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 W_cm is adjusted to 500 GeV for the convenience of comparison so that the luminosities are slightly different from those in Table 1.3. (Linear W_cm scaling rather than W_cm³ 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 W_cm=500 GeV for the parameter set A (thin solid) and Y (solid). The beam energy spread before collision is not included.

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

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