Speakers
Description
The GHOST collider final focus system is a pure quadrupole-drift beamline targeting $\beta^* = 2$ mm at four serial interaction points, with peak $\beta$-functions reaching ${\sim}65$ km in the final triplet. Beam tracking simulations reveal that a nominal bunch develops a pronounced C-shape in longitudinal phase space at IP1, where $\sigma_z$ grows from $0.15$ mm to ${\sim}2.3$ mm—a factor of ${\sim}15\times$ increase that directly reduces luminosity. This mechanism is identified as chromatically amplified betatron path length, where off-momentum particles acquire enlarged betatron amplitudes in the high-$\beta$ final triplet, generating excess path length via the geometric $\Delta z = - \frac{1}{2} \int (x'^2 + y'^2) \, ds$ integral. Within the monoenergetic Balandin framework, $\epsilon^2\xi_2$ with $\xi = - \frac{1}{2} \int \gamma \, ds$ dominates $\epsilon^2W^2$ by over four million times; the full beam $\sigma_z$ is a further factor of ${\sim}27$ larger, driven by $\sigma_\delta$-induced chromatic amplitude growth. Phase-advance scans confirm that $\sigma_z$ is insensitive to the apochromatic ($W \approx 0$) condition, and when combined with the geometric hourglass effect, this distortion poses a significant challenge to maximizing luminosity within the current lattice design.
| Paper status | Resubmitted proceeding files received and assigned to an editor. Accepted by Submitter. |
|---|