# Presentation: 156109

## BENCHMARKING

***Work Supported by US DOE Contract **
**No. DE-AC02-76CHO-3073**

**BENCHMARKING**

-  NSTX Shot 109070

| R0 | 0.88 | m |
| --- | --- | --- |
| A | 1.47 |  |
| kappa | 2.05 |  |
| delta | 0.43 |  |
| Bt | 0.49 | T |
| alpha_N | 0.02 |  |
| alpha_Ti | 0.80 |  |
| alpha_Te | 0.60 |  |
| fGW | 0.65 |  |
| Ip | 0.80 | MA |
| Zimp | 6.00 |  |
| fimp | 1.7% |  |
| Zeff | 1.50 |  |
| Beta_N_tot | 6.0% |  |

-  CTF design points were also verified by Strickler via SUPERCODE
-  Algorithms agree with ARIES-ST with suitable adjustments to input assumptions

|  | Total | Ions | Electrons | ∑I+e |  |
| --- | --- | --- | --- | --- | --- |
| P_alpha | 0.00 | 0.00 | 0.00 | 0.00 | MW |
| P_aux | 5.30 | 2.07 | 3.23 | 5.30 | MW |
| Beta_N thermal | 0.04 | 0.02 | 0.02 |  |  |
| T0 | 0.92 | 1.55 | 1.09 |  | keV |
| n | 4.58E+19 | 4.19E+19 | 4.58E+19 |  | 1/m^3 |
| P_ie | 0.00 | -0.91 | 0.91 | 0.00 | MW |
| P_rad | -0.02 | 0.00 | -0.02 | -0.02 | MW |
| P_tot | 5.28 | 1.16 | 4.12 | 5.28 | MW |
| W | 0.21 | 0.11 | 0.10 | 0.21 | MJ |
| HH | 1.29 | 1.00 | 0.77 |  |  |
| HH*Tau_E | 0.04 | 0.10 | 0.02 |  |  |
| W/(HH*Tau_E) | 5.28 | 1.16 | 4.12 | 5.28 | MW |

-  ST offers promise of relatively compact fusion devices
-  Much work needed in engineering development of ST device
- single turn center post
- multi-MA TF power supply
- continuous conducting shell
- Etc.
-  EXCEL SOLVER provides a surprisingly powerful tool for simple Systems Code studies

**CONCLUSIONS**

- Typical variable set adjusted by SOLVER...
- frad, fGW, N, qcyl, Pfusion, CD, JTF, fW
- Typical 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

**USE OF SOLVER**

-  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 fromtop of plasma (where outer PF coil will be located) to top of port for remote handling.
-  For high energy NBI (Enbi > 120keV) 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

**EFFECTIVE BLANKET AREA**

-  Useful thermal power is...
- 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

**THERMAL POWER CONVERSION**

-  If toggle is on for electricity production, operation of “balance of plant” is assumed to consume a fraction (fBOP=10%) of gross electric power production
-  Otherwise the balance of plant power is assumed to be 20MW
-  The net electric power production is...
-  Assume PF coils superconducting (P=0)
-  Conversion efficiencies...
- 		  TF  assume  90%
- 		  Paux assume 35% (DEMO), 45% (REACTOR)

**NET ELECTRIC POWER**

-  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 = (1-FBR)* QT-fueling

**NET TRITIUM CALCULATIONS**

*= req’d for mathematically valid solution*

- CTF...
- R0=1.0m
- 10m2 test module area
- Two cases...
-  1MW/m2
- - Enbi ≤ 120keV
-  4MW/m2
- - Enbi > 120keV (NINB)

