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K.Yokoya derived a theoretical expression of wakefield induced by the
collimators, which shall be compared to a measurement.
The emittance growth due to the wakefield is expressed by,
 
(3) 
where is the resistive
depth of material of the collimator, and is the conductivity, and N,
, , are the intensity/bunch, (vertical)
invariant emittance, vertical beam size, bunch length of the beam,
respectively. r_{e} is the electron classical radius. The geometrical
parameters of the collimator are displayed in Fig.3.
Figure 3:
Geometry of a collimator.

There is the optimal angle () minimizing the , that is,
. With this angle and
instead of and , the is,
 
(4) 
where is the Lorentz factor, E_{beam} /m_{e}.
The emittance growth should be less than 1% so that the total growth due to 6
collimators is less than 6%. Assuming that the surface of the collimator is
plated by copper, the aperture (a) of the collimator must be 250
(204)m corresponding to 70.4 (56.9) with the length of 20
(10)cm, N = 10^{10}/bunch =80m and =400m at
E_{beam}=750GeV, where the optimal angle () is 1.05^{o}
(1.17^{o}) .
Next: muon background
Up: Collimation
Previous: material
Toshiaki Tauchi
12/20/1999