ITG turbulence                     CTEM turbulence              RSAE        Summary        Properties of electrostatic and...
ITG turbulence              CTEM turbulence              RSAE                SummaryMotivations                 Reversed (...
ITG turbulence              CTEM turbulence              RSAE                SummaryMotivations                 Reversed (...
ITG turbulence          CTEM turbulence         RSAE          SummaryOutline     1   ITG turbulence spreading in RS plasma...
ITG turbulence          CTEM turbulence         RSAE          SummaryOutline     1   ITG turbulence spreading in RS plasma...
ITG turbulence                                           CTEM turbulence                                   RSAE   SummaryI...
ITG turbulence                                           CTEM turbulence                                      RSAE        ...
ITG turbulence                                         CTEM turbulence                      RSAE                          ...
ITG turbulence                                                     CTEM turbulence                                  RSAE  ...
ITG turbulence                                                     CTEM turbulence                              RSAE      ...
ITG turbulence                          CTEM turbulence                                        RSAE                     Su...
ITG turbulence          CTEM turbulence         RSAE          SummaryOutline     1   ITG turbulence spreading in RS plasma...
ITG turbulence                                                      CTEM turbulence                      RSAE             ...
ITG turbulence                                                    CTEM turbulence                 RSAE                 Sum...
ITG turbulence                               CTEM turbulence                                       RSAE                   ...
ITG turbulence            CTEM turbulence           RSAE              SummaryConclusions for electrostatic turbulence simu...
ITG turbulence                   CTEM turbulence                          RSAE                                 Summary    ...
ITG turbulence          CTEM turbulence         RSAE          SummaryOutline     1   ITG turbulence spreading in RS plasma...
ITG turbulence           CTEM turbulence         RSAE                    SummaryRSAE physics                              ...
ITG turbulence                                                    CTEM turbulence                              RSAE       ...
ITG turbulence            CTEM turbulence                              RSAE                           SummaryRSAE mode str...
ITG turbulence                                       CTEM turbulence              RSAE              SummaryRSAE fast ion e...
ITG turbulence           CTEM turbulence          RSAE             SummarySummary           GTC gyrokinetic particle simul...
ITG turbulence                CTEM turbulence                  RSAE                   SummaryOther GTC related presentatio...
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Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas

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Presented at 2010 International Sherwood Fusion Theory Conference

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Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas

  1. 1. ITG turbulence CTEM turbulence RSAE Summary Properties of electrostatic and electromagnetic turbulence in reversed magnetic shear plasmas Wenjun Deng University of California, Irvine, USA Ihor Holod1 , Yong Xiao1 , Xin Wang1,2 , Wenlu Zhang1,3 and Zhihong Lin1 1 University of California, Irvine, USA 2 IFTS, Zhejiang University, China 3 University of Science and Technology of China, China Supported by SciDAC GSEP & GPS-TTBP
