Global Gyrokinetic Simulations of Toroidal ETG Mode in Reversed Shear Tokamaks

1. Global Gyrokinetic Simulations of Toroidal ETG Mode in Reversed Shear Tokamaks Y. Idomura1), S. Tokuda1), and Y. Kishimoto1) 2) 1)Japan Atomic Energy Research Institute 2)Kyoto University 20th IAEA Fusion Energy Conference Vilamoura, Portugal, 1-6 November 2004 Outline Introduction Linear analysis and mixing length estimate of ETG modes ETG turbulence simulations in PS and RS tokamaks Summary

2. Introduction • ETG turbulence is experimentally relevant candidate of ce in tokamak • High suppression threshold wExB > g than TEM (Stallard 1999) • Stiff Te profile consistent with critical Lte of ETG (Hoang 2001) • Results from several ETG simulations contradict with each other • In PS tokamaks, local flux tube toroidal GK simulations (Jenko 2002) show extremely high ce~10cGB due to streamers • High ce was not recovered in local slab GF simulations (Li 2004) and large r* (r*-1~100) global toroidal GF simulations (Labit 2003) • In RS tokamaks, global slab GK simulations (Idomura 2000) show ce suppression by ETG driven microscopic zonal flows • To understand these qualitatively and quantitatively different results, ETG turbulence is studied using global toroidal GK simulations • Linear global analysis of toroidal ETG modes in PS/RS tokamaks • Correspondence between mixing length theory and r*-scaling • Zonal flow and streamer formations in PS/RS-ETG turbulence

3. ETG turbulence simulation using GT3D • GK toroidal PIC code based on finite element df PIC method • Gyrokinetic electrons with adiabatic ions (k^rti>>1) • Annular torus geometry with fixed boundary condition f = 0 • 1/N wedge torus model n = 0, N, 2N, 3N… • Realistic small r*=rte/a with quasi-ballooning representation • Global profile effects (ne, Te, q, 1/r) • Self-consistent Te, ne are relaxed by heat/particle transport • w*te-shearing effect • Reversed q(r) profile • Optimized particle loading • energy/particle conservation Validity of simulation is checked by conservation properties !

4. High-n solver with quasi-ballooning representation Realistic tokamak size a/rte~104: kqrte~1 (q=1.4) m=5000 • ~104 poloidal grids are needed without QB representation • ~102 poloidal grids are enough with QB representation mode structure on the poloidal plane mode structure along the field line jump condition for periodicity in q

5. Linear analysis and mixing length estimate of ETG modes

6. Linear ETG growth rate spectrum Cyclone like parameters (R0/Lte=6.9,he=3.12,a~8600rte~150rti) • Unstable region spreads over n~2000 (m~3000, kqrte~0.7) • RS-ETG mode is excited around qmin surface (Idomura 2000) • Almost the same gmax in PS and RS configurations analysis domain

7. Positive shear configuration Dr of PS-ETG mode is limited by w*-shearing effect (Kim 1994) Dr of RS-ETG mode is determined by q profile (Idomura 2000) Reversed shear configuration r* scan of eigenfunctions in PS/RS tokamaks a/rte~536 a/rte~536 ~45rte ~60rte non-resonant resonant a/rte~2146 a/rte~2146 ~40rte ~120rte qmin surface

8. Mixing length theory and r*-scaling • Mixing length theory of ETG modes in PS/RS plasmas • PS-ETG mode • RS-ETG mode • r* scan of the saturation amplitude in single-n simulations • Small r* PS-ETG modes give order of magnitude higher saturation level than RS-ETG and large r* PS-ETG modes Fixed local parameters R0/Lte=6.9, he=3.12 kqrte~0.3, a/R0=0.358 gNL: eddy turn over time

9. ETG turbulence simulations in PS and RS tokamaks (Cyclone like parameters with a/rte~8600)

10. Linear phase (tvte/Ln ~110) Saturation phase (tvte/Ln ~208) PS-ETG turbulence is dominated by streamers Streamers are characterized by ballooning structure and w~w*e Primary streamers (tvte/Ln ~175) Secondary streamers (tvte/Ln ~250) q r Streamer formation in PS-ETG turbulence weak field side q ~ 0 kqrte ~ 0.27 600rte kqrte ~ 0.17 w ~ w*e

11. Extremely high ce in PS-ETG turbulence (R0/Lte)crit~4.5 R0/Lte~5.5 ~5g -1 R0/Lte~6.9 zonal flows R0/Lte ce~10cGB <VExB>/vte ce/(vterte2/Lte) Te profile is strongly relaxed in a turbulent time scale ~5g-1

12. Linear phase (tvte/Ln ~110) Secondary mode (tvte/Ln ~255) RS-ETG turbulence show different behavior across qmin Zonal flows (streamers) appear in negative (positive) shear region Saturation phase (tvte/Ln ~207) Zonal flow formation (tvte/Ln ~380) q r Zonal flow formation in RS-ETG turbulence weak field side q ~ 0 kqrte ~ 0.27 600rte qmin

13. ce gap structure in RS-ETG turbulence (R0/Lte)crit~3.7 zonal flows R0/Lte qmin quasi-steady zonal flows ce suppression ce/(vterte2/Lte) <VExB>/vte qmin qmin Te gradient is sustained above its critical value in quasi-steady state

14. n-spectrum in NS region ZF generation similar to slab GK simulation (Idomura 2000) Secondary mode is excited at kqrte~0.1 Quasi-steady ZF spectrum peaks at krrte~0.1 Weak collisionless ZF damping for (krrte)2<<1 (Kim2003) Microscopic ZF spectrum decay with (Jenko2002) kr spectrum of zonal flows Properties of zonal flows in k spectrum |fn| negative shear side (r/a~0.48) krrte~0.1 secondary mode kqrte~0.1 primary mode kqrte~0.27 zonal flow kr spectrum zonal flows

15. Summary • ETG turbulence is studied using global toroidal GK simulations • Initial saturation levels consistent with the mixing length theory • Ballooning PS-ETG modes show Bohm like r*-scaling • Slab like RS-ETG modes show gyro-Bohm like r*-scaling • Small r* PS-ETG modes give order of magnitude higher saturation level than RS-ETG and large r* PS-ETG modes • PS/RS ETG turbulences show different structure formations • PS-ETG turbulence is dominated by streamers • Te profile is quickly relaxed by large ce~10cGB • RS-ETG turbulence is characterized by zonal flows (streamers) in negative (positive) shear region • Te profile is sustained by ce gap structure • These results suggest a stiffness of Te profile in PS tokamaks, and a possibility of the Te transport barrier in RS tokamaks