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The impact of rotation and anisotropy due to NBI energetic particles in toroidal magnetic confinement

The impact of rotation and anisotropy due to NBI energetic particles in toroidal magnetic confinement. M. J. Hole 1 , M. Fitzgerald 1 , G. von Nessi 1 , K. G. McClements 2 , J. Svensson 3 , R. Kemp 2 , L. C. Appel 2 , I. Chapman 2 , N. Walkden 4. Acknowledgement: R. Andre, PPPL, USA.

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The impact of rotation and anisotropy due to NBI energetic particles in toroidal magnetic confinement

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  1. The impact of rotation and anisotropy due to NBI energetic particles in toroidal magnetic confinement M. J. Hole1, M. Fitzgerald1, G. von Nessi1, K. G. McClements2, J. Svensson3, R. Kemp2, L. C. Appel2, I. Chapman2, N. Walkden4 Acknowledgement: R. Andre, PPPL, USA 1Res. School of Physics and Engineering, Australian National University, ACT Australia. 2EURATOM/CCFE Fusion Assoc., Culham Science Centre,Abingdon, Oxon OX14 3DB, UK 3 Max Planck Institute for Plasma Physics, Teilinstitut Greifswald, Germany 4University of Bath, Bath, UK, BA2 7AY 18th International StellaratorHeliotron Workshop & 10th Asia Pacific Plasma Theory Conference 29th January – 3rd February 2012

  2. Outline Rotation (toroidal and poloidal), anisotropy Axis-symmetric equilibrium Show large anisotropy for MAST (#18696), p/p|| = 1.7 Impact of anisotropy on stability through changes in q profile Implications on CAE, TAE mode frequencies for MAST #18696 Anisotropy / flow implications for Component Test Facility (CTF) Preliminary assessment of impact of flow, anisotropy on CTF Probabilistic (Bayesian) inference framework Provides model validation (equilibrium and mode structure) Harnessed to infer properties of plasma (e.g. energetic particle pressure) Toroidal field ripple: impact on injected beams Test particle simulations in presence of toroidal field ripple. Compute diffusivity due to field ripple KSTAR wave activity during RF and NBI heated discharges

  3. MHD with rotation & anisotropy • Inclusion of anisotropy and flow in equilibrium MHD equations [R. Iacono, et al Phys. Fluids B 2 (8). 1990]

  4. MHD with rotation & anisotropy • Inclusion of anisotropy and flow in equilibrium MHD equations [R. Iacono, et al Phys. Fluids B 2 (8). 1990] • Frozen flux gives velocity: Equilibrium eqn becomes: Set of 6 profile constraints

  5. Reduction to isotropic • Suppose Then and equilibrium eqn becomes: Set of 5 profile constraints

  6. Further reduction • Toroidal flow only Set of 4 profile constraints

  7. Further reduction • Toroidal flow only Set of 4 profile constraints • Static case Set of 2 profile constraints

  8. Rotation effects can be large for the ST • Expression for n(,R) in presence of flows. Centrifugal density shift

  9. Rotation effects can be large for the ST • Expression for n(,R) in presence of flows. Centrifugal density shift • “transonic” poloidal flows (~ sound speed csB/B)  G-S & Bernoulli eqns hyperbolicin part of solution domain  radial contact discontinuities where MHD fails • Two types of closure: • isentropic flux surfaces: () = p/ • isothermal flux surfaces: T() For isothermal flux surfaces, McClements & Hole show poloidal flow hyperbolicity threshold of G-S equation [PoP17, 082509] • lower for isothermal (cf isentropic) flux surfaces • lower for high performance ST plasmas, Ms0.7

  10. Expected impact of anisotropy • Small angle b between beam, field  p|| > p⊥ • Beam orthogonal to field, b=/2  p⊥ >p|| • If p||sig. enhanced by beam, p||surfaces distorted and displaced inward relative to flux surfaces Broad pressure profile Peaked pressure profile [Cooper et al, Nuc. Fus. 20(8), 1980] • If p⊥ > p||, an increase will occur in centrifugal shift : [R. Iacono, A. Bondeson, F. Troyon, and R. Gruber, Phys. Fluids B 2 (8). August 1990] • Compute p⊥ and p||, from moments of distribution function, computed by TRANSP Parallel pressure contours(solid) Flux surfaces (dashed) [M J Hole, G von Nessi, M Fitzgerald, K G McClements, J Svensson, PPCF 53 (2011) 074021] • Infer p⊥ from diamagnetic current J⊥ [see V. Pustovitov, PPCF 52 065001, 2010 and references therein]

  11. Anisotropy on MAST Magnetics • MAST #18696 • 1.9MW NB heating • Ip = 0.7MA, n=2.5 • TRANSP simulation available • Magnetics shows CAEs [M.P. Gryaznevich et al, Nuc. Fus. 48, 084003, 2008.; Lilley et al35th EPS Conf. Plas.Phys. 9 - 13 June 2008 ECA Vol.32D, P-1.057] • What is the impact on q profile due to presence of anisotropy and flow?