  2. 2. ITG turbulence CTEM turbulence RSAE SummaryMotivations Reversed (magnetic) shear (RS) in tokamak: safety factor q-profile has an off-axis minimum. This minimum value is called qmin . 1 Internal transport barrier (ITB) can form at the integer qmin flux surface and suppress turbulent transport. Some proposed mechanisms are based on electrostatic drift wave turbulence. We use global gyrokinetic particle code GTC [Lin et al., Science 1998] to study two modes of drift wave turbulence: the ion temperature gradient (ITG) and the collisionless trapped electron mode (CTEM) turbulence. 1/16
  3. 3. ITG turbulence CTEM turbulence RSAE SummaryMotivations Reversed (magnetic) shear (RS) in tokamak: safety factor q-profile has an off-axis minimum. This minimum value is called qmin . 1 Internal transport barrier (ITB) can form at the integer qmin flux surface and suppress turbulent transport. Some proposed mechanisms are based on electrostatic drift wave turbulence. We use global gyrokinetic particle code GTC [Lin et al., Science 1998] to study two modes of drift wave turbulence: the ion temperature gradient (ITG) and the collisionless trapped electron mode (CTEM) turbulence. 2 Reversed shear Alfv´n eigenmode (RSAE) at the qmin flux e surface can be driven unstable by fast ions and can cause fast ion loss. We use electromagnetic GTC to study RSAE and fast ion physics. The results using fast ions and antenna excitation without thermal particle kinetic effects are benchmarked with HMGC [Briguglio et al., PoP 1998] simulations. 1/16
  4. 4. ITG turbulence CTEM turbulence RSAE SummaryOutline 1 ITG turbulence spreading in RS plasmas (no ITB) 2 CTEM turbulence spreading in RS plasmas (no ITB) 3 Linear simulations of RSAE by antenna and fast ion excitation
  5. 5. ITG turbulence CTEM turbulence RSAE SummaryOutline 1 ITG turbulence spreading in RS plasmas (no ITB) 2 CTEM turbulence spreading in RS plasmas (no ITB) 3 Linear simulations of RSAE by antenna and fast ion excitation
  6. 6. ITG turbulence CTEM turbulence RSAE SummaryITG linear eigenmode: gap structures only for integer qmin Rarefaction of the rational surfaces causes a potential gap. 1.4 qmin = 1 1.2 1 q 0.8 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/a mode rational surface: nq(r) = m qmin = 1 n: toroidal mode # 10−5 φ2 m: poloidal mode # 10−6 10−7 nq(rblack ) = mmin 10−8 r/a nq(rred ) = mmin + 1 10−9 nq(rblue ) = mmin + 2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 etc. n ∈ [25, 95] 2/16
  7. 7. ITG turbulence CTEM turbulence RSAE SummaryITG linear eigenmode: gap structures only for integer qmin Rarefaction of the rational surfaces causes a potential gap. 1.4 qmin = 1 1.2 1 q 0.8 qmin = 0.9552 0.6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/a mode rational surface: nq(r) = m qmin = 1 n: toroidal mode # qmin = 0.9552 10−5 10−5 φ2 m: poloidal mode # φ2 10−6 10−6 10−7 nq(rblack ) = mmin 10−7 10−8 r/a nq(rred ) = mmin + 1 10−8 r/a 10−9 nq(rblue ) = mmin + 2 10−9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 etc. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 n ∈ [25, 95] 2/16
  8. 8. ITG turbulence CTEM turbulence RSAE SummaryITG nonlinear evolution: potential gap filled up 10−5 10−4 II III I φ2 I φ2 II V 10−5 III 10−6 10−6 10−7 qmin = 2 10−7 10−8 φ2 10−8 t/(R0 /cs ) snapshots r/a 10 −9 10−9 0 50 100 150 200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Three snapshots taken Radial structures of I, II, & III I II III 3/16
  9. 9. ITG turbulence CTEM turbulence RSAE SummaryITG nonlinear evolution: gap filled up by turbulence spreading 1.5e − 16 1e − 16 Integrated ΦE (a. u.) outward flow 5e − 17 0 10−5 II III −5e − 17 φ2 I −6 V inward flow 10 −1e − 16 r/a −1.5e − 16 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10−7 qmin = 2 Approximated E-field intensity −8 10 φ2 flux in the early nonlinear t/(R0 /cs ) snapshots −9 phase integrated from Snapshot 10 0 50 100 150 200 I to II. φ2 time history, just for reminding when the snapshots ΦE (r) ≡ E 2 vEr are taken Turbulence flows into the qmin region from both sides. 4/16
