Transverse Instabilities in the LIL

In view of a Beam Break Up (BBU) study, we have calculated and identified series of transverse deflecting modes in the S band sections of the LEP Injector Linacs (LIL). In these TW quasi-constant gradient structures with various iris diameters from 18 to 26 mm, only it-modes of the C band of the HEM11, having negative group velocities and phase velocities around c will lead to cumulative BBU. These deflecting π-modes occur at frequencies in the range from 4558 to 4290 MHz for diameters from 18 to 26 mm. Frequency variation with iris diameter is -15 MHz for each added mm for calculated and measured 0-modes and about twice that value for π-modes. Levels for starting transverse instabilities have been determined for various accelerated Beam Currents with different pulse widthes.