Chiara Marchetto Istituto di Fisica del Plasma, C.N.R., EURATOM-ENEA-CNR Ass.; Milan, Italy

1. Simulating an IBW propagating transversal to a tokamak confining field: non-linear kinetic effects and possibility for turbulence suppression Chiara Marchetto Istituto di Fisica del Plasma, C.N.R., EURATOM-ENEA-CNR Ass.; Milan, Italy INFM – Iniziativa Trasversale Calcolo Parallelo, Italy In collaboration with: M. Lontano1, F. Califano1,2 1Istituto di Fisica del Plasma, C.N.R., EURATOM-ENEA-CNR Ass.; Milan, Italy 2Dipartimento di Fisica, Universita’ di Pisa, Pisa, Italy

2. OUTLINE 1. Tokamak, turbulence suppression and IBW 2. The model, the code and the HTC 3. The macroscopic quantities 4. The kinetic quantities 5. Summary

3. TOKAMAK, TURBULENCE SUPPRESSION, IBW Tokamak: toroidal confinement device for nuclear-fusion purposes Turbulence: cause of poor confinement, main problem for tokamaks A way to affect turbulence: Shear Flow(flux of particles with average velocity in poloidal direction changing of sign andmodule along radial direction) reducing correlation length and of the amplitude of turbulenceBDT turbulence suppression criterion onthe shear flow , the turbulentdecorrelation frequency k, the corelationlength along the shear y and the Fourierwavenumber of the correlation lengthalong the flow kx Ion Bernstein Waves: electrostatic waves propagating a right angles to confining magnetic field at harmonics of the cyclotron frequency. 3

4. y z B B k,Ewave x k,Ewave THE MODEL - Aim: to model in a simplified way the interaction of an Ion Bernstein Wave with a tokamak plasma - k B0; E || k; B0uniform - monochromatic wave, modelled by: -   4Wci ; li  kli >1 - slab geometry: 3d (1x2v) - parameters from IBW-FTU : ne = 5 × 1013 cm-3Te = 1 keV, B0 = 7.8 T (Le = -mi/me , Li = 1) 4

5. THE CODE and the HTC • - We start from Mangeney, Califano, Cavazzoni, Travnicek 2002, Journ. Comp. Phys., 179, 1, accurate up to second order in time, position, velocity; high resolution in velocity, requiring a large numerical effort. • - Periodic spatial boundary conditions, x  [0,3] (= pumpwavelength). At t=0 the electron and ion distribution functions are Maxwellian and no electromagnetic field is present. • Pump applied to the system throughout the interaction time. • Upgrade: Electrons following EB drift, System response electrostatic  Eliminated Vlasov eq for electrons, set Ey 0 and BzB0, eliminated all Maxwell equations except Poisson (for Ex) [Marchetto, et al., 2002]. • High Throughput Computing (large amounts of fault-tolerant computational power over prolonged periods of time) via Condor Scheduler (specialised job and resource management system, enabled for Opportunistic Computing i.e. ability to use resources whenever they are available, without requiring 100% availability). 5

6. THE MACROSCOPIC QUANTITIES: - high wave amplitude, - peculiar relations between wave frequency and system frequencies - oscillations in space (=0) and time (=0,  =ci) - constant and uniform mean value - constant amplitude - spatial response can be non-linear, as ex: uiy and uix shown at t=144 for 0=0.35 6

7. - Plasma response to a great extent electrostatic (B unperturbed, Ey negligible) - - Ex of the order of the wave amplitude - Energy content of the systemincreasing during the interaction with the wave. <Ti> (the ion energy content averaged over space) plotted versus time for a=0.0001 and 0=0.35 Ex(x) as measured during the simulation 7

8. - The ion space-averaged fluid velocity in y direction oscillates at ci with mean value always negative and 2 to 4 orders of magnitude smaller than the ion thermal velocity: the flow! Ion space averaged fluid velocity versus time, for 0=0.35 and a=0.0001 8

