CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority Internal Transport Barriers and Improved Confinement in Tokamaks (Three possible trigger mechanisms) M Romanelli 1, F. Militello 1, G. Szepesi 1,2, A. Zocco 1 1 EURATOM/CCFE Fusion Association, UK 2 University of Warwick, UK Acknowledgments: F Crisanti, G Mazzitelli, F Zonca (ENEA), J Hastie and J Connor (CCFE) 14 th European Fusion Theory Conference, Frascati, Italy, September This work is funded by RCUK Energy Programme and EURATOM

Michele Romanelli – EFTC20112September Introduction Many different mechanisms can be responsible for improved confinement in tokamak plasmas. In this presentation I will introduce three such mechanisms that could concur or play an independent role in the formation of an Internal Transport Barrier (ITB) or lead to improved confinement of particles and heat  Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.  Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis  Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC20113September Introduction Discussion of triggering mechanisms:  Fast ion induced alpha stabilization : the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of EM mode stability.  Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis  Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC20114September Flat region 3.5 m t 48.6 s s (1 s time evolution) 20% of central temperature increase (same heating power) due to ITB q Fast ions α- stabilization T i [eV]  Microstability analysis of a JET hybrid discharge with GS2 (EM) JET #59137

Michele Romanelli – EFTC20115September Fast ions α - stabilization  Thermal profiles corresponding to t=10s (gradients have been taken at R=3.5 m)  Density profiles of NBI+ICRH fast H minority

Michele Romanelli – EFTC20116September Fast ions α - stabilization (EM)  Change of the long wavelength spectra when increasing the temperature of the minority species  Increasing α -> complete ITG stabilization for K  ρ i ≥0.6 -> EM modes

Michele Romanelli – EFTC20117September Fast ions α - stabilization (electrostatic)  Effect of changing L nfast and s' in the electrostatic limit  In the electrostatic limit α-stabilization is less effective (requires much higher values of α to stabilize ITG at given s and L nfast

Michele Romanelli – EFTC20118September Fast ions α - stabilization (EM). Microtering arise the presence of wave particle interaction as can be seen from the parallel component of Ohm’s equation, given by the parallel gradient of equation: The drive of the instability is the gradient of the electron temperature. The mode is destabilized by increasing the ion pressure gradient, at constant electron temperature and density gradient. In general, the parallel electric field will be non-zero and will have a direct contribution from the parallel vector potential, second term on the LHS, and from the non-adiabatic part of the distribution functions.  [21] Zonca F et al 1999 Phys. Plasmas  At high T H micro tearing modes are found to replace ITG-TEM for K  ρ i ≥0.6

Michele Romanelli – EFTC20119September Fast ions α - stabilization (EM)  By increasing the energy of the hydrogen minority the short wavelength modes (μT) are stabilized however for α>0.4 the long wavelength AITG modes are destabilized.

Michele Romanelli – EFTC201110September Introduction Discussion of triggering mechanisms:  Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.  Zonal perturbations: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis  Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC201111September Introduction The ITB can be caused by a region of plasma where the m=0, n=0 velocity shear is large, since there the correlation length of the turbulent eddies is reduced. Zonal Flows are m=0, n=0 secondary instabilities (i.e. they are linearly stable) which can arise from the interaction of drift waves. The generation of the Zonal Flows (and hence of the ITB) can be studied with a parametric instability approach. Details in Militello, Romanelli, Connor and Hastie, Nuclear Fusion (2011).

Michele Romanelli – EFTC201112September Model We study the problem with a fluid model in a slab: We assume T i =0, T e =const, small finite  and negligible dissipation. The time is normalized to the Alfven time and the length to a macroscopic size. d e is the electron skin depth and  s is the ion sound Larmor radius.  radial profiles

Michele Romanelli – EFTC201113September When density gradients are present, in the system appear: –Drift-Alfven waves (primary “instability”, linear): –Zonal perturbations (secondary instability coupled through sidebands, quasi-linear): Primary and secondary instabilities primary secondary

Michele Romanelli – EFTC201114September Normalized frequency of the Zonal perturbation Dispersion relation Linearizing the system around an equilibrium with a large primary instability leads to a (huge!) dispersion relation for the secondary instability (i.e. the Zonal Perturbation). Normalized growth rate of the Zonal perturbation Militello, Romanelli, Connor and Hastie, NF (2011)

