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Y.K.M. Peng 1,2 , A. Ishida 3 , Y. Takase 2 , A. Ejiri 2 , N. Tsujii 2 ,

Two-Fluid Equilibrium Considerations of T e /T i >> 1, Collisionless ST Plasmas Sustained by RF Electron Heating. Y.K.M. Peng 1,2 , A. Ishida 3 , Y. Takase 2 , A. Ejiri 2 , N. Tsujii 2 , T . Maekawa 4 , M. Uchida 4 , H. Zushi 5 , K. Hanada 5 , M. Hasegawa 5

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Y.K.M. Peng 1,2 , A. Ishida 3 , Y. Takase 2 , A. Ejiri 2 , N. Tsujii 2 ,

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  1. Two-Fluid Equilibrium Considerations of Te/Ti >> 1, Collisionless ST Plasmas Sustained by RF Electron Heating Y.K.M. Peng1,2, A. Ishida3, Y. Takase2, A. Ejiri2, N. Tsujii2, T. Maekawa4, M. Uchida4, H. Zushi5, K. Hanada5, M. Hasegawa5 1Oak Ridge National Laboratory, UT-Battelle, USA 2The University of Tokyo, Japan 3Nishi-Ku, Niigata City, Japan 4Kyoto University, Japan 5Kyushu University, Japan The Second A3 Foresight Workshop on Spherical Torus January 6 - 8, 2014 Tsinghua University, Beijing, PRC 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  2. Two-fluid equilibria approximating RF-driven ST plasmas in TST-2 are calculated for the first time Motivation: to calculate equilibrium for an apparently new ST plasma regime (TST-2, LATE, QUEST, MAST) • Understand the electron and ion fluid force balance properties • Provide a basis for orbit, stability, transport, current drive, and boundary studies Topics: • Experimental indications of interest • 2-fluid equilibrium model reduced from first principles • TST-2 experimental conditions to constrain choices • Initial results for TST-2 like plasmas • Improvements in calculations & suggested measurements • Equilibrium calculations for other ST’s and RF’s 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  3. RF-only-driven, inboard-limited ST plasmas in TST-2, LATE, and QUEST share many special features • LCFS (----) far within J boundary • Region of low density (1016-17 m-3) orbit-confined energetic electrons (100 – 500 keV) • Within LCFS: lower Ti (10 – 50 eV) and Te (50 – 300 eV), collisionless plasmas of modest densities (up to several 1018m-3) • Copious keV-level ion or neutral impact sites on tungsten coupons on wall (QUEST) • High current drive efficiency (0.1 – 0.4 A/W); ~1 A/W on MAST LATE example 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  4. Faster loss of energetic electrons than ions would lead to positive plasma potential and substantial ion flow • Faster loss of electrons than ions • Positive “ambipolar” plasma potential • Sufficiently large radial electric field  ion toroidal flow (Er x Bp) •  Substantial centrifugal and electrostatic forces on ions • For massless electrons of higher Te, -pe=JxB force balance largely retained Different electron and ion fluid force balance conditions, i.e., two-fluid equilibrium LATE example 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  5. These conditions cause Hall-MHD and one-fluid MHD approximations to lose accuracy 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  6. Second order partial differential and algebraic equations of six functionals of poloidal flux are solved • Start with continuity, force balance, and Ampere’s law • Transform in axisymmetric configuration to two 2nd order partial differential equations and six algebraic equations • Six functionals: Te, Ti, Fi(ion energy), Fe2(electron energy), K (toroidal magnetic flux), and i (ion poloidal momentum) as functions of  and canonical angular momentum Yi() [Phys. Plasmas 17 (2010) 122507; Phys. Plasmas 19 (2012) 102512] • Finite-differencing method combined with successive over relaxation (SOR) in progressive multi-grid convergence • In this work, free-boundary solutions are calculated within a numerical boundary that encloses no coil currents 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  7. TST-2 Experiment plasma conditions (shot #75467 @ 60ms) and device constraints Data: • Bt = 1.26 kG, Ip = 10 kA • Te ~ 300 eV, Ti ~ 10’s eV • ne ~ 8 x 1017/m3 • Inboard and outboard limiters •  values on numerical boundary interpolated from EFIT that uses flux loop data and modeled vessel eddy current Assumptions • Ilcfs ~ 0.6 Ip • Centrally peaked plasma profiles Obtain: • LCFS with elongation = 1.23 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  8. Relatively simple profile functions are chosen through trial and error - expressions (ion poloidal momentum) where 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  9. Relatively simple profile functions are chosen through trial and error – plots & toroidal current density Fe(X) K(X) 10*Fi(X) 10*Ti(X) 10*Ti(X) 10*Fi(X) Te(X) Fe(X) K(X) • Toroidal current density is set to zero at and beyond the outboard limiter 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  10. Initial result: poloidal magnetic flux and toroidalplasma current density • LCFS occupies a small area in the vessel cross section (?) • Jt distributed to the last flux surface defined by outer limiter (?) • Jt peak located within LCFS and outboard of magnetic axis (?) • Ilcfs = 0.59 Ip (?) • Iz ~ 0.05 Ip on midplane (?) (?) indicates largely arbitrary assumptions R Z Z R 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  11. Initial result: electron density and temperature • Electron density and temperature peaks located within LCFS and outboard of magnetic axis (?) • Larger fraction of plasma contained within LCFS • Finite ne and Te along the inboard numerical boundary (?) R Z Z R 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  12. Initial result: electrostatic potential, Ti, toroidalelectron and ion flow • Plasma potential largely confined within LCFS, with peak located outboard of magnetic axis • Plasma potential drop = 14 V (?) • Ti max = 10 eV, peak located at outboard edge of LCFS (?) • Ion flow in co-current direction (?) R Z 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  13. Initial result: plasma pressure, toroidal current density, Mach numbers, radial electric field, and electron & ion force balance • Plasma pressure max ~40 Pa (?) • Peaked toroidal current distribution (?) • What is plasma sound speed? • Large Er shear  ion orbit compression • Electron: largely satisfies pe = -JxB • Ion (outboard): roughly equal pi, centrifugal, and electrostatic forces balanced by -JxB 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  14. Areas of improvement and suggested measurements to further restrain assumed input functions Improvements: • More refined profile function to produce different plasma parameters in and out of the LCFS • Improve numerical convergence for ion force balance (fig. 6b) • Longer term: include gyrokinetic effects of energetic electrons Measurements suggested: • Shape and location of LCFS • Currents leaving plasma along open field lines • Plasma ne, Te, Jt profile information, including along inboard plasma boundary • Plasma potential, Ti, and ion flow velocity • Ion Mach number in two-Te plasma [Jones, PRL 35 (1975) 1349] 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

  15. Next work: comparison between different waves, ECW harmonics, and ST devices Different waves and harmonics: • Plasmas driven by EBW, ECW, LHW, and ICFW (on TST-2) • Multi-frequency and multi-harmonic heating of electrons (TST-2, LATE, QUEST) Different ST and vessels: • LATE: rectangular cross section, metal wall, perpendicular ECW launch with limited polarization control, up to 20 kA driven • QUEST: limiter and divertor configurations, metal wall, multiple ECW frequencies and harmonics, up to 65 kA driven • MAST: limiter and divertor configurations, graphite wall, 28 GHz (2nd harmonic), up to 75 kA driven with inboard X-mode launch 2nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

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