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

The analytical expression of the magnetic field distribution within the aperture of a circular vacuum chamber due to the induced eddy is derived. Two cases are discussed, one is the absence of iron, the other is that the vacuum chamber is between the iron poles, that implies the use of the image current methods. The current angular distribution in the vacuum chamber can be calculated from the ramping rate of the exposed field, then the contour integration is applied to the circular current to obtain the field distribution. The formula can be used to estimate the undesired fields from a circular beam box when it is exposed to a ramping field.