ABSTRACT:
This talk will discuss the systematic extension of the Hamiltonian gyrokinetic theory to two orderings [1,2] that are applicable to the edge region of tokamaks and other magnetic confinement devices, as well as to internal transport barriers. The first of the orderings [1] is based on the ratio of the sum of the E ! B velocity and the component of the parallel velocity perpendicular to the equilibrium magnetic field to the thermal velocity as the small ordering parameter !. For nonlinear fluctuations saturated at “mixing-length” levels (i.e., at a level such that driving gradients in profile quantities are locally flattened), ! is of order !/ Lp , where ! is the gyroradius and Lp is the equilibrium profile scale length, for all perpendicular perturbation scales ranging from ! to Lp . This allows for long wavelength components of the potential at thermal levels. Significant additional simplifications result from ordering Lp / LB = O ! ( ) , where LB is the spatial scale of variation of the magnetic field. The resulting equation set is straightforward to implement numerically, and a useful form for its conservation properties is easily derived. Useful subsidiary and reduced orderings are considered that result in considerable simplification and easier numerical implementation. The second of the orderings [2] uses ratio of the E ¡ÑB shearing rate to the gyrofrequency as the small parameter. This allows for long wavelength E ¡ÑB flows of order the thermal velocity, and is more general than the ordering in [1]. This theory generalizes prior work
[3-5] to allow for time dependence in the large long-wavelength component of the electric field, and a continuum of scales in the field components rather than just two distinct components at separated scales. The resulting system of equations poses a challenge for nonlinear numerical implementations in part because of new terms that were found [2]. These terms should be present at the second order in the theory even in the simplified case [4,5] of a two-component potential with a static large longwavelength component.
[1] A.M. Dimits, Phys. Plasmas 19, 022504 (2012).
[2] A.M. Dimits, Phys. Plasmas 17, 055901 (2010).
[3] M. Artun and W.M. Tang, Phys. Plasmas 1, 2682 (1994).
[4] A.J. Brizard, Phys. Plasmas 2, 459 (1995).
[5] T.S. Hahm, Phys Plasmas 3, 4658 (1996).
*This work was performed for U.S. DOE by LLNL under Contract DE-AC52-
07NA27344 and is part of the ESL.