Preconceptual Design of DNB Collimating Apertures

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Preconceptual Design of DNB Collimating Apertures
Steve Scott April 28, 2003
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Can Achieve 2.9 cm DNB Footprint with Two 3.0 cm
Apertures
Advertised DNB spot size 6.0 cm (1/e)
Beam Divergence 0.86o 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
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Footprint Size Increases Less than 1mm Assuming
More Conservative Divergence
Conservative DNB spot size 7.0 cm (1/e)
Beam Divergence 1.00o 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
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Motivation

• DNB full-width, half-max 8-9 cm.
• At plasma center, DNB is approximately at 45o
  with respect to Rmajor.
• Dr 8-9/sqrt(2) 5.6 6.4 cm (at
  r0)
• Dr / a 0.26 0.29
• Would like to get say FWHM 4 cm, corresponding
  to Dr / a 0.13

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Projection of MSE Fiber Sightlines in Horizontal
Midplane
DNB cutoff
DNB 1/e
DNB centerline
DNB 1/e
DNB cutoff
Assumed Beam Size 9 cm (1/e) with cutoff at 12
cm
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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

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There is Significant Channel Overlap with Present
Beam Size (9 cm 1/e, 12 cm cutoff)
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8
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Emission from Full-Energy DNB
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5
4
3
2
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Note Channel 4 has significant overlap with
channels 2,3,5 and a little overlap with channels
1 and 6!
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Imposing an 8-cm cutoff Provides Reasonable
Radial Resolution at the Plasma Edge, but still
Poor at the Center
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6-cm cutoff
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4-cm cutoff Moderate Radial Resolution in
Plasma Core
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2-cm cutoff (original assumption) Little
Channel Overlap
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Slotted Aperture of width 4, 3, 2 cm causes
signal reduction of factor 1.9, 2.5, 3.6
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TFTR DNB Scraper Schematic
bellows
liner
scraper
grid

• Oval copper lining
• Not adjustable
• Takes only small fraction of power
• No active cooling
• Radiation conduction to vacuum vessel

• 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

Thanks to Gerd Schilling
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Procedure to Compute Effect of Apertures on Beam
Size

• Launch vectors from grid, through focal point,
  onto target.
• Establish circular grid on target with diameter
  beamlet size corresponding to beam divergence.
• For each point on target grid, decide whether ray
  from grid to target hits aperture or Target.
• Increment computed power to Aperture 1, Aperture
  2 or target as appropriate.

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Aperture Distance 220 Aperture
width 10 (WIDE) FWHM
6.3 MSE
Signal 176
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Aperture Distance 220 Aperture width 2.0 FWHM 4.
6 MSE Signal 71
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Moving Aperture Closer to Plasma Makes it More
Effective (duh )
Aperture Distance 320 Aperture
width 2.0 FWHM
2.2
MSE Signal
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Summary of Single-Aperture Performance for
Locations at 2.2 and 3.2 meters from the DNB Grid
-------- 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

Not great
Pretty good, but signal is compromised
Assumptions 10 cm diameter grid, focal length
400 cm, target at 400 cm,
(1/e) beamlet divergence 1.1o beamlet
diameter 7.7 cm
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Calculations Using Two Apertures
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Summary of Two-Aperture Performance for
Locations at 2.2 and 3.2 meters from the DNB Grid
-------- 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

Assumptions 10 cm diameter grid, focal length
400 cm, target at 400 cm,
(1/e) beamlet divergence 1.1o beamlet
diameter 7.7 cm
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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
  t0, neglecting radiative losses
• DT (2q/k)(kt/p)0.5
• Copper k k / rC 1.16 10-4 m2/sec
• k 400 watts / meter / kelvin
• r 8900 kg/m3
• C 386 Joules / kg / Kelvin
• DNB qavg (5.0 Amps) (50,000) / p
  (0.09/2)2
• 3.9 107 watts/m2
• q qavg exp(-r2/s2) where s 0.6FWHM
  0.054 meters

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Surface Heating of Aperture by DNB, contd

• Assume 50 ms beam pulse DT 265 exp( -
  (r/0.054)2 ) kelvin
• Maximum surface temperature rise beam pulse for
  Copper
• Horizontal Aperture
  DTmax
• dimension (cm) 50 ms
  1000 ms
• 4 231 oC 1033
• 5 214 957
• 6 195 872
• 7 174 778
• 8 154 689
• Melting temperature of Copper 1083 oC.
• 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

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Surface Heating of Aperture by DNB, contd

• 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 1st one closer to grid
  takes most of the heat, 2nd one closer to plasma
  is inertially cooled.

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Tungsten and moly provide the best protection
against melting
Tmelt/DTheat
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Conclusions

• MSE cant provide radially-resolved q-profile
  measurements with the DNB in its present
  configuration.
• A two-aperture system looks technically feasible
  
• 1st aperture _at_end of DNB beamline - takes most of
  the heat actively cooled.
• 2nd aperture, closer to plasma, uncooled,
  provides final collimation.
• We lose about a factor 2-3 in signal strength to
  get 3 cm spatial resolution.