By R. Gupta
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Additional info for Thesis on Improving Design of Superconducting Magnets for Particle Accelerators
On the x-axis (midplane), = 0, these components become and on the y-axis Bx (x 0) = 0 By (x 0) = ; 2oaIo xa Bx (0 y) = 0 = 2oaIo ya By (0 y) = 2oaIo ya = 0: m;1 m;1 m;1 (1:5:97a) (1:5:97b) for m = 1 3 5 ::: for m = 2 4 6 ::: (1:5:98a) for m = 1 3 5 ::: for m = 2 4 6 ::: (1:5:98b) To obtain the eld outside the current sheet (r > a), Eqs. (1:5:44) is integrated using the trigonometric relations given in Eq. (1:5:90)and Eqs. (1:5:91) Z2 I r o o Az (r ) = ; 2 ln a cos (m ) d o 1 1 a nZ 2 X + 2o Io cos (m ) cos (n ( ; )) d n r n=1 m o therefore Az (r ) = 2omIo ar cos (m ) : The eld components for r > a are obtained using Eqs.
1:5:12). 2. Field Harmonic De nitions It is useful to describe the magnetic eld inside the aperture of accelerator magnets in terms of harmonic coe cients 96,140,144,175]. The discussion will be limited to 2dimensional analysis, which describes the eld in the body (or straight section) of a long magnet. When the magnetic eld is evaluated a few aperture diameters away from the two ends of the magnet, the axial component of the eld is negligible. The accelerator magnets examined here are those in which the eld is consists of one fundamental harmonic which is several orders of magnitude larger (usually 104) than any other harmonic present.
These are usually distinguished from the harmonics an and bn given in Eq. (1:5:17) by the use of the uppercase alphabet. The two are related as follows: By + iBx = 10;4BR0 An+1 = 10;4BR0 an Bn+1 = 10;4BR0 bn Cn+1 = 10;4BR0 cn: (1:5:21a) (1:5:21b) (1:5:21c) Using these, Eq. (1:5:20) can be written as : 1 X n;1 Cn Rz : (1:5:22) 0 n=1 In this case the summation begins from n = 1 instead of n = 0. Sometimes Cn is also written as C (n). S. laboratories. The European laboratories (such as CERN and HERA) use a slightly di erent de nition 179].
Thesis on Improving Design of Superconducting Magnets for Particle Accelerators by R. Gupta