  12. pll, p, flow from f(E,) moments See Fitzgerald S13.4 r/a=0.25 [35th EPS 2008; M.K.Lilley et al] p⊥/p|| ≈ 1.7  = toroidal flux [M J Hole, G von Nessi, M Fitzgerald, K G McClements and J Svensson, PPCF 53 (2011) 074021]

  13. Impact of anisotropy on equilibrium • Impact on configuration computed using FLOW [Guazzotto L, Betti R, Manickam J and Kaye S 2004 PoP11 604–14]  <0: p⊥/p|| ≈ 1.7  =0: p⊥/p|| = 1

  14. Impact of anisotropy on equilibrium • Impact on configuration computed using FLOW [Guazzotto L, Betti R, Manickam J and Kaye S 2004 PoP11 604–14]  <0: p⊥/p|| ≈ 1.7  =0: p⊥/p|| = 1 • Toroidal rotation does not change q appreciably with MA,φ 0.3 • Increase in q0 ~ 100% for case with anisotropy Low grid resolution of FLOW at core

  15. Impact of anisotropy on wave modes • How do predicted mode frequencies change due to changes in q produced by anisotropy and flow? n=-10 n=4 Adjacent n Doppler shift

  16. Frequency scaling with/without anisotropy TAE eigenfrequency [Cheng, Liu & Chance. Annals of Physics 161. 21 (1985)] Illustration TAE static equil. TAE flowing, anisotropic equil.

  17. Frequency scaling with/without anisotropy CAE eigenfrequency TAE eigenfrequency [Cheng, Liu & Chance. Annals of Physics 161. 21 (1985)] [Smith et al PoP 10(5),1437-1442,2003] Illustration Known: R0= major radius,  = ellipticity, n=-10 Inferred: p= poloidal mode no. = |n|qmn Unknown: s= radial mode no. = 0 (guess) 0= radial localisation of mode ~ a/2 (guess) TAE static equil. TAE flowing, anisotropic equil.

  18. Frequency scaling with/without anisotropy CAE eigenfrequency TAE eigenfrequency [Cheng, Liu & Chance. Annals of Physics 161. 21 (1985)] [Smith et al PoP 10(5),1437-1442,2003] Illustration aliased Known: R0= major radius,  = ellipticity, n=-10 Inferred: p= poloidal mode no. = |n|qmn Unknown: s= radial mode no. = 0 (guess) 0= radial localisation of mode ~ a/2 (guess) Static, isotropic equilibrium: qmn(R=R0+a/2 ) =1.3  p=13 TAE static equil. TAE flowing, anisotropic equil.

  19. Frequency scaling with/without anisotropy CAE eigenfrequency TAE eigenfrequency [Cheng, Liu & Chance. Annals of Physics 161. 21 (1985)] [Smith et al PoP 10(5),1437-1442,2003] Illustration aliased Known: R0= major radius,  = ellipticity, n=-10 Inferred: p= poloidal mode no. = |n|qmn Unknown: s= radial mode no. = 0 (guess) 0= radial localisation of mode ~ a/2 (guess) aliased Static, isotropic equilibrium: qmn(R=R0+a/2 ) =1.3  p=13 Flowing, anisotropic equilibrium: qmn(R=R0+a/2 ) =1.3  p=15. TAE static equil. TAE flowing, anisotropic equil.

