BACKGROUND

1
Design Point Studies for Future Spherical Torus
DevicesC. Neumeyer, C. Kessel, P. Rutherford, M.
PengPrinceton University Plasma Physics
Laboratory, Oak Ridge National Laboratory
Work Supported by US DOE Contract No.
DE-AC02-76CHO-3073
BACKGROUND
TF COIL
BEAM-TARGET FUSION

• System Code Studies performed for Next Step ST
• FORTRAN Physics algorithms developed by S.
  Jardin, C. Kessel et al
• Engineering algorithms developed specifically for
  LN2 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 -gt NSST -gt CTF -gt DEMO -gt
  REACTOR

TF Inner Leg geometry set by plasma geometry

• 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
• Qb-Egt400keV Qb-E400keV400/ Eb

TF Return Leg geometry set by shielding
considerations
SOL and gap 0.10m First wall 0.05m Blanket 0.5m S
hield 0.7m Gap 0.1m
Dimensions similar to those used for ARIES-ST,
sufficient to handle 7.5MW/m2 neutron flux on the
outboard midplane
Neutral Beam Driven Tokamak Fusion Reactors,
D. Jassby, Nuclear Fusion 17, 309 (1977)
Systems Analysis of a Compact Next Step Burning
Plasma Experiment, S Jardin et al, Fusion
Science and Technology, Vol. 43, March 2003

• INNER LEG ASSUMPTIONS
• Glidcop AL-25 material, ?87 IACS
• Flaring set to 60o w.r.t. horizontal starting at
  90 of the plasma height
• Water inlet temperature 35oC, flow velocity of
  10m/s
• Ohmic dissipation plus nuclear heating
• Limits on copper and water temperature set at
  150oC
• 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

PHYSICS LIMITS AND ASSUMPTIONS
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
ENERGY CONFINEMENT

• Two versions of the energy confinement time are
  used
• neoclassical
• ITER 98y,2 scaling
• For TiTe case ITER 98y,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

PRESSURE CALCULATIONS
Wong
Lin-Liu

• ??bN 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

POWER BALANCE

• Power balance equates net input power to stored
  energy/confinement time
• Toggle is provided to select whether TiTe or
  not. For Ti ? Te
• Expressions were supplied by Rutherford for
  partitioning of alpha and auxiliary power to the
  ions and electrons, and power flow between ions
  and electrons Pie

Average
0.7
Scaling used herein
Variable Menard Wong Lin-Liu
Max kappa(A) 1.461554.13281? -2.57812?21.41016?3 1.0822.747/A
Min qcyl(A) -0.11547914.5293? -27.4492?2 18.334?3 2.050.348A
Peakfactor ?(1-(x)2)alpha_T (1-(x)2)alpha_ndx-1 (xr/a) ?(1-(x)2)alpha_T (1-(x)2)alpha_ndx-1 (xr/a)
Max Beta_N(A) (6.96436-14.043? 45.5?2 -31.3086?3)/100 (3.093.35/A 3.87/A0.5) (?/3)0.5/ peakfactor0.5 (-0.77481.2869?-0.2921??20.0197?3) /(TANH((1.8524 0.2319?)/A0.6163)) A0.5523/10
kbs 0.3440.195A 0.67830.0446/A
fbs kbsBeta_P peakfactor0.25/A0.5 kbsBeta_P peakfactor0.25/A0.5
BOOTSTRAP CURRENT DRIVE

• kBS per physics assumption
• Assume NBI current drive (NINB if E gt 120keV)
• Set beam energy based on calculations by
  Mikkelsen showing that required
• beam energy for parabolic deposition profiles
  with tangential injection at R0
• can be approximated by...
• Eb 100 ltne-20gt Lb
• where...
• Lb (R0 a)2 R021/2

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 PSOL 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/m2
• Allowable peak heat flux at first wall 1.0
  MW/m2

PLASMA GEOMETRY

• Plasma cross sectional shape for 95 flux
  surface is described by...
• R0 major radius (m) ?? elongation
• a minor radius (m) ?? triangularity
• A aspect ratio R0 /a ?? poloidal angle

• Efficiency parameter is defined as follows....
• Data for current drive efficiency from Start and
  Cordey was curve fit...
• Current to be driven is Ip(1-fBS), and the
  power (MW) requirement is...
• Solution is constrained in such a way that
  ?CD ?CDmax and PCD   Paux

?CDMAX efficiency in units 1020Ampere/Watt-m2 n2
0 electron density in units 1020Ampere/Watt-m2 I
CD current to be driven in MA PCD current
drive power in MW

• We define A100 and a100 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

Eb neutral beam energy Tavg average electron
temperature
NEUTRON WALL LOADING

• The fraction of neutrons incident on the narrow
  midplane region of the center stack is estimated
  based on line-of-sight considerations

• Assume parabolic profiles raised to a power
  for.
• density aN
• temperature aT (option for separate ion and
  electron profiles)
• NBI power deposition aNBI

D. Start, J. Cordey, Beam Induced Currents in
Toroidal Plasmas of Arbitrary Aspect Ratio,
Phys. Fluids, 23, 1477 (1980)
FUSION POWER CALCULATIONS

• 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
• Apfs Wdiv AdivWcs Acs Wcyl Acyl
• With the weighting functions established, the
  equation for normalized neutron flux to the
  outboard region as a function of z is
• nob(z) Wcyl 1.4318(1-z/1.016)

Ip CALCULATION

• thermal ion and beam-target fusion power are
  integrated over the plasma volume
• Alpha power due to thermal ions in a 5050 D-T
  mix is
• a0 -23.836 a -22.712 a1 -0.09393 a2
  7.994e-4 a3 -3.144e-6
• and.
• where fT is the tritium fraction

• ??? set to maximum allowable
• qcyl chosen by solver subject to minimum
  allowable
• Bt varied by solver, subject to engineering
  constraints