1. BACKGROUND Design Point Studies for Future Spherical Torus Devices Design Point Studies for Future Spherical Torus Devices C. Neumeyer, C. Kessel, P. Rutherford, M. Peng † Princeton University Plasma Physics Laboratory, † Oak Ridge National Laboratory System Code Studies* performed for Next Step ST FORTRAN Physics algorithms developed by S. Jardin, C. Kessel et al Engineering algorithms developed specifically for LN 2 cooled ST Began using EXCEL as algorithm development tool Developed stand-alone System Code using EXCEL Uses built-in SOLVER non-linear optimization code Performed Design Point Studies for a Component Test Facility (CTF) Continued to improve System Code with M Peng and P Rutherford Now Studying Range of Design Points along ST Development Path Provide Linkage NSTX -> NSST -> CTF -> DEMO -> REACTOR *Systems Analysis of a Compact Next Step Burning Plasma Experiment, S Jardin et al, Fusion Science and Technology, Vol. 43, March 2003 PHYSICS LIMITS AND ASSUMPTIONS Wong Average Lin-Liu 0.7 = Scaling used herein 1) J. Menard, et al,"Unified Ideal Stability Limits for Advanced Tokamak and Spherical Torus Plasmas" PPPL Report PPPL-3779, by J.E. Menard, et al. 2) C. Wong, J. Wesley, R. Stambaugh, E. Cheng, “Toroidal Reactor Designs as a Function of Aspect Ratio and Elongation”, Nuclear Fusion, 42 (2002) 547-556 3) Y. Lin-Liu and R. Stambaugh, “Optimum Plasma States for Next Step Tokamaks”, GA Report GA-A23980, 11/02 VariableMenardWongLin-Liu Max kappa(A) 1.46155+4.13281  -2.57812  2 +1.41016  3 1.082+2.747/A Min qcyl(A) -0.115479+14.5293  -27.4492  2 +18.334  3 2.05+0.348*A Peakfactor[∫(1-(x) 2 ) alpha_T (1-(x) 2 ) alpha_n dx] -1 (x=r/a) [∫(1-(x) 2 ) alpha_T (1-(x) 2 ) alpha_n dx] -1 (x=r/a) Max Beta_N(A) (6.96436-14.043  +45.5  2 -31.3086  3 )/100 (3.09+3.35/A+ 3.87/A 0.5 ) *(  /3) 0.5 / peakfactor 0.5 (-0.7748+1.2869  - 0.2921  2 +0.0197  3 ) /(TANH((1.8524 +0.2319  )/A 0.6163 )) A 0.5523 /10 kbs0.344+0.195*A0.6783+0.0446/A fbskbs*Beta_P* peakfactor 0.25 /A 0.5 kbs*Beta_P* peakfactor 0.25 /A 0.5 PLASMA GEOMETRY Plasma cross sectional shape for 95% flux surface is described by... R 0 = major radius (m)  = elongation a = minor radius (m)  = triangularity A = aspect ratio = R 0 /a  = poloidal angle We define A 100 and a 100 geometric quantities related to the 100% flux surfaces to determine the vacuum vessel geometry based on a linear fit to some sample equilibria by Kessel… Assume parabolic profiles raised to a power for…. -density  N -temperature  T (option for separate ion and electron profiles) -NBI power deposition  NBI  set to maximum allowable q cyl chosen by solver subject to minimum allowable B t varied by solver, subject to engineering constraints Ip CALCULATION TF COIL INNER LEG ASSUMPTIONS Glidcop AL-25 material,  =87% IACS Flaring set to 60 o w.r.t. horizontal starting at 90% of the plasma height Water inlet temperature 35 o C, flow velocity of 10m/s Ohmic dissipation plus nuclear heating Limits on copper and water temperature set at 150 o C VonMises stresses estimated w/factor of 2 accounting for cooling passages Inner leg stress limited to 100MPa OUTER LEG ASSUMPTIONS TF current is assumed to be returned through an Al outer shell thickness of horizontal sections typically 1.0m thickness of vertical section typically 0.75m SOL and gap0.10m First wall0.05m Blanket0.5m Shield 0.7m Gap0.1m TF Inner Leg geometry set by plasma geometry… TF Return Leg geometry set by shielding considerations… Dimensions similar to those used for ARIES-ST, sufficient to handle 7.5MW/m 2 neutron flux on the outboard midplane  N subject to physics limit Toggle provided for selection