  20. Outline Rotation (toroidal and poloidal), anisotropy Axis-symmetric equilibrium Show large anisotropy for MAST (#18696), p/p|| = 1.7 Stability: ideal (static) MHD – due to changes in equilibrium, Implications on CAE, TAE mode frequencies for MAST #18696 Anisotropy / flow implications for Component Test Facility (CTF) Preliminary assessment of impact of flow, anisotropy on CTF Exploiting probabilistic (Bayesian) inference framework Enables model validation (equilibrium and mode structure) Harnessed to infer properties of plasma (e.g. energetic particle pressure) Toroidal field ripple: impact on injected beams Test particle simulations in presence of toroidal field ripple. Compute diffusivity due to field ripple KSTAR wave activity during RF and NBI heated discharges

  21. Component Test Facility • CTF requirements [Abdou et al Fus. Techn. 29(1), 1996] • neutron power flux ~1-2 MW/m2, steady state, test area> 10m2, B>2T, neutron flux> 6MWm2/yr • stable steady state ST can provide fusion conditions necessary for components testing • operated in parallel with DEMO  complement and extend the anticipated database from IFMIF [G.M. Voss et al. / Fusion Engineering and Design 83 (2008) 1648–1653 • MHD stability without flow: • n = 1, 2, 3 stable if q0 > 2.1 • n = 1 external kink stable if Rw/a < 2.2 • [Hole et al Plasma Phys. Control. Fusion 52 (2010)]

  22. CTF base-line [Cottrell& Kemp, Nuc. Fus. 49 (2009) 042001; Voss. et al. Fus. Eng. Des. 83 (2008) 1648–1653]

  23. CTF Equilibrium NBI projections - top q02.17 NBI projections – pol. plane Ballooning mode threshold [Holeet al Plasma Phys. Control. Fusion 52 (2010)] • Rotation profile predicted using = 0.5i [G.A. Cottrell and R. Kemp, Nucl. Fusion 49 (2009) 042001.]

  24. CTF has weak anisotropy Beams heat off-axis plasma No significant anisotropy p⊥~ p|| P (kPa) P (kPa) R2: on-axis R1: off-axis, 30 p⊥> p|| p⊥< p|| 0 s 1 0 s 1 If beams turned off independently ... parallel perpendicular P (kPa) R1: off-axis, 30 R2: on-axis, horizontal R3: off-axis, horizontal n (m-3) s 0 s 0 1 1

  25. ...but strong rotation, which lowers q0 static equilibrium flowing equilibrium R /cs [Chapman et al, sub PPCF, 2011] s • flow-stabilised to ideal MHD modes for weak flow (MA<0.10) , but unstable to Kelvin-Helmholtz at large flow (MA>0.17). • eigenfunction peak at position of strongest rotation gradient N. R. Walkden, I. T. Chapman

  26. Outline Rotation (toroidal and poloidal), anisotropy Axis-symmetric equilibrium Show large anisotropy for MAST (#18696), p/p|| = 1.7 Stability: ideal (static) MHD – due to changes in equilibrium, Implications on CAE, TAE mode frequencies for MAST #18696 Compute anisotropy for Component Test Facility (CTF) Preliminary assessment of impact of flow, anisotropy on CTF stability Probabilistic (Bayesian) inference framework Provides model validation (equilibrium and mode structure) Harnessed to infer properties of plasma (e.g. energetic particle pressure) Toroidalfield ripple: impact on injected beams Test particle simulations in presence of toroidal field ripple. Compute diffusivity due to field ripple KSTAR wave activity during RF and NBI heated discharges

  27. Inference of energetic physics • ANU/CCFE/IPP developed a probabilistic framework based on Bayes’ theorem for validating models for equil. & mode structure • Motivation: • handle data from multiple diagnostics with strong model dependency • provides a validation framework for different equilibrium models: e.g. Two fluid with rotation, multi-fluid, MHD with anisotropy • yield uncertainties in inferred physics parameters (e.g. q profile) from models, data, and their uncertainties. • Can be inverted : By reducing force-balance model uncertainty to zero, use as a technique to infer physics difficult to experimentally diagnose directly (e.g. Energetic particle pressure)

  28. Bayesian equilibrium modelling Pick-up coils Flux loops TS spectra CXRS spectra MSE signals • Aims • Improve equilibrium reconstruction • Validate different physics models • Two fluid with rotation • [McClements & Thyagaraja Mon. Not. R. Astron. Soc. 323 733–42 2001] • Ideal MHD fluid with rotation • [Guazzotto L et al, Phys. Plasmas 11 604–14, 2004] • Energetic particle resolved multiple-fluid • [Hole & Dennis, PPCF 51 035014, 2003] • (3) Infer poorly diagnosed physics parameters see S10.1 Oliver Ford S12.5 Greg von Nessi

  29. Mean in posterior gives flux surfaces Current Tomography Poloidal flux surfaces • MAST #24600 @280ms • D plasma, 3MW NB heating • Ip = 0.8MA, n=3 Last closed flux surface of MSE& EFIT J and  surfaces plotted for currents corresponding to the maximum of the posterior [M.J. Hole, G. von Nessi, J. Svensson, L.C. Appel, Nucl. Fusion 51 (2011) 103005]