- Minimum R0 solutions which meet criteria assuming HHi and HHe ≤ 1.0

**SAMPLE CASES**

- DEMO...
- R0=2.1m
- 100MW net electric

- REACTOR...
- R0=3.0m
- 1GW net electric

|  | CTF | CTF | DEMO | REACTOR |
| --- | --- | --- | --- | --- |
| R0[m] | 1.20 | 1.20 | 2.50 | 3.00 |
| A | 1.50 | 1.50 | 1.50 | 1.50 |
| R0+a[m] | 2.00 | 2.00 | 4.17 | 5.00 |
| kappa | 3.20 | 3.20 | 3.20 | 3.20 |
| delta | 0.60 | 0.60 | 0.60 | 0.60 |
| qMHD | 13.34 | 8.72 | 9.14 | 9.56 |
| qcyl | 3.94 | 2.57 | 2.70 | 2.82 |
| qcyl/qcyl(A) | 153.0% | 100.0% | 104.9% | 109.6% |
| Bt[T] | 2.445 | 2.076 | 1.870 | 1.840 |
| fH20 | 25.0% | 25.0% | 25.0% | 25.0% |
| TH20max[degC] | 89.3 | 89.7 | 76.3 | 81.6 |
| TCumax[degC] | 150.0 | 150.0 | 99.8 | 108.8 |
| Sigmax[MPa] | 93.3 | 67.2 | 70.2 | 60.5 |
| Javgtf[A/m^2] | 5.1E+07 | 4.3E+07 | 2.4E+07 | 1.7E+07 |
| Itf[Amp] | 1.47E+07 | 1.25E+07 | 2.34E+07 | 2.76E+07 |
| Ip[MA] | 9.316 | 12.105 | 21.665 | 24.461 |
| Beta_N_thermal | 3.17% | 6.85% | 7.72% | 7.07% |
| Beta_N_total | 4.11% | 8.26% | 8.20% | 7.95% |
| Beta_N/Beta_N(A) | 49.8% | 100.0% | 99.3% | 96.3% |
| Beta_T_alpha | 2.7% | 7.6% | 3.1% | 5.5% |
| Beta_T_nbi | 1.8% | 2.7% | 0.2% | 0.3% |
| Beta_T_thermal | 15.1% | 49.9% | 53.6% | 47.0% |
| Beta_T_total | 19.6% | 60.2% | 57.0% | 52.9% |
| Beta_P | 93.5% | 132.2% | 156.1% | 149.5% |
| xne[1/m^3] | 7.5E+19 | 2.0E+20 | 2.1E+20 | 1.6E+20 |
| fGW | 18.2% | 38.3% | 95.0% | 91.0% |
| alpha_n | 0.250 | 0.250 | 0.220 | 0.220 |
| alpha_T | 1.000 | 1.000 | 0.220 | 0.220 |
| fBS | 60.0% | 84.8% | 94.7% | 90.7% |
| Tempavg[keV] | 16.7 | 14.7 | 12.5 | 12.6 |
| Tavgi[keV] | 26.0 | 18.8 | 13.3 | 14.2 |
| Tavge[keV] | 9.3 | 11.5 | 11.8 | 11.2 |
| HH98 (global) | 2.07 | 2.12 | 1.68 | 1.25 |
| HHi | 0.13 | 1.00 | 1.00 | 0.50 |
| HHe | 0.93 | 1.00 | 0.96 | 0.60 |
| Tau_E_NC[sec] | 11.76 | 6.32 | 17.55 | 21.67 |
| Tau_E_98[sec] | 0.33 | 0.39 | 1.40 | 0.97 |
| Q | 3.2 | 12.6 | 95.8 | 118.6 |
| Zeff | 1.77 | 1.81 | 1.84 | 1.98 |
| P_Brem[MW] | 1.0 | 8.9 | 69.2 | 70.6 |
| P_rad_core[MW] | 7.7 | 15.4 | 42.0 | 119.0 |
| P_aux[MW] | 24.0 | 24.4 | 13.8 | 26.9 |
| E_nbi[keV] | 120.0 | 327.9 | 708.0 | 638.1 |
| P_fusion[MW] | 76.6 | 306.5 | 1326.3 | 3194.2 |
| P_alpha[MW] | 15.3 | 61.3 | 265.3 | 638.8 |
| fTC | 25.6% | 8.1% | 0.5% | 0.5% |
| Gamma_CD[10^20*A/W-m^2] | 0.14 | 0.19 | 0.44 | 0.40 |
| P_CD[MW] | 24.0 | 24.4 | 13.8 | 26.9 |
| Xnwall[MW/m^2] | 1.1 | 4.5 | 4.5 | 7.4 |
| Qn_wall[MW/m^2] | 0.58 | 2.31 | 2.31 | 3.86 |
| Qn_tm[MW/m^2] | 1.00 | 4.00 | 3.99 | 6.67 |
| Qn_om[MW/m^2] | 1.04 | 4.16 | 4.15 | 6.94 |
| Port Height (delta Z)[m] | 1.78 | 1.78 | 3.72 | 4.46 |
| #NBI Port | 1 | 1 | 1 | 1 |
| Available TM Area [m] | 17.8 | 17.8 | 92.9 | 133.8 |
| #Test Module Ports | 6 | 6 | 3 | 3 |
| A_cyl_blanket[m^2] | 45.1 | 45.1 | 188.6 | 270.0 |
| T fueling rate[gm/day] | 11.72 | 46.89 | 202.89 | 488.62 |
| fCS | 7.3% | 7.3% | 7.3% | 7.3% |
| fN | 81.5% | 80.7% | 87.1% | 87.4% |
| FBR | 101.9% | 100.8% | 108.9% | 109.3% |
| Net T usage [gm/day] | -0.23 | -0.38 | -17.98 | -45.46 |
| n/s/W | 9.02E+10 | 4.4E+11 | 1.3E+12 | 2.1E+12 |
| frad_core | 20.0% | 20.0% | 20.0% | 20.0% |
| Q_fw[MW/m^2] | 0.164 | 0.458 | 0.484 | 0.573 |
| frad_div | 50.5% | 77.6% | 61.8% | 82.8% |
| Q_div[MW/m^2] | 15.0 | 15.0 | 15.0 | 15.0 |
| P_aux_input[MW] | 68.6 | 69.7 | 30.8 | 59.9 |
| ∑P_tf[MW] | 177.2 | 127.9 | 249.0 | 266.8 |
| ∑P_pf[MW] | 0.0 | 0.0 | 0.0 | 0.0 |
| P_bop[MW] | 0.0 | 0.0 | 42.2 | 147.4 |
| ∑P_elec input[MW] | 245.8 | 197.6 | 322.0 | 474.1 |
| P_elec gen[MW] | 0.0 | 0.0 | 422.0 | 1474.1 |
| P_net elec[MW] | -245.8 | -197.6 | 100.0 | 1000.0 |
| Q_elec | 0.00 | 0.00 | 1.31 | 3.11 |
| Annual Elec Cost[$M] | 45.2 | 36.4 | -47.4 | -474.4 |
| Mass_TF_CS | 1.02E+05 | 1.0E+05 | 4.5E+05 | 7.2E+05 |
| Mass_TF_Outer | 7.45E+05 | 7.5E+05 | 1.7E+06 | 2.2E+06 |
| Mass_PF_Outer | 4.95E+05 | 6.5E+05 | 1.7E+06 | 2.2E+06 |
| P_Density[MW/m^3] | 1.58 | 3.20 | 3.02 | 4.21 |

- HH factors within limits
- TF within stress & temperature limits
- Divertor & first wall heat load limits
- Blanket midplane n wall loading limit
- Test module n wall loading = target
- Etc.