Theorem on magnet fringe field
- Brookhaven National Lab., Upton, NY (United States)
- Cornell Univ., Ithaca, NY (United States). Lab. of Nuclear Studies
Transverse particle motion in particle accelerators is governed almost totally by non-solenoidal magnets for which the body magnetic field can be expressed as a series expansion of the normal (b{sub n}) and skew (a{sub n}) multipoles, B{sub y} + iB{sub x} = {summation}(b{sub n} + ia{sub n})(x + iy){sup n}, where x, y, and z denote horizontal, vertical, and longitudinal (along the magnet) coordinates. Since the magnet length L is necessarily finite, deflections are actually proportional to ``field integrals`` such as {bar B}L {equivalent_to} {integral} B(x,y,z)dz where the integration range starts well before the magnet and ends well after it. For {bar a}{sub n}, {bar b}{sub n}, {bar B}{sub x}, and {bar B}{sub y} defined this way, the same expansion Eq. 1 is valid and the ``standard`` approximation is to neglect any deflections not described by this expansion, in spite of the fact that Maxwell`s equations demand the presence of longitudinal field components at the magnet ends. The purpose of this note is to provide a semi-quantitative estimate of the importance of {vert_bar}{Delta}p{sub {proportional_to}}{vert_bar}, the transverse deflection produced by the ion-gitudinal component of the fringe field at one magnet end relative to {vert_bar}{Delta}p{sub 0}{vert_bar}, the total deflection produced by passage through the whole magnet. To emphasize the generality and simplicity of the result it is given in the form of a theorem. The essence of the proof is an evaluation of the contribution of the longitudinal field B{sub x} from the vicinity of one magnet end since, along a path parallel to the magnet axis such as path BC.
- Research Organization:
- Brookhaven National Lab., Upton, NY (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC02-76CH00016
- OSTI ID:
- 220539
- Report Number(s):
- BNL--62610; CONF-9510138--4; ON: DE96007743
- Country of Publication:
- United States
- Language:
- English
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