# Presentation: 740539

## DESIGN POINTSTUDIES FOR FUTURE ST DEVICES2003 ST WorkshopCharles Neumeyer17 September, 2003

## Topics

- Motivation
- Solver
- Physics Limit Basis
- Algorithms
- Design Point Descriptions

## BACKGROUND

- System Code Studies* for Next Step ST
- Physics algorithms developed at PPPL by S. Jardin, C. Kessel et al,
- Engineering algorithms developed specifically for LN2 cooled ST
- FORTRAN based
- Began using EXCEL as algorithm development tool
- Developed stand-alone System Code on 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 & ASSUMPTIONS

- 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.
-  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
-  Y. Lin-Liu and R. Stambaugh, “Optimum Plasma States for Next Step Tokamaks”, GA Report GA-A23980, 11/02

## Slide 5

| Variable | Menard | Wong | Lin-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 |  |
| alpha_n(A) = alpha_T(A) | (0.64-0.3)/2 | 0.25 |  |
| Peakfactor  | [∫(1-(x)2)alpha_T
(1-(x)2)alpha_ndx]-1
(x=r/a) | [∫(1-(x)2)alpha_T
(1-(x)2)alpha_ndx]-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/A0.5)
*(/3)0.5/
peakfactor0.5 | (-0.7748+1.2869-0.29212+0.01973)
/(TANH((1.8524
+0.2319)/A0.6163))
A0.5523/10 |
| kbs | 0.344+0.195*A | 0.6783+0.0446/A |  |
| fbs | kbs*Beta_P*
peakfactor0.25/A0.5 | kbs*Beta_P*
peakfactor0.25/A0.5 |  |

## Slide 6

## PLASMA GEOMETRY

- R0  = major radius (m)
- a = minor radius (m)
- A = aspect ratio = *R**0* /a
- = inverse aspect ratio = *1/A*

- = elongation
- = triangularity
- = poloidal angle

-  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...

## Ip CALCULATION

-  set to max allowable
-  qcyl chosen by solver subject to min allowable
-  Bt varied by solver, subject to engineering constraints

## TF COIL INNER LEG

-  Glidcop AL-25 material, =87% IACS
-  Flaring is set to 60o with respect to horizontal starting at 90% of the plasma height
-  Water inlet temperature of 35oC and flow velocity of 10m/s
-  In addition to ohmic dissipation, nuclear heating is added
-  Limits on copper and water temperature set at 150oC
-  VonMises stresses estimated with factor of 2 to account for cooling passages
-  Inner leg stress limited to 100MPa

## TF COIL OUTER RETURN

-  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

- _Allowances for Radial Build:_
- SOL and gap	0.10m
- First wall		0.05m
- Blanket		0.5m
- Shield 		0.7m
- 	Gap		0.1m
- Dimensions are similar to those used for ARIES-ST,
- and are sufficient to handle 7.5MW/m2 neutron flux 4
- on the outboard midplane

## POLOIDAL FIELD SYSTEM

-  Toggle is used to select copper PF coils or superconducing
-  If copper, need to account for power dissipation
- total current is assumed equal to the plasma current
- current density is assumed to be JPF = 5.0x106 amp/m2
- inboard edge is assumed to be 0.4m beyond the outboard edge of the VV
-  If superconducting the PF input power is assumed equal to zero
- -Refrigeration power assumed lumped with balance of plant power

## PRESSURE CALCULATIONS

- N subject to physics limit
-   Can run with combined ion-electron or separated

## CURRENT DRIVE

-  kBS per selected physics assumption
-  Assume NBI current drive
-  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 <ne-20> Lb
- where...
- 			Lb = [(R0 + a)2 – R02]1/2

## CURRENT DRIVE EFFICIENCY

- 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...
- Solver is constrained in such a way that CD≤ CDmax and PCD ≤  Paux

- CDMAX = efficiency in units 1020Ampere/Watt-m2
- n20 = electron density in units 1020Ampere/Watt-m2
- ICD = current to be driven in MA
- PCD = current drive power in MW

- Eb = neutral beam energy
- Tavg = average electron temperature

## FUSION POWER CALCULATIONS

-  Both “thermal” ions and beam-target fusion are integrated over the plasma volume
-  Alpha power due to “thermal” ions in a 50:50 D-T mix is ...
- a0 = -23.836	a* = -22.712	a1 = -0.09393	a2 = 7.994e-4	a3 = -3.144e-6
- And....