  30. Sampling of posterior gives distribution • Distributions generated by sampling, e.g. q profile No poloidal currents q profile #24600 Inference of poloidal currents: allow f() to be a 4th-order polynomial in  Errors < 5%, but are model dependant • Bayesian models for TS and CXRS

  31. Integrate force balance yields Penergetic Equilibrium Validation: MAST #24600 @280ms Uses MSE, pick up coils, flux loops Uses TS, CXRS Integrate residue Penergetic estimate MSE data range

  32. Outline Rotation (toroidal and poloidal), anisotropy Axis-symmetric equilibrium Show large anisotropy for MAST (#18696), p/p|| = 1.7 Stability: ideal (static) MHD – due to changes in equilibrium, Implications on CAE, TAE mode frequencies for MAST #18696 Compute anisotropy for Component Test Facility (CTF) Preliminary assessment of impact of flow, anisotropy on CTF stability Exploiting probabilistic (Bayesian) inference framework Enables model validation (equilibrium and mode structure) Harnessed to infer properties of plasma (e.g. energetic particle pressure) Toroidal field ripple: impact on injected beams Test particle simulations in presence of toroidal field ripple. Compute diffusivity due to field ripple KSTAR wave activity during RF and NBI heated discharges

  33. Toroidal field ripple on beam confinement [K. G. McClements, M. J. Hole, to be sub. PoP. ] Motivation: anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked to match the experimentally observed neutron rate and stored energy [M. Turnyanskiyet alNucl. Fusion 49, 065002 (2009).]

  34. Toroidal field ripple on beam confinement [K. G. McClements, M. J. Hole, to be sub. PoP. ] Motivation: anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked to match the experimentally observed neutron rate and stored energy [M. Turnyanskiyet alNucl. Fusion 49, 065002 (2009).] Possible sources of anomalous fast ion diffusion: MHD activity, turbulence or toroidal ripple

  35. Toroidal field ripple on beam confinement [K. G. McClements, M. J. Hole, to be sub. PoP. ] • Motivation: • anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked to match the experimentally observed neutron rate and stored energy • [M. Turnyanskiyet alNucl. Fusion 49, 065002 (2009).] • Possible sources of anomalous fast ion diffusion: • MHD activity, turbulence or toroidal ripple • Strategy: • Use full orbit code CUlham Energy-conserving orBIT (CUEBIT) to quantify ripple transport of beam ions in MAST • [B. Hamilton, K. G. McClements, L. Fletcher, & A. Thyagaraja, Sol. Phys 214, 339 (2003).] • CUEBIT modified to include collisions between suprathermal test-particles (hyrdrogenic beam ions) with bulk ions and bulk electrons (both Maxwellian populations)

  36. MAST toroidal field ripple • Assume ripple perturbation to B due to N toroidal coils  • Toroidal Field coils fully vertical  • For MAST Rcoil = 2.09m N = 12, Redge ~1.45m   ~1.2%. • Comparable to maximum ripple amplitude in ITER, predicted to cause fusion -particle losses of between 2% and 20%, depending on the magnetic shear profile. • [S. V. Konovalov, E. Lamzin, K. Tobita, and Yu. Gribov, Proceedings of the 28th • EPS Conference on Controlled Fusion and Plasma Physics, edited by C. Silva, C. • Varandas and D. Campbell (European Physical Society, Petit-Lancy, 2001), Vol. • 25A, p. 613.]

  37. MAST beam confinement • Track full orbits of beam ions with -function birth distributions at energies E1=65kEv, E2=51keV, E1/2, E2/2, E1/3, E2/3. tri-atomic ions diatomic ions Field = MAST Grad-Shafranovequil. (Ip=726 kA, B0=0.43T) + vacuum ripple. beam ion birth positions Example collisionless beam ion orbit

  38. launch N0 = 28,000 test-particles, track orbits, record # particles in plasma Nb(t), with /without toroidal ripple • Particle “lost” if crosses the last closed flux surface at any point on its trajectory. Nb(t) = N0(1 − t/c) fit gives c(no ripple) = 237ms No field ripple Field ripple ~1% loss c (ripple) = 224ms

  39. launch N0 = 28,000 test-particles, track orbits, record # particles in plasma Nb(t), with /without toroidal ripple • Particle “lost” if crosses the last closed flux surface at any point on its trajectory. Nb(t) = N0(1 − t/c) fit gives c(no ripple) = 237ms No field ripple Field ripple ~1% loss c (ripple) = 224ms • Anomolous diffusivity due to ripple transport: Dbripple a2/ cripple - a2/ cno ripple~ 0.1m2s−1 below anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked in order to match observed neutron rate and stored energy.

