Betatron Stopbands in the VEPP-2000 Collider

The final-focus solenoids of the VEPP‑2000 round-beam e⁺e⁻ collider are able to cause stopbands in the betatron tune plane. The available tune space in the most important region near the parametric resonances (above the integer tunes) is limited by this specific stopband domain. The combined effect of the decompensated solenoids and the parametric resonances at the integers is theoretically studied. The results are complemented with numerical investigations and simulation using the RING program. The stability domain boundaries in the betatron tune plane have been experimentally determined, and their position is in good agreement with the theoretical expectations.