Isotope mass and charge effects in tokamak plasmas Istvan Pusztai 1 Jeff Candy 2 Punit Gohil 2 (1) Chalmers University of Technology, Applied Physics, SE-412 96, Göteborg, Sweden (2) General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, USA This work was funded by Euratom-VR association and U.S. DOE., and grants from Chalmersska Forskningsfonden and Adlerbertska Forskningsstiftelsen. The computational resources of NCCS at ORNL were used for the nonlinear simulations.
Overview Motivation and historical puzzles Overview of target DIII-D discharges (H,D,He plasmas) Sequence of gyrokinetic simulations under imposed similarity Transport analysis of the target discharges Conclusions 1
Motivation: the isotope scaling problem Local drift wave turbulence is expected to be gyro-bohm. (for isotope i ) For fixed temperature it implies For fixed Theory: Confinement degrades with increasing mass Experiment: Confinement usually improves as one moves from hydrogen to deuterium or D-T plasmas. No robust theory of the isotope scaling. 2
Overview of target DIII-D discharges Different main ion species - Deuterium (129135, 1250 1300 ms) - Hydrogen (133778, 1225 1275 ms) - Helium (138767, 2700 2750 ms) L-mode phases from balanced-nbi discharges (minimal effect from rotation and rotation shear). Not similarity discharges. Lower single-nullnull plasmas, B t ~ 2 T, I p ~ 1 MA. Configuration: B t clockwise, I p counterclockwise from above. Auxiliary heating: ECRH and NBI. Carbon impurity present in all discharges. Deuterium minority in the hydrogen and helium discharges. Data pre-processed by ONETWO (D, H) and TRANSP (He,H) H) 3
Simulations under imposed similarity The profiles and magnetic geometry are taken from the deuterium discharge. Only the mass and charge of the main species are modified. Flows are neglected (balanced injection). 4
Linear simulations, adiabatic electrons Adiabatic electrons, no impurities, no ion-ion collisions. Charge and mass depencdence appears through c si and si. For ions with the same charge plots of frequencies against wave number should be the same when quantities are normalized to species units. The explicit appearance of charge in the Poisson eq. gives higher growth rates for Z > 1. in species units scales roughly as Z 1/2. ITG growth rates csi 1 m i si m i Z 5
With kinetic electrons, no collisions Perfect symmetry between H and D is broken due to the difference in the parallel dynamics of circulating electrons. Consistent with higher growth rates at reduced electron-to-ion mass ratio. ITG growth rates TEM growth rates 6
With kinetic electrons, no collisions Perfect symmetry between H and D is broken due to the difference in the parallel dynamics of circulating electrons. Consistent with higher growth rates at reduced electron-to-ion mass ratio. Qualitatively different behavior of TEM growth rates for helium. ITG growth rates TEM growth rates 6
With electron-ion collisions For hydrogen isotopes the difference between the ITG growth rates increases (in the favorable direction) due to the dependence of ei on m e. H plasma is similar to a D plasma with reduced mass ratio. 7
With electron-ion collisions For hydrogen isotopes the difference between the ITG growth rates increases (in the favorable direction) due to the dependence of ei on m e. H plasma is similar to a D plasma with reduced mass ratio. 7
With electron-ion collisions For hydrogen isotopes the difference between the ITG growth rates increases (in the favorable direction) due to the dependence of ei on m e. H plasma is similar to a D plasma with reduced mass ratio. The collisional stabilization of the TE mode in the H plasma is not as effective as in the D plasma. ei isthesamein same in absolute units but it is smaller in H species units. 7
Understanding species units fluxes If - the profiles in a pure plasma are similar - the electrons are adiabatic - the local limit * 0 is assumed then the fluxes normalized to the gyro-bohm flux of the species Q GBi n e T c e si 2 2 a m Z si are identical, independently d of isotope mass. (The same normalized equations are solved). The species units curve of the distribution of flux over poloidal wave numbers is universal to lowest order. i 8
Adiabatic vs. kinetic electron response Adiabatic electron Adiabatic electrons Kinetic el., collisions response: almost perfect gyro-bohm scaling of transport in hydrogen isotope plasmas. The deviations are due to finite * effects. With kinetic electrons and e-i collisions, favorable deviation from gyro-bohm scaling appears for H D,, but negligible effect for D T. 9 Q GBi n T c e e si 2 2 a m Z si i