  10. 10. ITG turbulence CTEM turbulence RSAE SummaryITG nonlinear evolution: gap filled up by turbulence spreading 1.5e − 16 10−4 1e − 16 Integrated ΦE (a. u.) 10−5 φ2 outward flow 5e − 17 0 10−6 −5e − 17 10−7 r/a = 0.427 inward flow r/a = 0.490 −1e − 16 10−8 r/a = 0.554 r/a −1.5e − 16 t/(R0 /cs ) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10−9 Approximated E-field intensity 0 50 100 150 200 flux in the early nonlinear φ2 near qmin grows after φ2 phase integrated from Snapshot outside the qmin region I to II. saturates, and it doesn’t grow exponentially, indicating not a ΦE (r) ≡ E 2 vEr linear effect. Turbulence flows into the qmin No linear mechanism for region from both sides. ITB formation. 4/16
  11. 11. ITG turbulence CTEM turbulence RSAE SummaryITG nonlinear evolution: no coherent structures influctuations near qmin III III (a. u.) Er (a. u.) χi (a. u.) χi r δTi r δTi Er 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7 0.8 r/a r/a No nonlinear mechanism for ITB formation. Conclusion: no linear or nonlinear mechanism for ITB formation near qmin in ITG turbulence. 5/16
  12. 12. ITG turbulence CTEM turbulence RSAE SummaryOutline 1 ITG turbulence spreading in RS plasmas (no ITB) 2 CTEM turbulence spreading in RS plasmas (no ITB) 3 Linear simulations of RSAE by antenna and fast ion excitation
  13. 13. ITG turbulence CTEM turbulence RSAE SummaryCTEM linear eigenmode only in the positive-shear region 10−2 Collisionless trapped electron mode (CTEM): IV 10−3 φ2 V V VI drift wave driven by trapped electron 10−4 III precessional drift resonance 10−5 qmin = 2 10−6 II II 10−7 φ2 I t/(R0 /cs ) snapshots 10−8 0 10 20 30 40 50 60 Six snapshots taken 10−3 φ2 I and II scaled to the same level 10−4 I 10−5 II r/a Linear eigenmode structure only in 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 positive-shear side due to precessional Linear eigenmode in I & II drift reversal in negative-shear side 6/16
  14. 14. ITG turbulence CTEM turbulence RSAE SummaryCTEM turbulence spreading into negative-shear region 10−2 II* φ2 III VI IV 10−3 V VI 10−4 r/a 10−5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 II*: scaled up 10−2 φ2 10−3 10−4 r/a = 0.2 Final turbulence structure r/a = 0.3 10−5 r/a = 0.4 Front propagation speed vts 0.43v∗e r/a = 0.71 t/(R0 /cs ) close to various theoretical estimates 10−6 0 10 20 30 40 50 60 [G¨rcan et al., PoP 2005; Guo et al., u Turbulence spreading from PRL 2009] positive-shear side to No linear mechanism for ITB negative-shear side formation 7/16
  15. 15. ITG turbulence CTEM turbulence RSAE SummaryCTEM nonlinear evolution: no coherent structures influctuations near qmin VI VI (a. u.) Er (a. u.) χ (a. u.) r δTe r δTe χi Er χe 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 r/a r/a No nonlinear mechanism for ITB formation. Conclusion: no linear or nonlinear mechanism for ITB formation near qmin in CTEM turbulence. 8/16
  16. 16. ITG turbulence CTEM turbulence RSAE SummaryConclusions for electrostatic turbulence simulations The electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of ITB in the reversed shear plasmas with an integer qmin . Other external mechanisms, such as sheared flows generated by MHD activities, are worth pursuing as possible agents to suppress the electrostatic drift wave turbulence and form the ITB when qmin crossing an integer. [Shafer et al., PRL 2009] Our nonlocal results raise the issue of the validity of previous local simulations finding the transport reduction due to the precessional drift reversal of trapped electrons or the rarefaction of mode rational surfaces. W. Deng & Z. Lin, Phys. Plasmas 16, 102503 (2009) 9/16
  17. 17. ITG turbulence CTEM turbulence RSAE Summary Global Gyrokinetic Toroidal Code (GTC) incorporates all physics in a single version • Non-perturbative (full-f) & perturbative (df) simulation • General geometry using EFIT & TRANSP data • Kinetic electrons & electromagnetic simulation • Neoclassical effects using Fokker-Planck collision operators conserving energy & momentum • Equilibrium radial electric field, toroidal & poloidal rotations; Multiple ion species GTC simulation of DIII-D shot #101391 using EFIT data • Applications: microturbulence & MHD modes full-f ITG • Parallelization >100,000 cores intensity df ITG intensity Global field-aligned mesh Parallel solver PETSc Advanced I/O ADIOS full-f zonal flows [Lin et al, Science, 1998] df zonal flows http://gk.ps.uci.edu/GTC/ time 10/16
