Resolution and systematic limitations in beam-based alignment

Beam-based alignment of quadrupoles by variation of quadrupole strength is a widely used technique in accelerators today. We describe the dominant systematic limitation of such algorithms, which arises from the change in the center position of the quadrupole as the strength is varied, and derive expressions for the resulting error. In addition, we derive an expression for the statistical resolution of such techniques in a periodic transport line, given knowledge of the line's transport matrices, the resolution of the beam position monitor system, and the details of the strength variation procedure. These results are applied to the Next Linear Collider main linear accelerator, an 11 km accelerator containing 750 quadrupoles and 5 000 accelerator structures. We find that, in principle, a statistical resolution of 1μm is easily achievable, but the systematic error due to variation of the magnetic centers could be several times larger.