Summary of MHD Topics 2nd IAEA Technical Meeting Theory of Plasma Instabilities Howard Wilson

1. Summary of MHD Topics 2nd IAEA Technical Meeting Theory of Plasma Instabilities Howard Wilson

2. Fast particle MHD • Sharapov reminded us of the challenge to separate a-physics from that due to the fast particles from heating schemes in ITER (isotropic vs anisotropic): • Need an improved understanding of competing effects now to interpret ITER later • Need improved diagnostics in time for ITER • Our knowledge of TAEs is becoming relatively advanced • Nonlinear theory (Berk et al) identifies 4 regimes for amplitude of TAE depending on how effectively collisions restore a gradient across the resonance: • Steady • Pitchfork • Chaotic • Explosive Observed on JET as ICRH power increases with time

3. Haggis used to interpret frequency-splitting (Pinches/Sharapov) Can get frequency-splitting phenomena eg on MAST: • Theory interpretation: • particle trapping in Alfven wave • predicts splitting dw~wb3/2t1/2 • use HAGIS to calculate Cj and hence dB/B from expt • HAGIS is just one of of a coordinated suite of codes being developed by IPP for analysing fast particle effects • LIGKA: linear gyrokinetics • CAS-3D: 3-D geometry • HAGIS: wave-particle interactions (Pinches)

4. Alfven Cascades or Reverse Shear Alfven Eigenmodes Close to a minimum in q, Alfven continuum is modified (Cheng, Sharapov): • Can get cylindrical Alfven eigenmode near qmin • localised about rational surface • Good agreement between expt and theory • Frequency depends on qmin • good diagnostic of qmin

5. Losses due to fast particle instabilities • Cheng showed that bursting TAE activity can expel fast particles from core: • Clearly a concern for ITER • Briguglio: modelling of TAE losses for ITER: • Monotonic q  little effect • Reverse shear  some broadening • Hybrid scenario  little effect • Increase drive  EPMs • Monotonic q  drop in core a’s • Reverse shear  more effect in outer region • Hybrid scenario  more effect at edge region Fast particle instabilities clearly remain an important issue for ITER

6. Impact of Fast Particles on Sawteeth (Graves) • Effect of flow shear has significant influence on internal kink mode • Anticipated flow in ITER (from NNBI) low, and not expected to influence internal kink • Unbalanced NBI injection can stabilise internal kink mode • Predictions of the fast particle pressure gradient from NNBI suggest stabilisation from NNBI could compete with that due to a-particles • Anisotropy is stabilising for all but most strongly trapped hot ion distributions

7. Neoclassical Tearing Mode Physics • Smolyakov summarised the physics Equilibrium current Inductive current Bootstrap current polarisation current • Need to generate “seed” island • additional MHD event • poorly understood? • Stable solution • saturated island width • well understood? 0 w • Unstable solution • Threshold • poorly understood • needs improved transport model • need improved polarisation current

8. Neoclassical Tearing Modes: Non-linear MHD simulation • Lutjens described results from non-linear, extended MHD XTOR code • Close to threshold, XTOR agrees with analytic modified Rutherford eqn (including linear corrections): • However, saturated island size from XTOR is somewhat lower than that predicted by modified Rutherford eqn No linear corrections analytical analytical with linear corrections Numerical (XTOR) Numerical (XTOR)

9. Multiple NTMs • Some experimental data suggests multiple NTMs do not co-exist (eg, ASDEX-Upgrade) • XTOR simulations can have multiple island chains (Lutjens) • This results in stochastic field due to island overlap, and a loss of pressure • If true, this is a major concern for ITER

10. Role of Polarisation current • Poli has employed drift-kinetic model for ions to calculate polarisation current • For given frequency (w=?) he finds it is destabilising for NTMs; effect of separatrix switches sign of polarisation current (as FLR model) • island rotation influences polarisation current • For narrow islands, polarisation current suppressed (but really need gyro-kinetic model here!)

11. Miscellaneous (but important!) NTM issues • Smolyakov described the role of ion sound waves • slab calculation, cold ions • contributes a stabilising term ~cs2/(VA2w) • Needs to be worked through in toroidal geometry • How do we determine island rotation frequency? • Depends on dissipation: • viscosity • Drift waves (shear damping) • non-ambipolar diffusion • thermal force effects …. • This is a key research issue, likely to require a solution of the NTM evolution, self-consistently with the plasma turbulence • A major challenge for integrated modelling!

12. Rotation and Tearing Modes • Coelho explored effect of sheared flow on linear stability • Found it is important to retain parallel magnetic and velocity fluctuations • Effect of flow shear on stability depends on viscosity • destabilising for low viscosity • stabilising for high viscosity • Chandra has considered the effect of flow on NTMs • Positive flow shear stabilises • Negative flow shear destabilises (usual tokamak case) Negative flow shear Positive flow shear

13. Non-linear MHD • Thyagaraja presented results from CUTIE code: • Explores interactions between global and “meso-scale” phenomena • simplified plasma physics model: Braginskii fluids • is this sufficient? • Shows interactions between these scales can give rise to interesting phenomena (eg interactions between turbulence and profile evolution) • Provides qualitative agreement with some experimental profile data • Useful tool for exploring MHD phenomena: off-axis sawteeth require dynamo With dynamo No dynamo

14. Dynamo Physics • Hughes was interested in the generation of magnetic field in the Sun • The MHD dynamo • Introduced the concept of mean field theory • provides a dynamo through the parameter a (for short turbulence correlation time) • appropriate models for a provide interpretations of MHD phenomena • But what about more realistic (solar) case, where correlation times are not small • Perform full turbulence calculation in model system • Calculation of a show it fluctuates wildly, and is small: is a-effect meaningful in such cases? But on the fine scales Do drive a dynamo Fine scale temperature fluctuations

15. Thunderbolts and lightning! • Ludwig described two applications exploring the effect of viscosity on stability • Experiment: attach a copper wire and fire a small rocket ~1km into a cloud • reliably triggers a lightning discharge, which one can then diagnose • one feature is that it breaks up into beads • Theory proposed as a form of Rayleigh-Taylor instability as the lightning column contracts • Low (classical) viscosity gives reasonable growth rate, but wavelength too short • Anomolously large viscosity gives both the correct wavelength and growth time