  18. 18. ITG turbulence CTEM turbulence RSAE SummaryOutline 1 ITG turbulence spreading in RS plasmas (no ITB) 2 CTEM turbulence spreading in RS plasmas (no ITB) 3 Linear simulations of RSAE by antenna and fast ion excitation
  19. 19. ITG turbulence CTEM turbulence RSAE SummaryRSAE physics vA m RSAE is a form of shear Alfv´ne ωRSAE ≈ R qmin −n wave in the toroidal geometry and is localized near the qmin flux surface. RSAE can be driven unstable by fast ions. RSAE exhibits a variety of phenomena, an important one being the “grand cascade” [Sharapov et al., PLA 2001]. The “grand cascade” is used for qmin temporal and spatial diagnosis in experiments. One example on the right [Sharapov et al., NF 2006]. 11/16
  20. 20. ITG turbulence CTEM turbulence RSAE SummaryBenchmark of RSAE antenna excitation (GTC & HMGC) 2.7 2.6 2.5 2.4 2.3 2.2 q 2.1 2 1.9 1.8 1.7 1.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 r/a q-profile φ spectrum from HMGC 1 (w/o coupling) m=6 m=7 GTC, e, m = 6 0.8 HMGC, e, m = 6 0.6 φ (a. u.) 0.4 ωA /(vA /R0 ) 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 20 40 60 80 100 120 140 160 r/a t/(R0 /vA ) Alfv´n continuum (n = 4) e time history of φ HMGC: Hybrid MHD-Gyrokinetic Code [Briguglio et al., PoP 1998] 12/16
  21. 21. ITG turbulence CTEM turbulence RSAE SummaryRSAE mode structure by antenna excitation m=5 m=6 m=7 |φ| (a. u.) 0 0.2 0.4 0.6 0.8 1 r/a φ poloidal structure from GTC m-harmonic decomposition from GTC φ poloidal structure from HMGC m-harmonic decomposition from HMGC 13/16
  22. 22. ITG turbulence CTEM turbulence RSAE SummaryRSAE fast ion excitation e, m = 7 m, m = 7 φ (a. u.) 0 50 100 150 200 250 300 350 t/(R0 /vA ) φ poloidal structure (GTC) φ time history (GTC) |φ| (a. u., log scale) GTC, m = 7 0 50 100 150 200 250 300 350 t/(R0 /vA ) φ poloidal structure (HMGC) 14/16
  23. 23. ITG turbulence CTEM turbulence RSAE SummarySummary GTC gyrokinetic particle simulations of electrostatic ITG and CTEM turbulence: the turbulence itself does not support either linear or nonlinear mechanism for the formation of ITB in the reversed shear plasmas with an integer qmin . GTC gyrokinetic particle simulations of electromagnetic RSAE: the first time using gyrokinetic particle approach to simulate RSAE; the mode can be excited either by antenna or by fast ion; for the antenna excitation, when kinetic effects of thermal particles are artificially suppressed, the frequency and mode structure in the GTC & HMGC simulations agree well with each other. GTC simulations of toroidal Alfv´n eigenmode (TAE) and e β-induced Alfv´n eigenmode (BAE) will also be reported in this e conference. 15/16
  24. 24. ITG turbulence CTEM turbulence RSAE SummaryOther GTC related presentations This afternoon: 1P34, O. Luk and Z. Lin, Collisional Effects on Nonlinear Wave-Particle Trapping in Mirror Instability and Landau Damping 2P17, X. Wang et al., Hybrid MHD-particle simulation of discrete kinetic BAE in tokamaks 2P19, H. S. Zhang et al., Gyrokinetic particle simulation of linear and nonlinear properties of GAM and BAE in Tokamak plasmas Tomorrow afternoon: 3P13, I. Holod, Kinetic electron effects in toroidal momentum transport 3P18, Z. Lin and GTC team, Nonperturbative (full-f) global gyrokinetic particle simulation 3P27, Y. Xiao et al., Verification and validation of gyrokinetic particle simulation 3P35, G. Y. Sun et al., Gyrokinetic particle simulation of ideal and kinetic ballooning modes 3P48, Z. Wang and Z. Lin, GTC Simulation of Cylindrical Plasmas Wednesday morning: Talk, W. Zhang, Gyrokinetic Particle Simulations of Toroidal Alfven Eigenmode and Energetic Particle transport in Fusion Plasmas 16/16

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