Carbon Wire Heating due to Scattering in the SNS

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SNS Wire Scanner Preliminary Design Review
Carbon Wire Heating due to Scattering in the SNS
By
C. J. Liaw, BNL
July 17, 2001
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Assumptions

• Beam Energy
• Injection Line H- beam, From 2.5 MeV (MEBT)
  to 1.0 GeV (HEBT)
• Accumulator ring RTBT 1.0 GeV Proton beam
• Beam profile
• 2-D Gaussian distributed in the injection line
• Quasi-uniform in the ring RTBT

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Assumptions
Carbon wire  Size 32 mm dia. Stationary at the
center of the beam
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Assumptions

• Possible wire heating scenarios in the injection
  line 
• Beam currents over a pulse
• 16 mA (1 MW case) and 36 mA (2 MW case)
• Repetition rate and pulse length
• 60 Hz,1 ms long
• 6 Hz, 1 ms long
• 6 Hz, 50 ms long

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Assumptions
Wire heating in the ring

• Beam current over a pulse
• 16 mA (1 MW case) and 32 mA (2 MW case)
• Repetition rate and pulse length 60 Hz and 1ms
  long
• Beam size (H x V)
• Increase from 3.1 mm x 3.8 mm to 56 mm x 68 mm
  in 1 ms or Cross section area A 6.45 x
  10-63.09t m2, where t time sec

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Assumptions
Wire heating in RTBT

• Beam current over a pulse
• 16 mA (1 MW case) and 32 mA (2 MW case)
• Repetition rate and pulse length 60 Hz and 695
  ns long
• Minimum beam size (H x V) 56 mm x 68 mm

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Assumptions
Radiative cooling is the only cooling
mechanism.  Thermal properties of
carbon  Density 2000 kg/m3 Radiant emissivity
0.8 Heat capacity (temperature dependent)
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Carbon Heat Capacity
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POWER DEPOSITION ON THE CARBON WIRE
Beam Energy Loss Due To Scattering

• For 2.5 MeV 1 GeV H- beam
• P 1/r(dE/dx)p rI x 2 Pe watts/m2
• For 1 GeV proton beam
• P 1/r(dE/dx)p rIx watts/m2
• where Pe 1/r(dE/dx)e rIx (1/r(dE/dx)ex lt Ps)
• Ps (1/r(dE/dx)ex gt Ps)
• Ps power to stop an electron beam
  eV,
• I beam current density A/m2
• 1/r(dE/dx)p and 1/r(dE/dx)e Collision
  energy loss of the proton and the electron beam
  through the carbon wire MeV/g/cm2.

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dE/dx of H- beam through carbon wire
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Heating Efficiency of Carbon Wire, h
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Power Deposition On The Carbon Wire
Pd P x h
Deposition power density
Beam energy loss density
Heating efficiency
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Governing Equation
dT/dt 4/(rpdc)(Ph-pse(T4-T04))  where T
wire temperature K To beam pipe
temperature 297 K d diameter
of the wire m t time sec
h heating efficiency
s Stefan Boltzmann constant 5.67 x 10-8
W/m2K4 r, e, c, and P are
defined above.
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Max. Wire Temperature In The Injection Line (1 MW
case)
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Max. Wire Temperature In The Injection Line (2 MW
case)
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Maximum Wire Temperature In The Ring
Stationary or crawling wire 1 MW case 398
K 2 MW case 450 K
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Maximum Wire Temperature In RTBT
Stationary or crawling wire 1 MW case 396 K 2
MW case 460 K
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CONCLUSIONS

• Carbon wires will survive (i.e. wire
  temperature lt 2000 K) in the entire injection
  line with a 6 Hz/50 ms H- beam and can only be
  used in the higher energy region with the 6 Hz/ 1
  ms and 60 Hz/1 ms H- beam.
• The wire temperatures in the ring and RTBT are
  low. Lifetime of the carbon wire is not an
  issue in these regions.