# Presentation: 740542

## 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

**BACKGROUND**

**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 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 -> 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

| 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 |  |
| 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 |  |

**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 = *R**0* /a		= 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 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
-  qcyl chosen by solver subject to minimum allowable
-  Bt varied by solver, subject to engineering constraints

**Ip CALCULATION**

**TF COIL**

- 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

- SOL and gap	0.10m
- First wall	0.05m
- Blanket	0.5m
- Shield 	0.7m
- Gap		0.1m

- 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**

-  kBS 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 R0
-   can be approximated by...
- 			Eb = 100 <ne-20> Lb
- where...
- 			Lb = [(R0 + a)2 – R02]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 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
- 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

**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 ...
- a0 = -23.836	a* = -22.712	a1 = -0.09393	a2 = 7.994e-4	a3 = -3.144e-6
- and....
- ...where fT 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...
- Qb-E>400keV  = Qb-E=400keV*400/ Eb

**“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 Ti=Te 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 Ti=Te 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

**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 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

-  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
- Apfs = Wdiv * Adiv+Wcs * 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)

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