to 1/rho(s) (k is wave number, rho(s), (c(s)/omega(ci)) c(s) is the sound velocity and omega(ci) is the ion cyclotron frequency) and results in energy condensation at \k\ approximate to 1/rho(s).