The vertical emittance of the MAX IV 3 GeV storage ring was specified in the DDR [1] to be 8 pm rad, aiming for the diffraction limit at 1 Å synchrotron radiation. A proposed high-brightness operation mode [2] requires 2 pm rad vertical emittance, while the vertical emittance resulting from lattice imperfections (magnet misalignments and field errors) is expected to be as low as 1.3 pm rad. Since operating with lower vertical emittance than required decreases Touschek lifetime and may even lead to increased emittance blowup from intrabeam scattering, the vertical emittance should therefore be adjusted to the desired values.

Studies have been performed [3] to increase vertical emittance in a controlled fashion by introducing vertical dispersion through skew quadrupole magnets in the arcs of the MAX IV 3 GeV storage ring. Following a systematic approach, sets of skew quadrupole magnets and their gradients have been determined to effectively raise the vertical emittance while restraining the effect on ID source properties in the long straight sections, as well as other deviations from design optics, to a minimum. Since Touschek lifetime scales roughly like the square root of vertical emittance, these successive closed vertical dispersion bumps (SCVDBs) offer a way to significantly increase beam lifetime.

The MAX IV 3 GeV ring has been equipped with a large number of auxiliary coils on sextupole and octupole magnets from the start that can, among others, be powered as skew quadrupoles. design_latticeWPiThese magnets are indicated in the figure to the left for one half of the achromat.

With scalingexamplesian approach based on singular value decomposition (SVD), sets of skew quadrupoles and their gradients can be found that generate vertical dispersion in the arc to a desired level while maintaining the design optics in the long straight sections where IDs are situated. The solid line in the figure to the right shows a vertical dispersion bump built with 3 independent skew quadrupole pairs that generate 6.6 pm rad vertical emittance in addition to 1.3 pm rad from lattice imperfections when applied to each achromat in the storage ring.

The vertical dispersion bump amplitude can easily be changed by varying gradients of the involved skew quadrupoles proportionally (dashed lines in above figure). scaling_epsyirmThe resulting vertical emittance is shown as a function of normalized skew quadrupole gradient for the ideal lattice (x) and a lattice including imperfections (o) in the figure to the left. The vertical emittance generated in the ideal lattice is proportional to the square of the quadrupole gradient, which simplifies the vertical emittance adjustments to desired values in practice.

The Touschek lifetime has been determined by tracking with the Tracy-3 code and including lattice imperfections. The results are shown in the figure below for three different sets of skew quadrupoles: Case 1, 2 and 3 employ 1, 2 and 3 independent pairs of skew quadrupoles, respectively, in each achromat to generate the desired vertical emittance. scaling_tauiDeviations from the design lattice can be minimized by employing additional pairs of skew quadrupoles (adding degrees of freedom). For Case 3, the resulting Touschek lifetime is close to what would be expected from the square root dependence of the Touschek lifetime on vertical emittance (indicated by the dashed line in the figure above). Studies have shown that the dynamic aperture in the long straight remains high, which is an important criterion for the planned on-axis injection.

One opportunity for verification of the implemented SCVDBs (except for LOCO fits and lifetime measurements) is the diagnostic beamline in the MAX IV 3GeV storage ring [4]. This beamline is based on imaging with visible to UV synchrotron radiation from a dipole bending magnet and is capable of resolving transverse beam sizes as well as dispersion. Since a large number of auxiliary coils are already equipped with magnet power supplies, a campaign including experimental implementation and verification of SCVDBs is in preparation and results are to be presented at IPAC 2016 [5].


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Last updated: June 9, 2016


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