Improving Touschek lifetime in ultralow-emittance lattices through systematic application of successive closed vertical dispersion bumps

In present ultralow-emittance storage ring designs the emittance coupling required for the production of vertically diffraction-limited synchrotron radiation in the hard x-ray regime is achieved and in many cases surpassed by a correction of the orbit and the linear optics alone. However, operating with a vertical emittance lower than required is disadvantageous, since it decreases Touschek lifetime and reduces brightness due to the transverse emittance increase from intrabeam scattering. In this paper we present a scheme consisting of closed vertical dispersion bumps successively excited in each arc of the storage ring by skew quadrupoles that couple horizontal dispersion into the vertical plane to a desired level and thereby raise the vertical emittance in a controlled fashion. A systematic approach to vertical dispersion bumps has been developed that suppresses dispersion and betatron coupling in the straight sections in order to maintain a small projected emittance for insertion devices. In this way, beam lifetime can be significantly increased without negatively impacting insertion device source properties and hence brightness. Using simulation results for the MAX IV 3 GeV storage ring including magnet and alignment imperfections we demonstrate that Touschek lifetime can be increased by more than a factor 2 by adjusting the vertical emittance from 1.3 pm rad (after orbit correction) to 8 pm rad (after application of dispersion bumps) using two to three independent skew quadrupole families all the while ensuring deviations from design optics are restrained to a minimum.

Figure 1

Design optics of the MAX IV 3 GeV storage ring in one achromat. The design vertical dispersion is zero everywhere. The positions of the magnets are indicated at the bottom in black. The positions and names of sextupole and octupole magnets, equipped with auxiliary coils to generate skew quadrupole gradients, are indicated below. The sequence of magnets repeats mirror-symmetrically throughout the second half of the achromat.

Figure 2

Ideal vertical dispersion in Cases 1 to 3. Approximately 6.6 pm rad of vertical emittance is created in the ideal lattice which gives on average 7.9 pm rad when including imperfections.

Figure 3

Difference between the design optics functions and the optics functions from SCVDB lattices. For all cases, the vertical emittance is 6.6 pm rad in the ideal lattice and on average 7.9 pm rad when including imperfections.

Figure 4

SCVDB scaling in the ideal lattice of Case 3. Indicated with a solid line is the vertical dispersion that creates 6.6 pm rad of vertical emittance in the ideal lattice and on average 7.8 pm rad when including imperfections. The dashed lines show the vertical dispersions of scaled SCVDBs that create ${\mathcal{E}}_{\mathrm{II}}=0.9$, 1.8, 4.1, 8.9 and 11.4 pm rad in the ideal lattice, respectively.

Figure 5

Vertical emittance scales with skew quadrupole gradient squared. Ideal lattice (x) and error lattice (o) with standard deviations from 10 error seeds. Only the $k$ of the strongest skew quadrupole involved in each case is considered.

Figure 6

Vertical dispersion in the entire storage ring (20 achromats) for the design lattice and Case 3 lattice with identical error seed for two scalings. The ideal lattice SCVDB is shown for comparison.

Figure 7

Detail of vertical dispersion Case 3 in five achromats. Adding the vertical dispersion from the two independent sources, lattice imperfections and SCVDBs, linearly leads to a good estimate of the vertical dispersion under the influence of lattice errors.

Figure 8

Beam tilt angle $\mathrm{\Theta }$ in the ideal lattice.

Figure 9

Vertical projected emittance ${\epsilon }_y$ (solid lines) and vertical eigenemittance ${\mathcal{E}}_{\mathrm{II}}$ (dashed lines) in the ideal lattice for the three cases. (Markers are displayed for Case 1 since traces partially overlap.)

Figure 10

Vertical projected emittance ${\epsilon }_y$ in the long straight sections (ID locations) including lattice imperfections (10 error seeds) for the design optics and the three SCVDB cases.

Figure 11

Touschek lifetime as a function of skew quadrupole gradient. Tracking with errors, average and standard deviation for 10 seeds. Only the gradient of the strongest skew quadrupole used in each case is considered in this plot.

Figure 12

Momentum aperture from 10 error seeds for the 3 cases, compared to design lattice (black) in the first achromat. The SCVDB lattices are scaled to approximately ${\mathcal{E}}_{\mathrm{II}}=8\mathrm{pm}\mathrm{rad}$ while the design lattice with errors is on average at 1.3 pm rad.

Figure 13

Dynamic aperture for the ideal lattice and 10 error seeds. (a) shows the design lattice and (b)–(d) show the three SCVDB cases. The DA was calculated at the center of the first long straight section, close to the injection point.

Figure 14

Amplitude dependent tune shifts [horizontal tune (${\nu }_x$)] for the design lattice and Case 1 and 3 SCVDB lattices, adjusted for ${\mathcal{E}}_{\mathrm{II}}=6.6\mathrm{pm}\mathrm{rad}$ without errors. Ideal lattice in blue (horizontal) and red (vertical). Ten error seeds in gray.

Figure 15

Chromatic tune shifts for the design lattice and the Case 3 SCVDB lattice, adjusted for ${\mathcal{E}}_{\mathrm{II}}=6.6\mathrm{pm}\mathrm{rad}$ without errors. Ideal lattice in blue (horizontal) and red (vertical). Ten error seeds in gray.