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 1 Oak Ridge National Laboratory, UT-Battelle, USA 2 The University of Tokyo, Japan 3 Nishi-Ku, Niigata City, Japan 4 Kyoto University, Japan 5 Kyushu University, Japan The Second A3 Foresight Workshop on Spherical Torus January 6 - 8, 2014 Tsinghua University, Beijing, PRC 1 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

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 2 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

RF-only-driven, inboard-limited ST plasmas in TST-2, LATE, and QUEST share many special features 3 LCFS (----) far within J boundary Region of low density ( m -3 ) orbit-confined energetic electrons (100 – 500 keV) Within LCFS: lower T i (10 – 50 eV) and T e (50 – 300 eV), collisionless plasmas of modest densities (up to several m -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 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

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

Second order partial differential and algebraic equations of six functionals of poloidal flux are solved 6 Start with continuity, force balance, and Ampere’s law Transform in axisymmetric configuration to two 2 nd order partial differential equations and six algebraic equations Six functionals: T e, T i, F i (ion energy), F e2 (electron energy), K (toroidal magnetic flux), and  i (ion poloidal momentum) as functions of  and canonical angular momentum Y i (  ) [Phys. Plasmas 17 (2010) ; Phys. Plasmas 19 (2012) ] 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 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

TST-2 Experiment plasma conditions (shot 60ms) and device constraints 7 Data: B t = 1.26 kG, I p = 10 kA T e ~ 300 eV, T i ~ 10’s eV n e ~ 8 x /m 3 Inboard and outboard limiters  values on numerical boundary interpolated from EFIT that uses flux loop data and modeled vessel eddy current Assumptions I lcfs ~ 0.6 I p Centrally peaked plasma profiles Obtain: LCFS with elongation = nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

Relatively simple profile functions are chosen through trial and error - expressions 8 (ion poloidal momentum) where CTe0CTe1CTe2CTe3CTe4CTe CTi0CTi1CTi2CTi3CTi4CTi CFi0CFi1CFi2CFi3CFi4CFi CFe0CFe1CFe2CFe3CFe4CFe CFe6CFe7CFe8CFe9CFe CK0CK1CK2CK3CK4CK nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

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

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

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

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

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

Areas of improvement and suggested measurements to further restrain assumed input functions 14 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 n e, T e, J t profile information, including along inboard plasma boundary Plasma potential, T i, and ion flow velocity Ion Mach number in two-T e plasma [Jones, PRL 35 (1975) 1349] 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma

Next work: comparison between different waves, ECW harmonics, and ST devices 15 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 (2 nd harmonic), up to 75 kA driven with inboard X-mode launch 2 nd A3 STWS – 2-fluid equilibrium considerations for Te/Ti >> 1 ST plasma