Stability of a colliding beam in a linear collider

Plasma fluid instabilities of a beam collision in a linear collider are studied. A dispersion relation for the instability of arbitrary order is derived from both the fluid equation and the kinetic equation. The analysis shows that for a single collision these instabilities are negligible even for a large disruption parameter (e.g., ≅ 10). However, in the multiple-bunch collision case, the cumulative effect of small growth of instability may reduce the luminosity in spite of the small disruption parameter for each bunch. (orig.)