# Presentation: 709490

## 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

## MOTIVATION

- Participation in System Code Studies* for Next Step ST
- Physics algorithms developed at PPPL by S. Jardin, C. Kessel et al, evolved over many years for many machine studies
- Engineering algorithms developed specifically for LN2 cooled ST
- FORTRAN based
- Began using EXCEL as algorithm development tool
- Found that EXCEL Solver was quite powerful and flexible
- Developed stand-alone System Code on EXCEL
- Performed Design Point Studies for a Component Test Facility (CTF)
- Continued to improve System Code with M Peng and P Rutherford
- Studied Range of Design Points along ST Development Path

- **Systems Analysis of a Compact Next Step Burning Plasma Experiment*, S Jardin et al, Fusion Science and Technology, Vol. 43, March 2003

## 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)
- Handles up to 200 non-linear variables with 100 constraints
- “Premium” packages available at a price
- Very easy to use compared to hard-coded

## PHYSICS LIMITS

-  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

## Menard formulations used in results reported herein

| 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 | 1.21+1.3A
-0.25A2 |  |
| 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) |  |
| 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 |

*Menard formulations used in results reported herein*

## 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...

## 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

## Elongation		max = 1.46155+4.13281-2.578122+1.410163

- Elongation		max = 1.46155+4.13281-2.578122+1.410163
- Triangularity	 selected on  case-case basis ~ 0.3 - 0.5
- 95% Flux Surface	Physics calculations based on 95% surfaces
- A100, a100 		Set based on curve fit to equilibria, used 			to set plasma “engineering” envelope

## MHD SAFETY FACTOR

- Minimum qcyl = -0.115479+14.5293-27.44922+18.3343

- Bt adjusted by SOLVER within Engineering Constraints

- Bt

## Ip

- With R0,a,, Bt and qcyl determined the plasma current (in MA) is calculated according to...

## Density and Temperature Profiles Assumed Parabolic

- Profile exponents chosen on a case-by-case basis or per Menard...
- N = T = (0.64-0.3)/2

## Beta Limit

## Bootstrap Current Fraction

## CONCLUSIONS

-  New Design Corrects All Defects of Original Design
-  Follow-on Activities Will Increase Confidence
-  Mechanical Prototype Testing
-  Electrical Prototype Testing
-  Instrumentation During Commissioning and Operations
- - resistance measurement (200A maintenance and real-time) system
- temperature, strain, displacement
-  NSTX Probably Represents the Limit on Bolted Demountable TF Joints
- - Next Step ST likely requires sliding joint ala MAST, Alcator C-MOD