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Ferrite and Compensator Symmetry Requirements for Gradient Magnets

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Submitted by:
Ruth A. Becker
Updated by:
Bruce C. Brown
Document Created:
19 Dec 1997, 00:00
Contents Revised:
19 Dec 1997, 00:00
Metadata Revised:
19 Dec 1997, 00:00
Actually Revised:
09 Jun 2003, 14:46
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19 Dec 1997, 00:00
Formulas are derived which relate strength and asymmetry between magnet top and bottom poles of ferrite and compensator to the strength and temperature compensation of the magnetic field and the skew quadrupole moment and its temperature dependence in dipole or gradient dipole magnets. Applying these formulas will allow one to judge to what extent the symmetry must be maintained separately for ferrite and compensator and the interaction between compensation and asymmetry. We find for Recycler Ring materials, if $\alpha \approx 1/40 $ is the ratio of the skew quad to the top-bottom asymmetry in magnetic potential, to keep $|a_1| < 1$ unit at operating temperature, we need the asymmetry of the ferrite, $\delta_F < 36$ units. Since the compensator contributes much less field change, $\delta_C < 394$ units is sufficient. This symmetry will result in $da_1/dT$ less than 0.02 units$^o$C which is sufficient for Recycler Ring requirements.
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