## BEAM-TARGET FUSION

-  Curve fits to 400keV were generated to match data from Jassby
-  To extend the results out to 1MeV it was assumed that Q should follow
- Qb-E>400keV  = Qb-E=400keV*400/ Eb

## CONFINEMENT

-  Two versions of the energy confinement time are used
- neoclassical
-  ITER 98[y,2] scaling
-  For the mode where Ti=Te, the ITER 98[y,2] scaling is used for the ions and electrons (with “HH” enhancement factor)
-  Otherwise the ion confinement is assumed neoclassical and the electrons per ITER 98 (both with “HH” enhancement)
-  Formulae for the neoclassical ion confinement scaling were provided by Rutherford

## POWER BALANCE

-  Power balance equates net input power to the stored energy divided by the energy confinement time...
- Toggle is provided to select whether Ti=Te or not. For Ti  Te ...
- Expressions were supplied by Rutherford for the partitioning of the alpha and auxiliary power to the ions and electrons, along with an expression for Pie

## HEAT LOADS

-  The power in the scrape-off layer is...
-  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 divetor 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

## n WALL LOADING TO CENTER STACK

-  The fraction of neutrons incident on the narrow midplane region of the center stack is estimated based on line-of-sight considerations...
-  The remaining neutron flux impinges on the remainder of the first wall

## n WALL LOADING TO BLANKET

-  Data was supplied by El Guebaly based on ARIES-ST work concerning n flux  distribution on a cylindrical blanket extending up to the plasma height *a
-  Weighting functions were developed which relate the peak to machine average flux on the center stack, divertor, and cylindrical blanket surfaces
- Apfs = Wdiv * Adiv+Wcs * Acs + Wcyl * Acyl
-  With the weighting functions established, the equation for normalized neutron flux to the outboard region is as follows...
- nob(z)= Wcyl *1.4318*(1-z/1.016)

## BLANKET

-  Blanket area is the total plasma facing surface area minus the effective areas of the divertor, center stack, and ports for the NBI, RF, and Diagnostics.
- Ablanket=Apfs-(Wcs*Acs-Wdiv*Adiv-Wport*dZport*(2*1.0m+Nnbi*Cnbi))
-  All midplane ports assumed to have the same height of at least 1.0m, or...
- dZport = MIN(2*(*R0/A-1.5),2**R0/A/3)
-  Preferred port height is 1/3 of the plasma but we reserve 1.5m from the top of the plasma (where an outer PF coil will be located) to the top of the port for remote handling.
-  For high energy NBI (Enbi > 200keV) negative ion injection methods are required, and the current density achievable through the NBI duct is assumed limited to Jnbi=40A/m2 which sets the number of NBI ports required

## THERMAL POWER CONVERSION

- fblanket = fraction of surface area covered by blanket
- fBEM   = blanket energy multiplication factor (assumed =1.2)
- k*div*     = toggle used to select divertor power recovery or not
-  If toggle is on to generate electicity, gross electrical power production is...
-  Conversion efficiency EC is typically assumed 35% for “conventional” power conversion and 45% for “advanced” power conversion” cycles

## NET ELECTRIC POWER

-  Otherwise the balance of plant power is assumed to be 20MW
-  The net electric power production is...
-  Conversion efficiencies...
- 		 	 PF superconducting (∞) or 95%
- 		 	 TF  assume  90%
- 		 	 Paux assume 45%

## NET TRITIUM CALCULATIONS

-  The  tritium fueling rate per day is...
- QT-fueling = P_fusion/6.54 gm/day
-  Blanket local T breeding ratio (TBR) assumed equal to 1.2
-  The net fractional breeding ratio (FBR) is as follows...
- FBR= fblanket *TBR
-  The net T consumption is...
- QT = FBR* QT-fueling

## EXCEL SOLVER

- Microsoft EXCEL Solver uses the Generalized Reduced Gradient nonlinear optimization code developed by L Lasdon, U of Texas at Austin, and A Waren, Cleveland State University (_[www.solver.com](http://www.solver.com/)_)
- Handles up to 200 non-linear variables with 100 constraints
- “Premium” packages available at a price for larger problms
- Very easy to use compared to hard-coded

## USE OF SOLVER

- Typical variable set adjusted by SOLVER...
- frad, fGW, N, qcyl, Pfusion, CD, JTF, fW
- Typical set of constraints
- frad ≤ Pbrem/P.
- Pfusion = 5*P.
-  CD ≤   CDmax (T) = 0.025<T>
-  PCD ≤  Paux
-  N ≤  Nmax
- qcyl ≥ qcylmin
- 0.1 ≤  fBS ≤  specified limit
- 0.1 ≤  fGW ≤  specified limit

-  TF  ≤  100MPa
- TTFCu ≤  150C
- TTFH20 ≤  150C
- 0.05 ≤  fW ≤  0.25
- HH = or ≤   an input value
- nwall = or ≤  an input value

*= required for a mathematically valid solution*

## CTF CASES

-  Following are four representative CTF cases.
-  The first two are at R0=1.0m, and the second two at R0=1.2m.
-  For each pair of cases, the first targets blanket test module loading at 1.0MW/m^2, and the second runs at maximum loading available. This turns out to be around 2.0MW/m^2 for R0=1.0m and 4.0MW/m^2 for R0=1.2m.
-  From these results it appears that the 1.0m design is adequate if module neutron wall loading need not exceed 1.0MW/m^2. For this case, positive ion NBI can be used and the test module area meets the 10m^2 requirement.
-  For higher loadings, it is necessary to go to a larger machine and negative ion NBI. The 1.2m design can provide 4MW/m^2 and still meet the 10m^2 requirement.

