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M.Becoulet G. Huysmans, E. Nardon

Non-linear MHD modelling of RMPs with toroidal rotation and resonant and non-resonant plasma braking. M.Becoulet G. Huysmans, E. Nardon Association Euratom-CEA, CEA Cadarache, F-13108, St. Paul-lez-Durance, France. Thanks to all USBPO RMPs team and especially to M. Schaffer and S. Sabbagh.

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M.Becoulet G. Huysmans, E. Nardon

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  1. Non-linear MHD modelling of RMPs with toroidal rotation and resonant and non-resonant plasma braking. • M.BecouletG. Huysmans, E. Nardon • Association Euratom-CEA, CEA Cadarache, F-13108, St. Paul-lez-Durance, France. • Thanks to all USBPO RMPs team and especially to M. Schaffer and S. Sabbagh • Outline: • MHD model with resonant (jxB) and non-resonant (NTV) plasma braking. • Example for 18 picture frame coils.

  2. code RMHD: reduced non-linear MHD [A.Y Aydemir, Phys.Fluids B4(11)1992,3469] in cylindrical geometry, but with some new physics included: -Doppler shift due to the toroidal rotation; -resonant (jxB) braking [Y.Kikuchi et al PPCF 48(2006)169],[E. Lazzaro et al PoP9(2002)3906] -non-resonant braking [K. Shaing, PoP 10(2003)1443],[W.Zhu et al PRL96,225002(2006)],due to the Neoclassical Toroidal Viscosity (NTV). Vorticity: Pressure (~0 here): Poloidal flux: Parallel velocity: (Source is adapted: )

  3. Calculation of Neoclassical Toroidal Viscosity (NTV) in collisionless regime.(W.Zhu PRL2006) -used here

  4. Complete eliptic integrals of first (K) and second (E) kind.

  5. Example of the spectrum from 18 picture-frame coils around ports in-vessel. R1= 8.608m; Z1=1.798; R2= 8.664; Z2=-0. 558df=12.620° ; Dc-c=20.° PF-coil currents (A) (nmax=4): 19140. 110000. 19140. -103400. -55000. 84260. 84260. -55000. -103400. 19140. 110000. 19140. -103400. -55000. 84260. 84260. -55000. -103400.

  6. Chirikov parameter and normalized radial magnetic field in cylindrical approximation for H-mode, Hybrid and ITB q-profiles. For peak current 110kAt,n=-4 edge (>0.9) is ergodized.

  7. Islands size in cylindrical approximation for H-mode, Hybrid and ITB q-profiles.

  8. Toroidal harmonic n=-4 of poloidal plux perturbation.

  9. Input for RMHD code: normalized ybnd at r=a. n=-4

  10. Equilibrium components needed for calculations of NTV. ITER H-mode.

  11. -magnetic field strength along non-perturbed line.

  12. Poloidal harmonics for magnetic field strength. Non-resonant m=0 is the largest=> typical for one-row coils.

  13. Integral Ilin the expression for NTV. Here only n=4 is taken into account. Possibly n=14 will be important. Non-resonant harmonics are more important. Also they are not screened by rotation, so one can take vacuum amplitudes for these harmonics.

  14. Plasma parameters (H-mode) for estimations of NTV from 18pf coils (n=4).

  15. NTV force and damping time (~0.4s on r=0.4) for ITER H-mode parameters with 18 picture-frame coils at I=110kA. Here only n=4 is taken into account. Possibly with n=14 damping time will be a bit shorter. Damping time NTV force

  16. Non-linear MHD modelling with rotation and only resonant braking. n=-4, m=10:14;ybnd=(2.5m=10;2m=11;1.5m=12; 1.25m=13;1m=14; )10-4; h(0)=10-8 (here plasma resistivility is higher compared to real one 10-9-10-10) Resistivity profile q-profile

  17. Central islands are more screened, but edge ergodisation persist : smaller rotation, larger resistivily=>less screening at the edge. 2p Vt=0; t=8000tA q 0 Vt=0.5610-2; t=8000tA, only resonant braking r 1. 0.7

  18. More external harmonics are less screened by rotation. ymn q=-m/n with (Vt=0.0056) and without rotation. Resonant braking near q=-m/n surfaces 6

  19. How the most central (most screened) harmonics n=-4,m=10 looks like: (t=8000tA)

  20. Convective cells are formed in the ergodic zone (seen also in JOREK code E. Nardon PoP 2007)=>density transport?

  21. Initial rotation profile corresponds to ft(0)~1kHz (ITER-like). Resonant (jxB) braking is localized near q=-m/n surfaces. With NTV global braking is observed. Here ‘normal’ toroidal viscosity :m//=10-6, NTV has a calculated form (p.13) with maximummNTV,max=10-6 . It’s a bit higher (to see more rapid braking in modelling) compared to our estimations ~5.10-7 on p.13) It is not stationary profile yet! Braking continues.

  22. Here similar weak screening for m=10 with jxb resonant braking and both jxB and NTV. Vt=0; t=8000tA jxB:Vt=0.0056; t=8000tA jxB+NTV: Vt=0.0056;t=80000tA

  23. More external harmonics are less screened by rotation=> edge erdodisation. ymn q=-m/n with (Vt=0.0056) and without rotation. Total braking near q=-m/n surfaces

  24. Conclusions (from previous presentation): -Penetration time increases like ~1/resistivity. For ITER~to the top of the pedestal~1s! -Larger amplitudes are less screened by rotation. -Edge islands are much less screened than ymnon q=-m/n. -Edge is ergodised even with strong rotation( DIII-D like). -ITER rotation screens central (m<8) non-resonant ,edge is ergodised. -Non-resonant harmonics are not screened by rotation. Conclusions (from this presentation): -one row design (here 18 picture-frame coils, but it’s typical for one row designs) give large amplitudes of non-resonant harmonics in the plasma centre, notice also that they are not screened by plasma rotation. -The NTV calculated according to K. Shaing in collisionless regime gives damping time ~0.4s at r~0.4 (ITER H-mode,18pf coils, n=4); -Edge ergodisation here is weakly influenced by plasma braking, since the initial rotation was already weak. More external islands (here m>10) are less screened by rotation, since resistivity is larger and rotation is slower. However , here we are still two orders of magnitude larger resistivity on the top of the pedestal, so screening is expected to be larger. To be continued...

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