Systems Analysis Development for ARIES Next Step C. E. Kessel 1, Z. Dragojlovic 2, and R. Raffrey 2 1 Princeton Plasma Physics Laboratory 2 University of California, San Diego ARIES Next Step Meeting, June 14-15, 2007, General Atomics

Outline Basic systems code flow Explanation of what is in the Engineering Module Inboard thickness examples –Inboard TF coil thickness versus B T (fixed area fraction model) –Inboard shield thickness versus N w at plasma (Laila correlation) Example of rejecting power when q peak exceeds critical value Scan showing impact of radiated power fraction in divertor Future work

Systems Code Being Developed Plasmas that satisfy power and particle balance Inboard radial build and engineering limits Top and outboard build, and costing physicsengineeringbuild out/cost Systems analysis flow Scan several plasma parameters to generate large database of physics operating points Screen physics operating points thru physics filters, engineering feasibility, and engineering filters Surviving feasible operating points are built out and costed, graphical display of parameters (COE)

Engineering Module: Physics Filters, Engineering Feasibility, and Engineering Filters Example of physics filter: P CD > P aux, reject operating point f BS > 1.0, reject operating point Determine plasma power and radiated power from core/mantle: P plas = P alpha + P aux P rad = P brem + P cycl + P line Calculate average and peak heat flux on FW: Q peak FW = P rad x f peaking / A FW Q ave FW = P rad /A FW A FW = 2  R x 2  a x √(1+  2 )/2* If Q peak FW > 1.0 MW/m 2, reject operating point Calculate power to divertor: P div = P plas - P rad P div rad = P div x f div rad P outboard cond = (P div - P div rad ) x f outboard P inboard cond = (P div - P div rad ) x f inboard

Engineering Module: Physics Filters, Engineering Feasibility, and Engineering Filters Cont’d Q peak div,out = P outboard cond / [2  (R-a/2) x f exp out x pow ] Q peak div,in = P inboard cond / [2  (R-a) x f exp in x pow ] Q peak div,rad,out = (P div rad x f div rad,out ) / [2  (R-a/2) x 2 x (a/2)] Q peak div,rad,in = (P div rad x f div rad,in ) / [2  (R-a) x 2 x (a/4)] Q peak out = Q peak div,out + Q peak div,rad,out Q peak in = Q peak div,in + Q peak div,rad,in If Q peak out or Q peak in > 20 MW/m 2, reject operating points Neutron powers: P neut = 4 x P alpha / 5 P neut2 = M blkt x P neut Electric Power: P elec =  th x [P neut2 + (P plas - P plasx )] x (1 - f pump - f subs ) - P aux /  aux If Q peak out or Q peak in > 12 MW/m 2, reject power If Q peak FW > 0.75 MW/m 2, reject power P recir = P aux /  aux +  th x [P neut2 + (P plas - P plasx )] x (f pump - f subs )

Engineering Module: Physics Filters, Engineering Feasibility, and Engineering Filters Cont’d Inboard Radial Build: (red signifies model available)  SOL,  FW,  gap1,  blkt,  gap2,  shld,  gap3,  VV,  gap4,  TF,  gap5,  BC,  gap6,  PF  shld = x ln(N w /3.26) TF coil: I TF = B T x 2  R / (  o N TF ) R TF out = R - a -  SOL -  FW -  gap1 -  blkt -  gap2 -  shld -  gap3 -  VV -  gap4 B T max =  o N TF I TF / 2  R TF out If B T max > 21 T, reject operating point J TF overall = [0.9 x  all - (B t max ) 2 / 2  o ] / [  all x (1/J SC +1/J cu + (R B t max / ) x ln(R TF outboard / R TF inboard ) -  Cu / J cu ] A TF = N TF I TF / J TF overall R TF in = √[(R TF out ) - A TF /  ] Also have a fixed area fraction model, and a stress model

Engineering Module: Physics Filters, Engineering Feasibility, and Engineering Filters Cont’d Bucking Cylinder: R BC out = R TF in -  gap5 h BC = 1.2 x (2a  ) Pressure = (R BC out / R TF ave ) x [(B T max ) 2 / 2  o ] R BC in = √[(R BC out ) 2 x (1 - (2 x Pressure) /  BC max ))] Also a buckling limit, not checked yet PF coil: (center stack only) R PF out = R BC in -  gap6 h PF = h BC  =  o RI p x (l ext + (l i / 2) + C ejima ) B PF max =  / (2 x  R PF out ) If B PF max > 16 T, reject operating point Loop over R PF in, to reach J SC < J SC lim

Engineering Module: Physics Filters, Engineering Feasibility, and Engineering Filters Cont’d Examples of Engineering Filters: 975 ≤ P elec ≤ > to isolate 1000 MW e points P aux ≤ 80 MW ---> isolate lowest auxiliary power solutions (similar to lowest P recir, but not exactly) 0.25 ≤ (P div rad / P div ) ≤ > isolate radiated power fraction to have feasible divertor design and power balance B T examine how being more aggressive on magnets can enlarge your operating space ……

Systems Code Test: Physics Database Intended to Include ARIES-AT Type Solutions Physics input: (not scanned) A = 4.0  = 0.7  n = 0.45  T =  = 2.1 li = 0.5 C ejim = 0.45  CD = 0.38 r CD = 0.2 H min = 0.5 H max = 4.0 Z imp1 = 4.0 f imp1 = 0.02 Z imp2 = f imp2 = 18.0 T edge /T(0) = 0.0 n edge /n(0) = 0.27 Physics input: (scanned) B T = T  N = q 95 = n/n Gr = Q =  He * /  E = 5-10 R = m Generated physics operating points

TF Coil Thickness versus B T, Using 3 Different Models

Inboard Shield Thickness versus N w at the Plasma

Impact of Rejecting Power in Divertor and FW if Q peak Exceeds a Limit We have thrown out operating points that can not produce P elec = 1000 MW, when divertor/FW power is rejected, but we have also brought in higher P fusion operating points with enough neutron power to compensate

Examine Impact of Radiated Power Fraction in the Divertor The plasma power is given by P alpha + P aux Some of this power is radiated from the plasma core/mantle to the first wall, P brem + P cycl + P line The remainder goes to the divertor –We then assume some fraction is radiated in the high density / low temperature divertor slot –What ever is not radiated is conducted along the field line to the target plate Examine the difference in surviving operation space when f div, rad is 30, 60, and 90% Use same physics database, and engineering module with divertor and FW heat rejection when the heat flux is too high, and blanket sizing from Laila’s correlation

Scan of f div,rad Only at high radiated power fraction can we access the small major radius plasmas, and low peak heat flux in outboard divertor ITER ELMy H-mode P fusion ITER ELMy H-mode P aux ITER

Scan of f div,rad ITER

Scan of f div,rad ITER

Scan of f div,rad ITER

Future Work Now that costing is available, coordinate scans with Zoran, and begin looking at technical trends and graphical presentation –Need to exercise the systems code to decide what needs to be done Physics module –Have numerical volume, area, perimeter calculation, will incorporate and make consistent with artificial flux surfaces –Separate electron and ion power balances have been worked out, need to input  Ee (or  Ei ) to solve equations –Have input specification for ITER H-mode and SS mode, working on ARIES-I, etc. –Multiple fusion reactions, etc, etc Engineering Module –PF coil algorithm based on plasma boundary and coil contour –Any upgrades to TF model? –Even if blanket can only be treated by neutronics, can a model be made for VV, etc, etc