Parametric Study: Energy Deposition in the Triplet

1
Parametric Study Energy Deposition in the
Triplet

• Franck Borgnolutti, Francesco Cerutti, Marco
  Mauri,
• Alessio Mereghetti, Ezio Todesco, Elena Wildner,
• AB/ATB and AT/MDE

2
Outline

• Background
• Parameters
• Beam Screen/Beam Pipe
• Results
• Peak energy deposition
• Total loads
• Particle Fluences
• Conclusion

3
Background, recall

• Present Triplet at 7 TeV gradient 215 T/m
• Larger aperture with same gradient
• New technology (Nb3Sn )
• Smaller beta larger apertures required
• However, with longer triplets we get lower
  gradients
• Luminosity 2.5 1034 cm-2 s -1

4
Parameter Space

• Q1 Positioned at 23 m from the IP
• Gaps between magnets 1.3 m
• Impacts the peak in energy deposition we get on
  the following magnet
• Symmetric triplet
• All magnets have the same aperture
• All magnets have the same gradient
• Q1 and Q3 have the same length
• Q2 is split in two parts of equal length
• Magnets have costheta design
• Two layers

We get one family of solutions (Aperture,
gradient, length linked)
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The Triplet Layouts
Aperture (mm) Gradient (T/m) L(Q1,Q3) (m) L(Q2a,b) (m) Total length (m)
90 156 8.69 7.46 36.2
115 125 9.98 8.42 40.7
130 112 10.81 9.04 43.6
140 104 11.41 9.49 45.7
Max (cable length)
TAS
Symmetric
Q1 Q2a Q2b Q3
IP1
Total Length
No Corrector in triplet Half Crossing angle 220
mrad vertical TAS aperture 55 mm
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The scoring

• Cable
• We make the binning for the scoring so that it
  corresponds to a minimum volume of equilibrium
  for the heat transport (cable transverse
  dimensions, with a length corresponding to the
  twist pitch of the cable)
• Total power deposited in the magnets
• The outer diameter of the magnets (cold mass) is
  the same
• The power deposited per meter of magnet
• Azimuthal integration of the power in the
  longitudinal bins

Scoring volume AL
Transverse area of cable (A)
Length (L) 10 cm (twist pitch)
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The magnet ends

• The magnets have in this study the same length as
  the magnetic length
• mechanical length magnetic length
• No coil ends are modeled (the same transverse
  layout over the whole magnet)
• No 3D field or hard edge approximation

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Beam pipe/Beam Screen dimensioning
Cold Bore Tube and Beam Screen act as shielding.
For parametric study get the minimum necessary
thicknesses for the different cases chosen

• For the Cold Bore Tube (Beam Pipe)
• Relation thickness (t) and diameter (D), valid
  for stainless steel (pressure vessel code, 25 bar
  ) t 0.0272D
• For the Beam Screen
• Calculations gave the same minimum thickness for
  all cases
• we have used 2 mm (similar as for the previous
  simulations of the upgraded triplet)

Aperture mm BP thickness mm BS thickness mm
90 2.4 1.0
115 3.0 1.0
130 3.4 1.0
140 3.7 1.0
G. Kirby, C. Rathjen
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Peak Power Deposition I
Power
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Peak Power Deposition II
Peak energy deposition in the coil for the four
analysed lay-outs versus a rescaled longitudinal
coordinate, making all magnets of the same
length.
Power
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Peak Power Deposition III
Maximum of the peak energy deposition in the coil
versus triplet aperture in Q1, Q2a, Q2b and Q3
Power
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Space available for shielding in Q1
Shield simply scaled from the study on the 130 mm
triplet for the upgrade phase1 (Q1) For proper
shielding estimation we need to run with FLUKA
Ap (mm) Beta(Q1) (m) sigma (m) beam size (m)
90 5785 0.0017 0.070
115 6529 0.0018 0.073
130 6917 0.0019 0.075
140 7194 0.0019 0.076
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Total Heat Load
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Particle type distribution, all 4 magnets

• Fluence scored in the first cable over each
  magnet.
• Interactions from material inside aperture
  (Beam Screen and Beam pipe)
• Smallest (90mm) and largest (140 mm) aperture
  will be shown

      90mm case 140mm case
photons    87.0        86.0 
neutrons    6.0         7.8
electrons   3.5         3.3
positrons   2.5         2.3
pions (/-) 0.4         0.4
protons    0.15        0.15
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Neutron Fluence 90mm/140mm
Expected tolerable limit is 1018 cm -2
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Neutron Spectra 90mm/140mm
Integral values 0.14 part cm-2 coll-1 for the 
90mm case 0.09 part cm-2 coll-1 for the 140mm
case
1 MeV neutrons most critical for damage
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Horizontal/Vertical Crossing
Can we use our results to scale without
re-computing?
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Conclusion

1. The energy deposition behavior with aperture has
   been evaluated
2. If scaled with length, we see a very similar
   deposition pattern.
3. The total heat load on the triplet is decreasing
   (up to 140 mm at least)
4. 90 mm and 36.2 m long triplet has a heat load of
   about 507 W, whereas the 130 mm aperture and 43.6
   m long has a heat load of 426 W, i.e. 16 less,
   including the beam screen.
5. The distribution of particle types in Q1 of
   particles is very similar for 90 and 140 mm. Peak
   neutron fluences below required limits (both
   cases).
6. Spectra similar, 1.5 time higher fluence for 90
   mm
7. Pattern of energy deposition is not identical for
   the two insertions (1 and 5).