Scaling Laws for $e^+ e^-$ Linear Colliders

Design studies of a future TeV e+e- Linear Collider (TLC) are presently being made by five major laboratories within the framework of a world-wide collaboration. A figure of merit is defined which enables an objective comparison of these different designs. This figure of merit is shown to depend only on a small number of parameters. General scaling laws for the main beam parameters and linac parameters are derived and prove to be very effective when used as guidelines to optimize the linear collider design. By adopting appropriate parameters for beam stability, the figure of merit becomes nearly independent of accelerating gradient and RF frequency of the accelerating structures. In spite of the strong dependence of the wake-fields with frequency, the single bunch emittance preservation during acceleration along the linac is also shown to be independent of the RF frequency when using equivalent trajectory correction schemes. In this situation, beam acceleration using high frequency structures becomes very advantageous because it enables high accelerating fields to be obtained, which reduces the overall length and consequently the total cost of the linac.