### Theory Weekly Highlights for July 2011

##### July 29, 2011

A new theoretical model for the penetration of gas jets into magnetized plasmas predicts that a jet from a high pressure burst disc injector can penetrate more than 40 cm into a nominal ITER post Thermal Quench (TQ) plasma with a fueling efficiency of over 70%. The model assumes that the gas jet is neutral and insulating and that it is supersonic with respect to its own internal thermal speed but is deeply subsonic with respect to the plasma. The assumption that it is supersonic implies that the penetration distance of the core is limited by a “shock bubble” blown into the plasma, much like the braking of the supersonic solar wind by a termination shock at the heliopause. The other assumptions indicate that the drag on the jet is due to sound wave propagation and is quite weak. For DIII-D the model predicts a jet will completely penetrate a post TQ plasma but, will not enter a normal plasma. Both predictions are consistent with recent Tore Supra results.

##### July 22, 2011

In considering the plasma response to an external magnetic perturbation, a distinction can be made between an equilibrium or MHD response and a transport response. The equilibrium response is the re-establishment of force balance on an Alfvenic time scale and a possible fast resistive change in magnetic topology. The transport response is due to changes in the transport coefficients due to the different equilibrium. These can be local or more global if the equilibrium topology is changed as in the case of the formation of a stochastic region. In the framework of the extended MHD stability model, the transport response can be considered as the nonlinear part of the response and can involve neoclassical and kinetic effects. In the context of the nearby perturbed equilibrium formulation of the response, the final state is determined by the kinds of profile constraints that relate the initial and final equilibrium states. The appropriate constraints are strongly dependent on whether the changes are adiabatic, where the changes are much slower than the Alfvénic response that re-establishes force balance, or non-adiabatic. This has implications for interpreting numerical simulations where an external non-axisymmetric field is turned on instantaneously, whereas experimentally, the field is ramped up slowly.

##### July 15, 2011

A complete scan of an n=3 reverse shear Alfven eigenmode (RSAE) frequency sweep in DIII-D discharge #142111 near t=725ms has been rendered with the new GYRO GKEIGEN global eigenvalue solver (see highlight at https://fusion.gat.com/theory/Weekly0411 for April 29 2011). An interconnected trio of Alfvén eigenmodes, an RSAE and two toroidal Alfven eigenmodes (TAEs), are unstable over most of the qmin sweep range of 3.0 ≤ qmin ≤ 3.3 as shown in the attached figure. Frequencies (neglecting rotation) agree with experiment within about 20%, representing one of the earliest successes in gyrokinetic simulation of Alfvén eigenmodes. Many mode features, including a ubiquitous poloidal shearing, which is absent in MHD but seen in experimental ECE data, and shifted locations of poloidal harmonic peaks, are only detectable with a self-consistent energetic ion treatment like the one used in this GYRO scan. Such details of the eigenfunction shape likely produce the observed linear pinching and will certainly be important in upcoming nonlinear flux calculations.

##### July 08, 2011

The capability of launching multiple waves with different frequency from each launcher has been added to the general ray tracing code GENRAY. For simulating heating and current drive in GENRAY from lower hybrid (LH) waves or fast waves (FW), multiple grills in the poloidal plane are modeled. In general, each grill can launch a different frequency wave into the plasma but in the previous version every grill was assumed to launch the same frequency wave. Therefore, to model cases where each grill launches a different frequency, separate simulations were needed for each frequency and the heating and driven current from each grill summed to compute the total. The upgraded GENRAY code can now launch a different frequency from each grill. Test runs are being done for several cases such as ECCD in ITER, LHCD in FDF, and ICCD and LHCD in ARIES.

Steve Jardin from PPPL is visiting GA this week to collaborate with Nate Ferraro, Alan Turnbull, and Ben Tobias on modeling of sawteeth using the M3D-C1 code running in full nonlinear mode.

##### July 01, 2011

Static external resonant magnetic field perturbations (RMPs) have been added to GYRO. This allows nonlinear gyrokinetic simulations of the nonambipolar radial current flow jr, and the corresponding plasma torque jr.Bp/c, induced by magnetic islands that break the toroidal symmetry of a tokamak. The focus has been on electrostatic full torus (Δn=1) simulation of externally induced q=m/n=6/3 islands with widths w/a ~ 5%, or 20 ion gyroradii. Up to moderately strong ExB rotation, the torque scales with the radial electric field at the resonant surface, Er, the island width, and the intensity I of the high-n ITG/TEM turbulence, as τ ~ wIEr. Most surprisingly the null torque is at the null Er location rather than where the toroidal rotation vanishes. This means that while the expected magnetic breaking occurs at strong co and counter current rotation, for null toroidal rotation, there is a small co-directed magnetic acceleration up to the small diamagnetic co-rotation corresponding to the null Er and null torque point. This could be called residual stress from an external island. Finite beta GYRO simulations demonstrate the RMP field screening and n=3 mode locking at strong Er.

**Disclaimer**

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