Ion temperature gradient turbulence simulations and plasma flux surface shape

A generalization of the circular (s) over cap-alpha local magnetohydrodynamic (MHD) equilibrium model to finite aspect ratio (A), elongation (kappa), and triangularity (delta) has been added to a gyrokinetic stability code and our gyrofluid nonlinear ballooning mode code for ion temperature gradient (ITG) turbulence. This allows systematic studies of stability and transport for shaped flux surfaces with the same minor midplane radius label (r), plasma gradients, q, (s) over cap, and alpha while varying A, kappa, and delta. It is shown that the (linear, nonlinear, and sheared) ExB terms in the equation of motion are unchanged from a circle at radius r with an effective field B-unit=B(0)rho d rho/rdr, where chi=B(0)rho(2)/2 is the toroidal flux, r is the flux surface label, and B-0 is the magnetic axis field. This leads to a "natural gyroBohm diffusivity" chi(natural), which at moderate q=2 to 3 is weakly dependent on shape (kappa) at fixed B-unit. Since B-unit/B(0)proportional to kappa and <\del r\(2)>approximate to(1+kappa(2))/(2 kappa(2)), the label independent chi(ITER)=chi(natural)/<\del r\(2)> at fixed B-0 scales as 2/(1+kappa(2)) with much weaker scaling at high-q and stronger at low-q where increased kappa is stabilizing. The generalized critical ExB shear rate to be compared to the maximum linear growth rate is a flux surface quantity (r/q)d/dr(cq/rB(unit)d phi(0)/dr)=(r/q)d(E-x0/BpR)/dr. (C) 1999 American Institute of Physics. [S1070-664X(99)01411-1].