### Theory Weekly Highlights for July 2006

##### July 28, 2006

The Porcelli model for fast ion stabilization of the internal kink was applied to two DIII-D L-mode discharges with giant and small sawteeth to understand whether the kinetic contribution from energetic beam ions accelerated by fast waves can play a role in modifying the sawtooth period. The predicted stability windows are quite different for the two discharges, qualitatively following the trend of experiments. For the discharge with giant sawteeth, the calculations show the fast ion contribution is sufficient to stabilize the ideal internal kink, consistent with experimental results. For the discharge exhibiting small sawteeth, however, the analytic Bussac model for the internal kink predicts stability even before the RF is on. The discrepancy may be attributed to the considerable departure from a top-hat displacement predicted by the ideal MHD GATO code (see the June 23 2006 highlight) so that the Bussac analytic model may not be appropriate for this equilibrium. Further analysis with the NOVA-K code is planned.

##### July 21, 2006

The apparent contradiction between edge pedestal height being constrained by peeling-ballooning stability, and edge pedestal height sometimes depending on input power, has been resolved by studying the dependence of peeling-ballooning stability limits on the Shafranov shift. It has been established on DIII-D and other tokamaks that the pedestal height is generally constrained by intermediate-n peeling-ballooning stability limits, which do not explicitly depend on power. However, in some database studies it is observed that the pedestal height appears to increase with input power. We find that the increased input power increases the Shafranov shift (proportional to βp), and that the increasing Shafranov shift improves pedestal stability, thereby allowing a higher pedestal. From calculations using the ELITE code, both the approximate size of the effect, and the increased effect with stronger shaping are consistent with observations. Other factors, such as the increase in pedestal width with input power, may also contribute.

##### July 14, 2006

The theory of the spectrum of the Kinetic Alfven Wave (KAW) in tokamaks with general cross-section has been formulated in terms of a linear combination of the weakly damped, natural eigenmodes of the tokamak, and its spectrum studied numerically. The discrete spectrum depends on the plasma density, safety factor and temperature profiles. Therefore, the KAWs may be driven resonantly to large amplitudes by appropriate boundary perturbations at the resonant frequencies of specific eigenmodes by driving mechanisms such as the frequency of a natural rotating magnetic island. The resultant amplitude depends on the damping mechanism. A consequence of these excited KAW includes the possibility of both steady state current drive and the scatting of energetic particles. This may provide an explanation for the observation of the clamping of the q0 value in hybrid discharges in the presence of a rotating 3/2 island.

##### July 07, 2006

Microturbulence can cause loss of confinement through transport but it can also provide some compensating turbulent heating. Starting from the fundamental collisional Vlasov equation, a radial energy continuity (transport) equation has been derived, which includes both turbulent transport and heating that can be evaluated with GYRO gyrokinetic simulations. In addition to the usual gyrokinetic energy transport a small, finite gyroradius energy flow is found and, more importantly, some gyrokinetic heating. Neither of these new effects has been accounted for in previous studies. The heating takes the ohmic form δj*δE, where δj and δE are the perturbed current density and electric field and where the perpendicular part is give by a curvature drift perturbed current density. It is estimated that the extra heating could compensate for 10% to 30% of the transport loss when properly evaluated by GYRO. A paper on this formulation of gyrokinetic turbulent heating has been submitted to Physics of Plasmas.

**Disclaimer**

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

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