On the dynamics of turbulent transport near marginal stability

A general methodology for describing the dynamics of transport near marginal stability is formulated. Marginal stability is a special case of the more general phenomenon of self-organized criticality. Simple, one field models of the dynamics of tokamak plasma self-organized criticality have been constructed, and include relevant features such as sheared mean flow and transport bifurcations. In such models, slow mode (i.e., large-scale, low-frequency transport events) correlation times determine the behavior of transport dynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers’) and sheared flow models. For the minimal model, z=1 (indicating ballistic propagation) and D∼(S20)1/3, where S20 is the noise strength. With an identically structured noise spectrum and flow with shearing rate exceeding the ambient decorrelation rate for the largest-scale transport events, diffusion is recovered with z=2 and D∼(S20)3/5. This indicates a qualitative change in the dynamics, as well as a reduction in losses. These results are consistent with recent findings from dimensionless scaling studies. Several tokamak transport experiments are suggested.