1. Slide 1 DNB Aperture Preconceptual Design.ppt Preconceptual Design of DNB Collimating Apertures Steve Scott April 28, 2003

2. Slide 2 DNB Aperture Preconceptual Design.ppt Can Achieve 2.9 cm DNB Footprint with Two 3.0 cm Apertures Beam Divergence 0.86 o Aperture widths Aperture 1 3.0 Aperture 2 3.0 Aperture heights Aperture 1 20.0 Aperture 2 20.0 Aperture positions Aperture 1 220 Aperture 2 340 DNB footprint (FWHM) 2.96 MSE signal strength 81.9 Power to Aperture 2 15.0% Max Ap 2 power dens 4.6 Advertised DNB spot size = 6.0 cm (1/e)

3. Slide 3 DNB Aperture Preconceptual Design.ppt

4. Slide 4 DNB Aperture Preconceptual Design.ppt Footprint Size Increases Less than 1mm Assuming More Conservative Divergence Beam Divergence 1.00 o Aperture widths Aperture 1 3.0 Aperture 2 3.0 Aperture heights Aperture 1 20.0 Aperture 2 20.0 Aperture positions Aperture 1 220 Aperture 2 340 DNB footprint (FWHM) 3.03 MSE signal strength 65.1 Power to Aperture 2 16.6% Max Ap 2 power dens 3.9 Conservative DNB spot size = 7.0 cm (1/e)

5. Slide 5 DNB Aperture Preconceptual Design.ppt

6. Slide 6 DNB Aperture Preconceptual Design.ppt

7. Slide 7 DNB Aperture Preconceptual Design.ppt

8. Slide 8 DNB Aperture Preconceptual Design.ppt

9. Slide 9 DNB Aperture Preconceptual Design.ppt

10. Slide 10 DNB Aperture Preconceptual Design.ppt

11. Slide 11 DNB Aperture Preconceptual Design.ppt DNB: full-width, half-max = 8-9 cm. At plasma center, DNB is approximately at 45 o with respect to Rmajor.  r = 8-9/sqrt(2) = 5.6 – 6.4 cm (at r=0)  r / a = 0.26 – 0.29  Would like to get say FWHM = 4 cm, corresponding to  r / a = 0.13 Motivation

12. Slide 12 DNB Aperture Preconceptual Design.ppt DNB centerline DNB 1/e DNB cutoff DNB 1/e DNB cutoff Assumed Beam Size: 9 cm (1/e) with cutoff at 12 cm Projection of MSE Fiber Sightlines in Horizontal Midplane

13. Slide 13 DNB Aperture Preconceptual Design.ppt DNB centerline DNB 1/e DNB cutoff DNB 1/e DNB cutoff Projection of MSE Fiber Sightlines in RZ Plane Assumed Beam Size: 9 cm (1/e) with cutoff at 12 cm 1. Very little radial resolution is lost by the vertical extent of the fiber bundle. 2. Vertical extent of fiber bundle is only ~ +/- 2 cm, smaller than size of DNB

14. Slide 14 DNB Aperture Preconceptual Design.ppt 1 2 3 4 5 6 7 8 9 10 There is Significant Channel Overlap with Present Beam Size (9 cm 1/e, 12 cm cutoff) Emission from Full-Energy DNB Note: Channel 4 has significant overlap with channels 2,3,5 and a little overlap with channels 1 and 6!

15. Slide 15 DNB Aperture Preconceptual Design.ppt Imposing an 8-cm cutoff Provides Reasonable Radial Resolution at the Plasma Edge, but still Poor at the Center

16. Slide 16 DNB Aperture Preconceptual Design.ppt 6-cm cutoff

17. Slide 17 DNB Aperture Preconceptual Design.ppt 4-cm cutoff: Moderate Radial Resolution in Plasma Core

18. Slide 18 DNB Aperture Preconceptual Design.ppt 2-cm cutoff (original assumption): Little Channel Overlap

19. Slide 19 DNB Aperture Preconceptual Design.ppt Slotted Aperture of width 4, 3, 2 cm causes signal reduction of factor 1.9, 2.5, 3.6

20. Slide 20 DNB Aperture Preconceptual Design.ppt TFTR DNB Scraper Schematic Scraper 1-2 cm thick copper plate Located at end of DNB beamline, about ½ distance from grid to plasma (like CMOD) Opening adjustable. When closed, forms calorimeter Small overlap to ensure closure in spite of possible warping Cooling at back … inertially cooled during 0.5 sec beam pulse grid bellows Oval copper lining Not adjustable Takes only small fraction of power No active cooling… Radiation + conduction to vacuum vessel scraper liner Thanks to Gerd Schilling

21. Slide 21 DNB Aperture Preconceptual Design.ppt Procedure to Compute Effect of Apertures on Beam Size Aperture #1Aperture #2TargetGrid Focal Distance 1.Launch vectors from grid, through focal point, onto target. 2.Establish circular grid on target with diameter = beamlet size corresponding to beam divergence. 3.For each point on target grid, decide whether ray from grid to target hits aperture or Target. 4.Increment computed power to Aperture #1, Aperture #2 or target as appropriate.