## Slide 29

| R0[m] | 1.000 | 1.000 | 1.200 | 1.200 |
| --- | --- | --- | --- | --- |
| A | 1.500 | 1.500 | 1.500 | 1.500 |
| R0+a[m] | 1.67 | 1.67 | 2.00 | 2.00 |
| kappa | 3.201 | 3.201 | 3.201 | 3.201 |
| delta | 0.400 | 0.400 | 0.400 | 0.400 |
| qMHD | 8.907 | 7.498 | 11.680 | 7.498 |
| qcyl | 3.05 | 2.57 | 4.01 | 2.57 |
| qcyl/qcyl(A) | 118.8% | 100.0% | 155.8% | 100.0% |
| Bt[T] | 1.944 | 1.826 | 2.467 | 2.067 |
| fH20 | 25.0% | 25.0% | 25.0% | 25.0% |
| TH20max[degC] | 81.7 | 83.0 | 86.7 | 90.4 |
| TCumax[degC] | 150.0 | 150.0 | 150.0 | 150.0 |
| Sigmax[MPa] | 63.9 | 56.4 | 94.9 | 66.6 |
| Javgtf[A/m^2] | 5.2E+07 | 4.9E+07 | 5.1E+07 | 4.3E+07 |
| Itf[Amp] | 9.72E+06 | 9.13E+06 | 1.48E+07 | 1.24E+07 |
| Ip[MA] | 7.953 | 8.872 | 9.235 | 12.050 |
| Beta_N_thermal | 4.47% | 5.84% | 3.50% | 6.74% |
| Beta_N_total | 5.87% | 7.68% | 4.55% | 8.26% |
| Beta_N/Beta_N(A) | 71.0% | 93.0% | 55.1% | 100.0% |

## Slide 30

| R0[m] | 1.000 | 1.000 | 1.200 | 1.200 |
| --- | --- | --- | --- | --- |
| Beta_T_alpha | 5.8% | 8.1% | 3.5% | 6.6% |
| Beta_T_nbi | 2.7% | 5.3% | 1.4% | 4.5% |
| Beta_T_thermal | 27.4% | 42.6% | 16.4% | 49.1% |
| Beta_T_total | 36.0% | 56.0% | 21.3% | 60.2% |
| Beta_P | 102.5% | 112.7% | 105.2% | 130.0% |
| xne[1/m^3] | 8.6E+19 | 1.4E+20 | 8.3E+19 | 2.3E+20 |
| fGW | 17.1% | 24.4% | 20.4% | 43.6% |
| alpha_n | 0.250 | 0.250 | 0.250 | 0.250 |
| alpha_T | 1.000 | 1.000 | 1.000 | 1.000 |
| fBS | 65.8% | 72.3% | 67.5% | 83.4% |
| Tempavg[keV] | 16.7 | 14.3 | 16.7 | 12.6 |
| Tavgi[keV] | 23.7 | 18.5 | 22.6 | 14.1 |
| Tavge[keV] | 11.1 | 10.9 | 12.0 | 11.3 |
| HH98 (global) | 2.54 | 2.20 | 2.35 | 1.85 |
| HHi | 1.00 | 1.00 | 1.00 | 1.00 |
| HHe | 1.00 | 1.00 | 1.00 | 1.00 |
| Tau_E_NC[sec] | 7.08 | 4.95 | 9.74 | 4.89 |
| Tau_E_98[sec] | 0.27 | 0.25 | 0.40 | 0.35 |

## Slide 31

| R0[m] | 1.000 | 1.000 | 1.200 | 1.200 |
| --- | --- | --- | --- | --- |
| Q | 3.5 | 4.3 | 4.5 | 7.2 |
| Zeff | 1.77 | 1.77 | 1.78 | 1.78 |
| P_Brem[MW] | 0.9 | 2.2 | 1.5 | 11.2 |
| P_rad_core[MW] | 5.0 | 8.7 | 6.2 | 18.6 |
| P_aux[MW] | 15.2 | 24.7 | 17.1 | 42.7 |
| E_nbi[keV] | 115.1 | 183.6 | 133.0 | 372.0 |
| P_fusion[MW] | 53.1 | 106.3 | 76.6 | 306.5 |
| P_alpha[MW] | 10.6 | 21.3 | 15.3 | 61.3 |
| fTC | 24.2% | 24.6% | 21.4% | 13.3% |
| Gamma_CD[10^20*A/W-m^2] | 0.15 | 0.14 | 0.18 | 0.13 |
| P_CD[MW] | 15.2 | 24.7 | 17.1 | 42.7 |
| Xnwall[MW/m^2] | 1.1 | 2.2 | 1.1 | 4.5 |
| Qn_wall[MW/m^2] | 0.58 | 1.16 | 0.58 | 2.31 |
| Qn_tm[MW/m^2] | 1.00 | 2.00 | 1.00 | 4.00 |
| Qn_om[MW/m^2] | 1.04 | 2.08 | 1.04 | 4.16 |

