A linear perturbation theory analysis has used to evaluate the impact of a) kick errors and b) gradient errors in this transport line. The results of this analysis can be used to estimate the response of the beam to, and thus ascertain accelerator performance in the presence of, three fundamental classes of error arising in a transport line. These are 1) alignment errors, 2) excitation errors, and 3) errors in magnetic field quality.

1) Alignment Error Effects have been studied to determine the influence of dipole and quadrupole transverse and longitudinal misalignments and roll. The principle effect of such errors is to transversely kick the beam, resulting in betatron oscillations and orbit errors. Constraining the magnitude of such orbit errors imposes a limit on the magnitude of the error source.

2) Excitation Error Effects have been studied to determine the steering effect of dipole excitation errors and the focusing effects of dipole and quadrupole excitation errors. The steering from dipole excitation errors kicks on the beam, leading to betatron oscillations and consequential orbit errors. Limits on DC dipole excitation errors can thus be set by constraining the magnitude of the resultant orbit error to some desired level. AC excitation errors lead to AC beam motions, which can be interpreted as spot size growth and/or emittance dilution. Limits on AC excitation errors may therefore be set by imposing constraints on the resultant emittance dilution.

Excitation error driven focusing effects are due to gradient errors imposed on the beam, lead to betatron mismatch and dispersion errors, and result in beam mismatch and spot growth. Specifying limits on such mismatch and growth yields constraints on the allowable associated excitation error.

3) Errors in Magnet Field Quality can be variously experienced as excitation or gradient errors. They can therefore lead either to steering (of the centroid, or differentially across the beam) or focusing effects. Field flatness, linearity, gradient, and end-field roll-off specifications can then be generated by estimating the magnitude of, and imposing limits on, the changes in beam properties driven by any of these error sources.

Last modified: 10 March 1997
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