Adiabatic vs. kinetic electron response Adiabatic electron response: almost perfect gyro-bohm scaling of transport in hydrogen isotope plasmas. The deviations are due to * effects. With kinetic electrons and e-i collisions, favorable deviation from gyro-bohm scaling appears for H D,, but negligible effect for D T. Adiabatic electrons Kinetic el., collisions 9 Q GBi n T c e e si 2 2 a m Z si i
Including carbon impurity can dramatically reduce the energy fluxes. Carbon can decrease linear growth rates, but the effect on nonlinear fluxes is more pronounced. Effect of carbon impurity Pure plasma With carbon (Z eff = 2) 10
Helium plasmas The electron energy flux in a He plasma is much higher than the gyro-bohm prediction due to the high h linear growth rates in a He plasma. This is balanced by the lower ion density for the ion energy fluxes. Carbon does not affect the magnitude of the fluxes as much as in hydrogenic plasmas. In absolute units the fluxes in the He+D+C plasma are similar to those in a D+C plasma. No carbon With carbon n T c 2 11 GBi e e si si i Q a 2 m Z
Transport analysis Experimental turbulent energy fluxes are calculated by TGYRO via power balance. The neoclassical transport calculated by NEO is subtracted. Non-linear GYRO simulations around three radial locations with all ion species included. Mean toroidal and poloidal flows for each species are computed by NEO, by calculating E r first matching the measured toroidal rotation of carbon at outer midplane. NEO is more accurate than NCLASS TGYRO available for use by anyone 12
Transport analysis D, He In SI units the fluxes are roughly constant t on the studied radial domain. Gyro- Bohm fluxes increase rapidly towards the edge, where gyrokinetics break down. Reasonably good agreement between exp. and GYRO. Consistently tl with similarity il it studies, Q e ~Q i for given shot. But gyro-bohm fluxes should be similar in the D and He discharges. Differences in the profiles cannot be disregarded Electron energy flux Ion energy flux 2 5/ 2 13 Q[ QGBD ] Q[MW/m ]/( nete )
Transport analysis D, H Consistently with similarity studies, the gyro-bohm energy fluxes for the two hydrogen isotopes are comparable, Q ih being somewhat lower than Q id. Since the hydrogen discharge was the coldest it gives lower SI fluxes in the hydrogen than in the deuterium case. Electron energy flux Ion energy flux 2 5/ 2 14 Q[ QGBD ] Q[MW/m ]/( nete )
Transport analysis D, H Electron energy flux Ion energy flux In the hydrogen discharge the experimental gyro-bohm fluxes are enormous (especially the ion energy flux), far from the GYRO prediction. 15
Can it be drift-wave turbulence? Deuterium discharge Nonlinear GYRO and TGLF simulations give similar flux predictions for these discharges. Predictive TGYRO-TGLF/NEO simulations were used to determine what profiles were necessary to reproduce the experimental level of energy fluxes. Reasonable profiles for the D and He discharges. 16
Can it be drift-wave turbulence? Nonlinear GYRO and TGLF simulations give similar flux predictions for these discharges. Predictive TGYRO-TGLF/NEO simulations were used to determine what profiles were necessary to reproduce the experimental level of energy fluxes. Reasonable profiles for the D and He discharges. But extremely steep profiles for the H discharge. These high fluxes cannot be reproduced even - without collisions - without impurities - accounting for energetic ions Same results with ONETWO and with TRANSP inputs. Same anomaly for another similar hydrogen discharge. No significant MHD activity is present 16 Deuterium discharge Hydrogen discharge
Conclusions For Z >1 main ions, as for helium, the appearance of charge in the Poisson equation leads to higher linear growth rates. Accordingly, the transport in He plasmas is significantly higher than the gyro-bohm prediction. Carbon impurity can dramatically reduce the transport in hydrogen isotope plasmas, but it has only minor effect in He plasmas. In a comprehensive transport simulation all non-trace impurity species should be included. d There can be considerable (favorable) deviations from gyro-bohm scaling in the plasma core if flows, collisions and impurites are taken into account. However, these are probably not sufficient to explain a strong favorable mass scaling of the global energy confinement. In the deuterium and helium plasmas analyzed here nonlinear gyrokinetic (and gyrofluid) simulations could reproduce the energy transport quite well, while in the hydrogen plasma the transport is much higher than what dift drift-wave turbulence could explain. 17
Overview of target DIII-D discharges Deuterium discharge Hydrogen discharge Helium discharge