By G. Dugan
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Extra info for Intro To Accelerator Physics [univ. lecture presentations]
Sample text
Calculate the cosinelike and sinelike trajectories for the line from the fields in the magnet lattice. 3. Propagate the lattice functions from the staring point through the line using the relations discussed in lecture 5. This is straightforward except for step 1. 11/21/01 USPAS Lecture 6 7 11/21/01 USPAS Lecture 6 8 If the starting point of the transfer line is the exit of a circular accelerator, then the lattice functions at this point are well-defined: they are those of the circular accelerator at the point of extraction.
5 m 11/26/01 USPAS Lecture 7 20 Linear deviations from an ideal lattice: Dipole errors and closed orbit deformations We now begin to examine the results of field errors: the differences between the real fields in a machine, and the idealized fields on which the lattice design is based. We’ll start with the simplest kind of field errors: those due to dipole fields. Dipole field errors can come from a variety of sources. Some of them are: 11/26/01 USPAS Lecture 7 21 • Dipole fields due to quadrupoles not being aligned on the reference orbit (this is usually the biggest source of error) • Differences between the idealized dipole field and the true dipole field, due to fabrication errors in the magnets, and/or due to remnant field effects • Horizontal dipole fields (causing vertical orbit errors) due to rotated dipole magnets • Dipole field errors due to misalignments of combined function magnets • Stray fields on the reference orbit from other accelerator components From Lecture 3, p 7: The trajectory equations, to lowest order in dipole field errors, are 11/26/01 USPAS Lecture 7 23 11/26/01 22 USPAS Lecture 7 ∆By ( s) 1 ; x ′′ + x k + 2 = − B0 ρ ρ y ′′ − yk = ∆Bx ( s) B0 ρ Both of the form ∆B( s) z ′′ + Kz = B0 ρ We will treat dipole errors in the “kick approximation”: Write the above equation as ∆B( s)∆s ∆( BL) = B0 ρ B0 ρ in which the field error is taken to be highly localized over a length L.
We’ll discuss several simple types of matched insertions. The result is 7 11/26/01 USPAS Lecture 7 8 s1 = µI 2 2 s = α sin µ I F = − α 2 γ γ γ 35 tan 30 Beta (m) 25 20 15 Typically, to maximize the length of the straight section s2, we α2 1 , s2 + s1 = β . For this choose µΙ = π/2, so that s1 = , s2 = γ γ insertion to match in both x and y, we need to have αx = -αy, which will be the case for a thin-lens FODO cell. 5 The insertion raises the tune of the machine by 1/4. 5 20 9 11/26/01 40 60 s(m) 80 100 10 USPAS Lecture 7 “Missing magnet” dispersion suppressor -f To fix the dispersion mismatch, we need another type of insertion: f -f f 2f -f Straight section 2.