1 Global Gyrokinetic Simulations of Toroidal ETG Mode in Reversed Shear Tokamaks Y. Idomura, S. Tokuda, and Y. Kishimoto Y. Idomura 1), S. Tokuda 1), and Y. Kishimoto 1) 2) 1) Japan Atomic Energy Research Institute 2) Kyoto University 20 th 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

2Introduction ETG turbulence is experimentally relevant candidate of  e in tokamak – High suppression threshold  ExB >  than TEM (Stallard 1999) – Stiff T e profile consistent with critical L te 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  e ~10  GB due to streamers – High  e was not recovered in local slab GF simulations (Li 2004) and large  * (  *-1 ~100) global toroidal GF simulations (Labit 2003) – In RS tokamaks, global slab GK simulations (Idomura 2000) show  e 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  * -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  f PIC method Gyrokinetic electrons with adiabatic ions (k   ti >>1) Annular torus geometry with fixed boundary condition  1/N wedge torus model n = 0, N, 2N, 3N… Realistic small  * =  te /a with quasi-ballooning representation Global profile effects (n e, T e, q, 1/r) – Self-consistent T e, n e are relaxed by heat/particle transport –  * 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/  te ~10 4 : k   te ~1 (q=1.4) m=5000 – ~10 4 poloidal grids are needed without QB representation – ~10 2 poloidal grids are enough with QB representation jump condition for periodicity in  mode structure on the poloidal plane mode structure along the field line

5 Linear analysis and mixing length estimate of ETG modes

6 Linear ETG growth rate spectrum Cyclone like parameters (R 0 /L te =6.9,  e =3.12,a~8600  te ~150  ti ) – Unstable region spreads over n~2000 (m~3000, k   te ~0.7) – RS-ETG mode is excited around q min surface (Idomura 2000) – Almost the same  max in PS and RS configurations analysis domain

7  * scan of eigenfunctions in PS/RS tokamaks Positive shear configuration –  r of PS-ETG mode is limited by  * -shearing effect (Kim 1994) –  r of RS-ETG mode is determined by q profile (Idomura 2000) Reversed shear configuration non-resonant resonant ~60  te ~120  te a/  te ~536 a/  te ~2146 a/  te ~536 q min surface ~45  te ~40  te

8 Mixing length theory and  * -scaling Mixing length theory of ETG modes in PS/RS plasmas – PS-ETG mode – RS-ETG mode  * scan of the saturation amplitude in single-n simulations – Small  * PS-ETG modes give order of magnitude higher saturation level than RS-ETG and large  * PS-ETG modes Fixed local parameters R 0 /L te =6.9,  e =3.12 k   te ~0.3, a/R 0 =0.358  NL : eddy turn over time

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

10 Streamer formation in PS-ETG turbulence Linear phase (t v te /L n ~110) Saturation phase (t v te /L n ~208) – PS-ETG turbulence is dominated by streamers – Streamers are characterized by ballooning structure and  ~  * e Primary streamers (t v te /L n ~175) Secondary streamers (t v te /L n ~250) k   te ~ 0.27 k   te ~ 0.17  ~  * e weak field side  ~  te  r

11 Extremely high  e in PS-ETG turbulence  e /(v te  te 2 /L te ) /v te R 0 /L te R 0 /L te ~6.9 R 0 /L te ~5.5 (R 0 /L te ) crit ~4.5 ~5  -1 zonal flows  e ~10  GB T e profile is strongly relaxed in a turbulent time scale ~5  -1

12 Zonal flow formation in RS-ETG turbulence Linear phase (t v te /L n ~110) Secondary mode (t v te /L n ~255) – RS-ETG turbulence show different behavior across q min – Zonal flows (streamers) appear in negative (positive) shear region Saturation phase (t v te /L n ~207) Zonal flow formation (t v te /L n ~380) q min k   te ~ 0.27 weak field side  ~  te  r

13  e gap structure in RS-ETG turbulence  e /(v te  te 2 /L te ) /v te R 0 /L te (R 0 /L te ) crit ~3.7 q min zonal flows T e gradient is sustained above its critical value in quasi-steady state quasi-steady zonal flows  e suppression

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

15Summary 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  * -scaling – Slab like RS-ETG modes show gyro-Bohm like  * -scaling – Small  * PS-ETG modes give order of magnitude higher saturation level than RS-ETG and large  * PS-ETG modes PS/RS ETG turbulences show different structure formations – PS-ETG turbulence is dominated by streamers T e profile is quickly relaxed by large  e ~10  GB – RS-ETG turbulence is characterized by zonal flows (streamers) in negative (positive) shear region T e profile is sustained by  e gap structure These results suggest a stiffness of T e profile in PS tokamaks, and a possibility of the T e transport barrier in RS tokamaks