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1.4.2.5 Luminosity Spectrum

The electrons(positrons) emit synchrotron radiation during the collision due to the electromagnetic field (several kilo Tesla) created by the opposing beam. This phenomenon is called `beamstrahlung'. Due to the beamstrahlung the particles loose a few percent of their energies on the average. This causes a spread in the center-of-mass energy in addition to the initial beam energy spread from linacs.

The expected luminosity spectrum $d{\cal L}/dW_{cm}$is plotted in Figure 1.5 for A and Y. The high-energy end is shown in Figure 1.6. For these figures Wcm is adjusted to 500 GeV for the convenience of comparison so that the luminosities are slightly different from those in Table 1.3. (Linear Wcm scaling rather than Wcm3 is used here.) The beam energy spread before collision is not included. In Figure 1.6 the highest bin ( $499.75\leq W_{cm} \leq 500$ GeV) contains 49% (46%) for A (Y) of the total luminosity.

Both the luminosity and the average loss by beamstrahlung is proportional to the bunch population squared. When the parameter set A is achieved and if a much narrower energy spread is desired, one can reduce the beamstrahlung loss by a factor of four by making the bunch population half but with pulse structure the same as in Y. The reduction of luminosity from A is only a factor of two rather than four. This is technically even easier than A (same loading, relaxed tolerances).


  
Figure 1.5: Luminosity spectrum at Wcm=500 GeV for the parameter set A (thin solid) and Y (solid). The beam energy spread before collision is not included.


  
Figure 1.6: High-energy end of the luminosity spectrum at Wcm=500 GeV for the parameter set A (thin solid) and Y (solid). The beam energy spread before collision is not included.


next up previous contents
Next: Bibliography Up: 1.4.2 Overview of JLC Previous: 1.4.2.4 Beam Energy Spread
ACFA Linear Collider Working Group
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