  40. Ripple insufficient to account for fast ion transport • launch N0 = 28,000 test-particles, track orbits, record # particles in plasma Nb(t), with /without toroidal ripple • Particle “lost” if crosses the last closed flux surface at any point on its trajectory. Nb(t) = N0(1 − t/c) fit gives c(no ripple) = 237ms No field ripple Field ripple ~1% loss c (ripple) = 224ms • Anomolous diffusivity due to ripple transport: Dbripple a2/ cripple - a2/ cno ripple~ 0.1m2s−1 below anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked in order to match observed neutron rate and stored energy.

  41. Ripple insufficient to account for fast ion transport • launch N0 = 28,000 test-particles, track orbits, record # particles in plasma Nb(t), with /without toroidal ripple • Particle “lost” if crosses the last closed flux surface at any point on its trajectory. Nb(t) = N0(1 − t/c) fit gives c(no ripple) = 237ms No field ripple Field ripple ~1% loss c (ripple) = 224ms • Anomolous diffusivity due to ripple transport: Dbripple a2/ cripple - a2/ cno ripple~ 0.1m2s−1 below anomalous fast ion diffusion (Db ∼ 0.5 m2 s−1)invoked in order to match observed neutron rate and stored energy. • Redge = 1.37m; 0.3%: Redge =1.51m; 2.3% • ripple-induced power loss:

  42. Outline Rotation (toroidal and poloidal), anisotropy Axis-symmetric equilibrium Show large anisotropy for MAST (#18696), p/p|| = 1.7 Stability: ideal (static) MHD – due to changes in equilibrium, Implications on CAE, TAE mode frequencies for MAST #18696 Compute anisotropy for Component Test Facility (CTF) Preliminary assessment of impact of flow, anisotropy on CTF stability Exploiting probabilistic (Bayesian) inference framework Enables model validation (equilibrium and mode structure) Harnessed to infer properties of plasma (e.g. energetic particle pressure) Toroidal field ripple: impact on injected beams Test particle simulations in presence of toroidal field ripple. Compute diffusivity due to field ripple KSTAR wave activity during RF and NBI heated discharges

  43. KSTAR electron fishbone, BAE M. J. Hole, C. M. Ryu, M. H. Woo, J. G. Bak, J. Kim #2181 • In 2009 evidence for electron driven fishbones at ~5kHz in ECRH plasmas. #4220 • In 2010, evidence of BAE activity was observed at ~40kHz during NBI. #4220 MISHKA  BAE gap mode CSCAS continuum

  44. KSTAR aliased TAE, ion fishbone M. J. Hole, C. M. Ryu, K. Toi, M. H. Woo, J. G. Bak, J. Kim 5980 5980 5988 • (m,n)=(1,1) aliased TAE frequency 5988 • ion fishbone # 5968

  45. Summary • Anisotropy • Computed anisotropy for MAST #18696, showing p⊥/p|| ≈ 1.7 • Showed impact on equilibrium largely affects q profile. • Explored impact on plasma wave modes: CAEs and TAEs • Bayesian validation framework for equilibrium & mode structure • Provides q profile and uncertainty. • Motivation: validate equilibrium models • Exploited force balance discrepancy to infer Penerg • Toroidal field ripple: impact on full orbits of injected beams • ripple transport diffusivity below that invoked to match neutron loss, • Toroidal field ripple contributes 1% to fast ion loss. • CTF • Computed impact of flow and anisotropy on CTF: flow dominates effect • Separate work: showed A=3 CTF flow-stabilised to ideal MHD modes for weak flow, but unstable to Kelvin-Helmholtz at large flow. • KSTAR mode activity: electron, ion fishbone, BAE, TAE

  46. Ongoing work • Bayesian inference: • Parameterise Gaussian core localised pressure to infer penergertic • Use diamagnetic loop to obtain p • Add TRANSP pressure as a constraint ? • Anisotropy • EFIT with anisotropy. S13.4 Michael Fitzgerald • Analysis of wave activity in MAST, KSTAR and H-1 • P1.10 ZipingRao • “Observations of chaotic orbits in a simple 2D ripple model”.

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