By Bichowsky F.R., Urey H.C.
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Extra info for A Possible Explanation of the Relativity Doublets and Anomalous Zeeman Effect by Means of a Magnetic Electron
7 11 Horizontal/Vertical and Skew Quadrupole Correctors Specialized Magnets Specialized magnets are used for injection and/or extration of charged particle beams into/out of accelerator rings. Normally, injection requires the buildup of current into the ring and occurs after previously stored beam is circulating in the ring. In order to ensure that the injected beam is stored (incorporated with the previously injected beam), it must be injected as transversely close to the central orbit of the circulating beam as possible.
Therefore, dA dV_ i dy dy and B* = Bx - iBy = iF'(z) ( dA dV\ dA \ dy dy J dy dV dy . Equating the real and imaginary parts of the expression, from eq. 16), Bx = -^and Bv = - ^ eta; ax or from eq. 17), Bx = ^ - and B y = - — . 19) Either the vector or scalar potentials can be used. The Cauchy-Riemann conditions are satisfied for the complex conjugate of the field, B*, but not for B = Bx + iBy. The expressions in two dimensions are consistent with the more general three-dimensional expressions.
The mathematical conformal mapping algorithms developed in the last chapter are useful for desigining a quadrupole magnet whose field quality corresponds to the uniformity of a window-frame dipole. The following example describing the means of designing a septum quadrupole demonstrates this technique. The Septum Quadrupole Colliders typically intersect high energy particle beams travelling in opposite directions crossing at narrow angles. In order to maximize the number of collisions, the two beams must be tightly focused with final focus lenses longitudinally close to the interaction point.