22. Slide 22 DNB Aperture Preconceptual Design.ppt Aperture Distance 220 Aperture width 10 (WIDE) FWHM 6.3 MSE Signal 176

23. Slide 23 DNB Aperture Preconceptual Design.ppt Aperture Distance220 Aperture width2.0 FWHM4.6 MSE Signal71

24. Slide 24 DNB Aperture Preconceptual Design.ppt Aperture Distance 320 Aperture width 2.0 FWHM 2.2 MSE Signal 62 Moving Aperture Closer to Plasma Makes it More Effective (duh …)

25. Slide 25 DNB Aperture Preconceptual Design.ppt -------- Aperture ----------- ----- DNB Size ---- MSE Signal Location Width FWHM 1/e 95% 220 10.0 6.3 7.6 13.0 176 3.0 4.6 5.5 9.4 101 2.5 4.6 5.5 9.4 86 2.0 4.6 5.5 9.0 71 1.5 4.6 5.5 9.0 54 320 10.0 6.2 7.5 11.8 172 4.0 3.8 4.6 6.6 112 3.0 3.0 3.6 5.8 88 2.5 2.6 3.1 5.0 75 2.0 2.2 2.7 4.6 62 1.5 1.9 2.3 3.8 47 Summary of Single-Aperture Performance for Locations at 2.2 and 3.2 meters from the DNB Grid Assumptions: 10 cm diameter grid, focal length = 400 cm, target at 400 cm, (1/e) beamlet divergence = 1.1 o … beamlet diameter = 7.7 cm Not great Pretty good, but signal is compromised

26. Slide 26 DNB Aperture Preconceptual Design.ppt Calculations Using Two Apertures

27. Slide 27 DNB Aperture Preconceptual Design.ppt -------- Aperture ----------- Power MSE DNB Ap-1 Ap-2 SIGNAL Width-2 Width-2 FWHM 2.25 2.70 2.98 55% 15% 53 2.50 3.00 3.18 51% 14% 62 3.00 3.00 3.08 43% 17% 70 3.20 3.23 43% 16% 73 3.30 3.31 43% 15% 74 3.50 3.45 43% 15% 77 3.75 3.62 43% 11% 80 4.00 3.77 43% 10% 83 Summary of Two-Aperture Performance for Locations at 2.2 and 3.2 meters from the DNB Grid Assumptions: 10 cm diameter grid, focal length = 400 cm, target at 400 cm, (1/e) beamlet divergence = 1.1 o … beamlet diameter = 7.7 cm

28. Slide 28 DNB Aperture Preconceptual Design.ppt Surface Heating of Aperture by DNB Gas evolution from aperture surface leading to reionization loss Possible local melting of surface Model: canonical semi-infinite slab of uniform material, uniform heat flux q applied starting at t=0, neglecting radiative losses:  T = (2q/k)(  t/  ) 0.5 Copper:  = k /  C = 1.16 10 -4 m 2 /sec k = 400 watts / meter / kelvin  = 8900 kg/m 3 C = 386 Joules / kg / Kelvin DNB: q avg = (5.0 Amps) (50,000) /  (0.09/2) 2 = 3.9 10 7 watts/m 2 q = q avg exp(-r 2 /s 2 ) where s = 0.6*FWHM = 0.054 meters

29. Slide 29 DNB Aperture Preconceptual Design.ppt Surface Heating of Aperture by DNB, cont’d Assume 50 ms beam pulse:  T = 265 exp( - (r/0.054) 2 ) kelvin Maximum surface temperature rise beam pulse for Copper: Horizontal Aperture  T max dimension (cm) 50 ms 1000 ms 4 231 o C1033 5 214 957 6 195 872 7 174 778 8 154 689 Melting temperature of Copper = 1083 o C. Conclusion: gas evolution may be an issue for a 50 ms beam, and melting may be a problem for a long-pulse beam. For the short-pulse beam, we could eliminate gas evolution by continuously heating the aperture to maintain its temperature > 150 o C.

30. Slide 30 DNB Aperture Preconceptual Design.ppt Surface Heating of Aperture by DNB, cont’d For the long-pulse beam, we could: Tilt the aperture to spread the incident heat flux over a larger area – limited by available space. Actively cool the aperture – more expensive. Could use 2 apertures – 1 st one closer to grid takes most of the heat, 2 nd one closer to plasma is inertially cooled.

31. Slide 31 DNB Aperture Preconceptual Design.ppt ~ Tmelt/  T heat Tungsten and moly provide the best protection against melting

32. Slide 32 DNB Aperture Preconceptual Design.ppt Conclusions MSE can’t provide radially-resolved q-profile measurements with the DNB in its present configuration. A two-aperture system looks technically feasible: –1 st aperture @end of DNB beamline - takes most of the heat; actively cooled. – 2 nd aperture, closer to plasma, uncooled, provides final collimation. We lose about a factor 2-3 in signal strength to get ~ 3 cm spatial resolution.