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The analytical expression of the magnetic field distribution within theaperture of a circular vacuum chamber due to the induced eddy is derived. Twocases are discussed, one is the absence of iron, the other is that the vacuumchamber is between the iron poles, that implies the use of the image currentmethods. The current angular distribution in the vacuum chamber can becalculated from the ramping rate of the exposed field, then the contourintegration is applied to the circular current to obtain the fielddistribution. The formula can be used to estimate the undesired fields from acircular beam box when it is exposed to a ramping field.

An expression for the eddy field in a circular vacuum chamber for HEPS booster dipole