A4 Magnetic Field Errors and Misalignment

Topic

No real magnet exactly reproduces the ideal magnetic field assumed in the design of the optics described in fundamentals: manufacturing imperfections, assembly tolerances and the physical position of the magnet with respect to the ideal path inevitably introduce small deviations from the nominal behavior. A dipole magnet whose field differs slightly from the design value, or is slightly misaligned from the ideal path, introduces a small deviation in the beam orbit at that point, which is then propagated and amplified through the rest of the machine according to the local optics; the sum of many of these small errors distributed over thousands of magnets across a large machine can produce a cumulative orbit distortion considerably larger than any individual error, if not actively corrected. Similarly, a misaligned quadrupole not only imperfectly defocuses the beam but, being offset from the axis, also introduces an unwanted parasitic dipole effect, also contributing to orbit distortion. To counteract these effects, every modern machine includes an orbit correction system: a set of small corrective magnets distributed throughout the machine, whose current is adjusted from the readings of the beam position monitors that the diagnostic part describes, to cancel the measured distortion and return the orbit as close as possible to the design trajectory, thus closing the loop between error measurement and its correction. Beyond shifting the orbit, these same field errors can also directly excite the dangerous resonances already identified, especially when the error has a periodicity that matches the nominal betatronic wavenumber of the beam. That is why this module, which opens with magnets that are never perfect, closes with a correction system that compensates for that imperfection only because it was previously measured precisely.

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