## Slide 32

| R0[m] | 1.000 | 1.000 | 1.200 | 1.200 |
| --- | --- | --- | --- | --- |
| Port Height (delta Z)[m] | 1.46 | 1.46 | 1.78 | 1.78 |
| #NBI Port | 1 | 2 | 2 | 2 |
| Available TM Area [m] | 11.7 | 8.8 | 16.1 | 16.1 |
| #Test Module Ports | 7 | 6 | 6 | 6 |
| A_cyl_blanket[m^2] | 32.1 | 32.1 | 45.1 | 45.1 |
| T fueling rate[gm/day] | 8.13 | 16.26 | 11.72 | 46.89 |
| fCS | 7.3% | 7.3% | 7.3% | 7.3% |
| fN | 80.6% | 73.8% | 78.0% | 78.7% |
| FBR | 100.8% | 92.3% | 97.5% | 98.3% |
| Net T consumption rate[gm/day] | -0.06 | 1.26 | 0.29 | 0.77 |
| n/s/W | 1.12E+11 | 1.8E+11 | 9.9E+10 | 3.6E+11 |
| frad_core | 20.0% | 20.0% | 20.0% | 20.0% |
| Q_fw[MW/m^2] | 0.160 | 0.298 | 0.145 | 0.562 |
| frad_div | 47.0% | 71.7% | 37.7% | 82.3% |
| Q_div[MW/m^2] | 15.0 | 15.0 | 15.0 | 15.0 |

## Slide 33

| R0[m] | 1.000 | 1.000 | 1.200 | 1.200 |
| --- | --- | --- | --- | --- |
| P_aux_input[MW] | 43.5 | 70.5 | 48.8 | 122.1 |
| ∑P_tf[MW] | 92.0 | 81.4 | 164.8 | 116.4 |
| ∑P_pf[MW] | 0.0 | 0.0 | 0.0 | 0.0 |
| P_bop[MW] | 0.0 | 0.0 | 0.0 | 0.0 |
| ∑P_elec input[MW] | 135.5 | 151.8 | 213.6 | 238.5 |
| P_elec gen[MW] | 0.0 | 0.0 | 0.0 | 0.0 |
| P_net elec[MW] | -135.5 | -151.8 | -213.6 | -238.5 |
| Q_elec | 0.00 | 0.00 | 0.00 | 0.00 |
| Annual Elec Cost[$M] | 24.9 | 27.9 | 39.3 | 43.9 |
| Mass_TF_CS | 1.05E+05 | 1.1E+05 | 1.6E+05 | 1.6E+05 |
| Mass_TF_Outer | 6.27E+05 | 6.3E+05 | 7.4E+05 | 7.4E+05 |
| Mass_PF_Outer | 3.90E+05 | 4.4E+05 | 4.9E+05 | 6.4E+05 |
| P_Density[MW/m^3] | 1.89 | 3.78 | 1.58 | 6.32 |

## DEMO (100MWe) AND REACTOR (1GWe) CASES

|  | DEMO | REACTOR |
| --- | --- | --- |
| R0[m] | 2.100 | 2.800 |
| A | 1.600 | 1.600 |
| kappa | 3.090 | 3.382 |
| delta | 0.400 | 0.500 |
| Bt[T] | 2.527 | 1.951 |
| Ip[MA] | 20.9 | 23.9 |
| HH98 (global) | 1.58 | 1.22 |
| HHi | 1.00 | 1.00 |
| HHe | 0.93 | 0.63 |
| Q | 69.1 | 193.2 |
| P_fusion[MW] | 1598 | 3097 |

## Slide 35

|  | DEMO | REACTOR |
| --- | --- | --- |
| FBR | 104.2% | 107.7% |
| Q_fw[MW/m^2] | 0.939 | 0.723 |
| Q_div[MW/m^2] | 15.0 | 15.0 |
| ∑P_elec input[MW] | 380.2 | 376.3 |
| P_elec gen[MW] | 487.9 | 1406.5 |
| P_net elec[MW] | 107.7 | 1030.2 |
| Q_elec | 1.28 | 3.74 |
| P_Density[MW/m^3] | 7.24 | 5.41 |