Remarks on the Concept of Dispersion in a Curved Linac

摘要

A next-generation linear collider is expected to span tens of kilometers in length. For various reasons, it may be desirable to house such an accelerator in a tunnel that follows the earth's curvature rather that in a 'laser-straight' tunnel. One side effect of opting for a curved linac is the introduction of vertical dispersion. In recent years, much work has been dedicated to understand and evaluate the impact of the presence of dispersion on emittance preservation. While performing simulations with our in-house code (CHEF) we observed a discrepancy between the dispersion function it produces and that computed using other codes in use within the accelerator community. Understanding the origin and the meaning of this discrepancy required a re-examination of the meaning of the concept of dispersion in the context of a linac. The object of this note is to document our findings. We establish that the default dispersion algorithm used by CHEF corresponds to a different, and ultimately more appropriate, definition of the dispersion in presence of acceleration. Not surprisingly, a consistent definition of dispersion restores agreement between codes.