Theory Weekly Highlights for March 2002

March 29 2002

The theory of Greene, Johnson and Weimer for tokamak equilibria has been extended to include equilibria with a central current hole region. The current hole region is shown to be connected with the external region with a regular equilibrium profile through a contact singularity, where the magnetic field is continuous, with the possibility of a discontinuous current density distribution, but no singular currents. However, equilibria with a negative current density region between the current hole and an external positive current region have been shown to not exist in general. These conclusions are consistent with the observation of current holes in tokamaks and the fact that negative currents have never been observed to develop in the current holes.

March 22 2002

The GYRO global gyrokinetic code has reached maturity after three years of development. Since December 2001, the code has been used to simulate the transport power flow for specific L-mode DIII-D core plasmas profiles with a high degree of physical reality: ITG and trapped-passing electrons at finite beta in real geometry. The ExB and general profile shear cause significant reduction in transport as expected. The simulated power flows are rather close to the experimental flows in the one case we have studied. We simulate both electron and ion energy as well as plasma diffusivity, and recently we have added simulation of toroidial viscosity and turbulent electron-ion exchange. We have recently released the GYRO code to PPPL for application to NSTX (and C-mod). A full description, recent papers and playable movies of simulations are available at: http://web/ Also, see the real geometry movie at

March 08 2002

For support of ITPA modeling group activities at DIII-D, the ability to store ONETWO data has been added to MDSplus. This allows a direct graphical comparison between raw data with uncertainties, fitted data with uncertainties, and power balance output from TRANSP and ONETWO.

March 01 2002

Recent experiments in various tokamaks observed a “current hole” near the magnetic axis with virtually zero current. A model, in which the hole is sustained by the beam particle source and the resulting outward mass flow, was developed earlier. An alternative model has now been proposed that, while still ensuring a true steady-state equilibrium, removes some of the restrictions of the earlier model. Specifically, the new model is not restricted to unity poloidal beta and includes the neoclassical bootstrap current effect. This results in a Grad Shafranov equation with two prescribed flux-surface functions - the total particle source rate within a flux surface and the parallel bootstrap current distribution. Since the mass flow is ineffective right at the hole boundary where q is infinite, a diffusive-like hyper-resistivity (Boozer) term is included in Ohms law that effectively replaces the loop voltage and allows for true steady state. An expansion analysis near the hole edge finds a Bessel function solution for the fields, without a singular current at the hole boundary; these profiles also satisfy the 1994 Hegna-Callen high m tearing instability criterion, justifying the use of the Boozer term.

These highlights are reports of research work in progress and are accordingly subject to change or modification