Michele Romanelli – EFTC201115September Normalized frequency of the Zonal perturbation Dispersion relation Linearizing the system around an equilibrium with a large primary instability leads to a (huge!) dispersion relation for the secondary instability (i.e. the Zonal Perturbation). Normalized growth rate of the Zonal perturbation Electrostatic Branch Electromagnetic branch Solid lines: Guzdar et al. PRL (2001) Militello, Romanelli, Connor and Hastie, NF (2011)

Michele Romanelli – EFTC201116September Not only Zonal flows Zonal magnetic fields (with d e ≠0) and zonal density can be generated as well (new result). The zonal Fields can provide a drive for the Tearing mode. (Militello et al., PoP 2009) Zonal densityZonal fields

Michele Romanelli – EFTC201117September ITB criterion As noted before, self-sustained Zonal Perturbations appear for >1. Around a resonant surface: We can define a width around the surface where the condition is always met: To shear the eddies, x cr must be larger than  s : or equivalently:

Michele Romanelli – EFTC201118September ITB criterion II The criterion is a necessary condition but it is not sufficient (it does not say anything about the nonlinear evolution). Assumption: a barrier survives if a sufficient amount of energy goes from the turbulence to the zonal perturbation. Only the resonant modes transfer energy to the zonal perturbation. Low order helicities have more resonant modes. Conclusion: an ITB forms and survives when a low order rational surface enters the palsma and:

Michele Romanelli – EFTC201119September Introduction Discussion of triggering mechanisms:  Fast ion induced alpha stabilization: the role of fast ion pressure in stabilizing the thermal-ion gradient driven modes is discussed in the context of e-m mode stability.  Zonal currents: the interplay between drift-Alfvén wave turbulence and electromagnetic zonal perturbation is examined in the framework of a parametric instability analysis  Impurities: improved electron confinement along with the expulsion of impurities is explained in terms of change in the turbulent spectrum and turbulent driven particle fluxes in the presence of a light impurity

Michele Romanelli – EFTC2011September Impurity triggered inward e - pinch Turbulent particle fluxes (in the simplest case of electrostatic turbulence) arise from the phase shift between electrostatic potential fluctuations and density fluctuations  In the presence of impurities the electron and deuterium fluxes are decoupled; the phase shift between electron-deuterium density fluctuations and electrostatic potential might become significantly different and inward pinches can appear. In strongly electron driven turbulence, impurities are expected to stabilise the ETG modes [ Reshko M. and Roach C.M Plasma Phys. Control. Fusion ]  Impurity ions will change the turbulence spectrum moving the peak toward higher

Michele Romanelli – EFTC201121September Plasma parameters Plasma parameters have been taken from an FTU discharge where in the presence of Lithium Limiter improved confinement and strong density peaking was observed  Mazzitelli G. et al 2011 Nucl. Fusion  A. Peeters et al, Computer Physics Communications 180 (2009) 2650–2672 The effect of one light impurity (Li) species on (D-e-) plasma microstability has been investigated with the flux tube gyrokinetic code GKW.

Michele Romanelli – EFTC201122September Impurity effect on spectrum (GKW)

Michele Romanelli – EFTC201123September Linear particle fluxes

Michele Romanelli – EFTC201124September Linear particle fluxes  The change in sign of the fluxes coincides with the change of unstable mode from ITG to TEM  Extensive parametric scan is presented in M Romanelli, G Szepesi et al Nucl. Fusion 51 (2011) (9pp)

Michele Romanelli – EFTC201125September Nonlinear particle fluxes at r/a=0.6, t=0.3s

Michele Romanelli – EFTC201126September Summary Different triggering mechanisms can be responsible for the transition to improved confinement in tokamak plasmas. In this presentation three such mechanisms have been dsicussed  Fast ions induced α - stabilization: M Romanelli, A Zocco et al Plasma Phys. Control. Fusion 52 (2010)  Criteria for ITB formation in low shear plasmas: F Militello, M Romanelli, J Connor and J Hastie, Nuclear Fusion (2011).  Impurity induced inward deuterium and electron pinch: M Romanelli, G Szepesi et al Nucl. Fusion 51 (2011) (9pp) This work is funded by RCUK Energy Programme and EURATOM