9. - The wave-vector spectra show the typical behaviour of a cascade toward the small scales. |Ek| plotted versus k at t=630 (sx) and |E| plotted versus  at x= 0.026 (dx), for 0=0.35 and a=0.0001. All in dimensionless units. - The frequency spectra present a maximum at the wave frequency and peaks at the ion cyclotron frequency and at its harmonics 9

10. The intensity of the wave-induced flow presents a peak for a value of the wave frequency comprised between 0=0.34 and 0=0.38 (4 ci =0.32) (a) (b) Flow versus frequency for a=0.0001 (a) and a=0.00005 (b). All in normalised units. 10

11. Preliminar estimates of the shear flow - Variation of the flow intensity with the pump wave frequency interpreted as a variation of flow intensity with the position, ie as shear flow - By assuming profiles for B(r) and n(r), it is possible to relate a variation in the normalised wave frequency /pi to a variation in the normalised coordinates x/a - Shear flow: - BDT criterion in our geometry: - For drift turbulence (T=1keV, B=7.5104gauss, Ln=a=30cm,xk=li/0.2): - Almost sufficient for turbulence suppression- Recent calculations show it is enough (F. Califano, et al., 30th EPS Conf. on Contr. Fus. and Plasma Phys., S.Petersbourgh, July 2003). 11

12. THE KINETIC QUANTITIES: • - Fdp: plateau and population inversion for vx  v, secondary peaks for vx = 2v Perpendicular Ion Landau Damping (ILD) despite the presence of a strong confining magnetic field • Up to now: plasma in magnetic field considered as unmagnetised for high frequencies (0  30 ci) and for short times (few wave cycles). • Our simulations: ILD for0  4 ci and several wave cycles The ion distribution function fi(x,vx,vy) is plotted versus vx, at x=0.026 and vy=0, for 0=0.35 and a=0.0001, for t=0 (dashed line) and t=630 (solid line). 12

13. - The contour plot (x,vx) of Fdp shows vortexes, typical symptom of particle trapping: same structures as in simulations performed withB = 0, and as found for Electron Landau Damping in literature (Brunetti, Califano, Pegoraro, Phys Rev E 62 4109 (2000)) - velocity trapping region fits well with plateau Contour plot (x,vx) of the ion distribution function for 0=0.35 and a=0.0001, for t=630. Contourplot (x,vx) of the ion distribution function if B=0, 0=1,.9305 and a=0.001, for t=13. 13

14. - Fdp presents plateau and population inversion also as a function of vy, i.e. for vy  v, with secondary peaks for vy = 2v The ion distribution function fi(x,vx,vy) is plotted versus vy at x=0.026 and vx=0, for 0=0.35 and a=0.0001, for t=0 (dashed line) and t=630 (solid line). 14

15. - Even the contour plot (x,vy) presents vortexes: the magnetic field adds a mixing effect that makes it possible to propagate the perturbation to the Fdp also in the vy direction, and the effect is stronger around vy  - v, than around vx  v - This localisation of the perturbation of the distribution function in the negative range of vy is responsible for the negative flow in the y direction 15

16. Thefinger-like structures: Contour plot (vx,vy) of the ion distribution function at x=0.026, for 0=0.35 and a=0.0001, for 4 instants of time for a=0.0001 and a=0.00005. The contour plots are seen as “ellipses”, instead of as “circles”, due to the difference of the abscissa and the ordinata scales in the plot. 16

17. SUMMARY • - This wave-plasma interaction produces a flowin y direction, its intensity is from 2 to 4 orders of magnitude smaller than vthi • Flow intensity: peak for  strictly larger than 4 ci,- Flow shear almost enough to reduce plasma turbulence (for drift- like turbulence) • - Ion distribution function noticeably different from Maxwellian: plateau, population inversion, Transverse Ion Landau Damping, trapping • - Magnetic field mixing effect, causing perturbation propagation to the vy direction,is supposed to be theorigin of the flow 17