Trapped Modes in LHC Collimator II

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Trapped Modes in LHC Collimator (II) Liling
Xiao Advanced Computations Department SLAC
National Accelerator Laboratory
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Beam Frequency Spectrum
s7.6cm
900MHz
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Simulation Model for LHC Collimator
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Longitudinal Trapped Modes
With magnetic boundary conditions on x and y
symmetric planes, modes with Ez component on
z-axis are determined.

A quarter structure When the beam crosses
the collimator, these modes will be excited that
result in beam energy loss and collimator power
dissipation. Beam heating due to these trapped
modes will vary depending on the opening of the
two jaws. When the two jaws are fully opened with
gap42mm, the beam heating is getting the
largest. So we only calculated the trapped modes
when the two jaws are fully opened.
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Loss Factors
Gap42mm
Form factor not included.
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Lower Longitudinal Trapped Modes
E-Field
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Lower Longitudinal Trapped Modes
Round Tank
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Power Dissipation
For gap42mm with rectrangular tank
Pdissipation15 W For gap42mm with round tank
Pdissipation515 W In round tank, modes spread
around the tank and have higher Q. In
rectangular tank, modes localize between the jaw
and the chamber wall and have lower Q.
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Shunt Impedance
Rlt10Kohm
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How To Reduce the Q
2. Put the lossy material along the jaws.
What is the acceptable number for the power
dissipation on the wall?
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Transverse Trapped Modes
With magnetic boundary condition on y-plane and
electric boundary on x-plane, modes with strong
Ey component between the two jaws are determined.
When beam crosses the collimator, these
modes will be excited and generate transverse
kick in the y-direction as well as beam energy
loss. Due to the small gap of the jaws, the Ey
component is very strong over the full length of
the collimator especially when the two jaws are
fully inserted with gap2mm. So we only
calculated trapped modes when the two jaws are
closed.
A quarter structure
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Kick Factors of Trapped Modes
Form factor not included
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Loss Factors of Trapped Modes
Rectangular Tank
Round Tank
Form factor not included Loss factors of
transverse modes depend on the beam offset.
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Power Dissipation
These modes can also cause beam energy loss that
strongly depends on the beam offset.