between combined ion-electron (global) or separate ion and electron confinement and loss channels Pressure from fast ions is included PRESSURE CALCULATIONS k BS per physics assumption Assume NBI current drive (NINB if E > 120keV) Set beam energy based on calculations by Mikkelsen showing that required beam energy for parabolic deposition profiles with tangential injection at R 0 can be approximated by... E b = 100 L b where... L b = [(R 0 + a) 2 – R 0 2 ] 1/2 BOOTSTRAP & CURRENT DRIVE Efficiency parameter is defined as follows.... Data for current drive efficiency from Start and Cordey* was curve fit... Current to be driven is I p *(1-f BS ), and the power (MW) requirement is... Solution is constrained in such a way that  CD ≤  CDmax and P CD ≤ P aux  CDMAX = efficiency in units 10 20 Ampere/Watt-m 2 n 20 = electron density in units 10 20 Ampere/Watt-m 2 I CD = current to be driven in MA P CD = current drive power in MW E b = neutral beam energyT avg = average electron temperature *D. Start, J. Cordey, “Beam Induced Currents in Toroidal Plasmas of Arbitrary Aspect Ratio”, Phys. Fluids, 23, 1477 (1980) FUSION POWER CALCULATIONS “thermal” ion and beam-target fusion power are integrated over the plasma volume Alpha power due to “thermal” ions in a 50:50 D-T mix is … a 0 = -23.836a * = -22.712a 1 = -0.09393a 2 = 7.994e-4a 3 = -3.144e-6 and…. …where f T is the tritium fraction Curve fits to 400keV were generated to match data from Jassby* To extend the results out to 1MeV it was assumed based on suggestions from Mikkelsen that Q should follow 1/E dependence… Q b-E>400keV = Q b-E=400keV *400/ E b *“Neutral Beam Driven Tokamak Fusion Reactors”, D. Jassby, Nuclear Fusion 17, 309 (1977) BEAM-TARGET FUSION Two versions of the energy confinement time are used neoclassical ITER 98[y,2] scaling For T i =T e case ITER 98[y,2] scaling is used globally for the ions and electrons For Ti  Te the ion confinement assumed neoclassical and electrons per ITER 98 “HH” enhancement multipliers allow variation above or below the scaling laws ENERGY CONFINEMENT Power balance equates net input power to stored energy/confinement time… Toggle is provided to select whether T i =T e or not. For T i  T e … Expressions were supplied by Rutherford for partitioning of alpha and auxiliary power to the ions and electrons, and power flow between ions and electrons P ie POWER BALANCE HEAT LOADS The power in the scrape-off layer is… Double null divertor geometry is assumed Models were developed by Kessel for flux expansion as a function of A which are used to relate P SOL to the peak divertor heat flux Solver equations adjust the radiation fraction at the divertor and enhanced core radiation to suit the allowable peak heat flux on the divertor and first wall The following constraints are typically applied… Allowable peak heat flux at divertor = 15.0 MW/m 2 Allowable peak heat flux at first wall = 1.0 MW/m 2 The fraction of neutrons incident on the narrow midplane region of the center stack is estimated based on line-of-sight considerations… NEUTRON WALL LOADING Data was supplied by El Guebaly fo n flux distribution on a cylindrical blanket extending up to the plasma height  *a, based on ARIES-ST work Weighting functions were developed which relate the peak to machine average flux on the center stack, divertor, and cylindrical blanket surfaces A pfs = W div * A div +W cs * A cs + W cyl * A cyl With the weighting functions established, the equation for normalized neutron flux to the outboard region as a function of z is… n ob (z)= W cyl *1.4318*(1-z/1.016) *Work Supported by US DOE Contract No. DE-AC02-76CHO-3073