Toward a diffraction limited light source

This paper introduces a storage ring lattice design for synchrotron radiation sources which fulfills all the required features for the realization of a diffraction limited light source. Insertion devices half gaps of $2.5\mathrm{m}\mathrm{m}$ are assumed and enabled by the design of dedicated straight sections. The use of long straight sections is possible for such a lattice and led to the definition of a set of transparency conditions used to minimize the effect of such insertions for on- and off- energy beam dynamics. The design proposed enables an extremely long Touschek lifetime and beam accumulation. A real case study will be shown for large circumference storage ring upgrade lattices.

Figure 1

Dynamic aperture and Touschek lifetime for some of the past, present, and future SR light sources. The size of the circles is representative of the DA and the color is proportional to TL. The data sources for this figure are found in [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36].

Figure 2

Optics functions and magnet layout for a DBA lattice cell.

Figure 3

Optics functions and magnet layout for a 7BA lattice cell.

Figure 4

Optics functions and magnet layout for the EBS H7BA cell.

Figure 5

Optics functions and magnet layout for an H6BA lattice cell designed for a 6 GeV, 72 cells SR lattice.

Figure 6

Footprint of an SR similar to PETRA composed of 72 cells divided in eight ARCs, four long straight sections, and four short straight sections. One of the short straight sections is dedicated to rf and one to injection.

Figure 7

H6BA CELL-D lattice cell.

Figure 8

Example of the long straight section, $L=103\mathrm{m}$, with two peculiar regions with ${\beta }_h={\beta }_v=5\mathrm{m}$ at $s\sim 30$ and 120 m.

Figure 9

Injection straight section, beam abort septum at $s=42\mathrm{m}$, and injection septum at $s=67\mathrm{m}$ with ${\beta }_h=42\mathrm{m}$.

Figure 10

Variation of tunes with amplitude at the center of an ID straight section (${\beta }_h={\beta }_v=2.25\mathrm{m}$) for a lattice composed of only Cell-U ($CEL{L}_U$ in the legend) or including eight SSs ($FULL$ in the legend) following the transparency conditions.

Figure 11

Variation of tunes with momentum at the center of an ID straight section (${\beta }_h={\beta }_v=2.25\mathrm{m}$) for a lattice composed of only Cell-U ($CEL{L}_U$ in the legend) or including eight SSs ($FULL$ in the legend) following the transparency conditions.

Figure 12

Possible ring layout including five ARC-Us, three ARC-Ds, three short (56.8 m) SSs, four long (103 m) SSs, and one injection SS.

Figure 13

Chromaticity working point scan. The size of each dot is proportional to the DA (also mentioned in red text in mm). The color is proportional to the average EA along s (Mom. Acc. in the figure label). All values are averaged for five seeds of small alignment errors ${\sigma }_x={\sigma }_y=1\mathrm{\mu }\mathrm{m}$ in all quadrupoles and sextupoles (without correction). The tune working point for this scan is fixed to ($Q_h=134.2$, $Q_v=73.2$). For DA and EA, 6D tracking with rf and radiation is performed for 2048 turns. The emittance contour lines correspond to the average emittance of lattices without optics correction.

Figure 14

CELL-U Tune working point scan. The size of each dot is proportional to the DA (also mentioned in red text in mm). The color is proportional to the average EA along s (Mom. Acc. in the figure label). All values are averaged for five seeds of small alignment errors ${\sigma }_x={\sigma }_y=1\mathrm{\mu }\mathrm{m}$ in all quadrupoles and sextupoles (without correction). For DA and EA, 6D tracking with rf and radiation is performed for 2048 turns.

Figure 15

OD1 and DECF working point scan (variation compared to starting values). The size of each dot is proportional to the DA (also mentioned in red text in mm). The color is proportional to the average EA along s (Mom. Acc. in the figure label). The values are averaged for five seeds of small alignment errors ${\sigma }_x={\sigma }_y=1\mathrm{\mu }\mathrm{m}$ in all quadrupoles and sextupoles (without correction). For DA and EA, 6D tracking with rf and radiation is performed for 2048 turns. The emittance contour lines correspond to the average emittance of lattices without optics correction.

Figure 16

Dynamic aperture scaled at ${\beta }_{h,v}=(32.0,11.8)$ for four cases: the full ring layout (including eight SSs), a lattice without long straight sections (“U-D cells only” in legend corresponds to perfect ring), a full ring coupled layout including SSs and random skew quadrupoles to produce full coupling and a full ring with errors. DA limits are determined using 6D tracking simulations of 2048 SR turns with rf and radiation. Tunes and chromaticities for each case are listed in Table 4. Tunes and chromaticities for the case with errors are corrected to the full ring case.

Figure 17

Maximum horizontal dynamic aperture vs $\delta p/p$ energy deviation scaled at ${\beta }_{h,v}=(32.0,11.8)\mathrm{m}$ for four cases: the full ring layout (including 8 SSs), a lattice without long straight sections (“U-D cells only” in legend corresponds to perfect ring), a full ring coupled layout including SSs and random skew quadrupoles to produce full coupling and a full ring with errors. The limits are determined using 6D tracking simulations of 2048 SR turns with rf and radiation. Tunes and chromaticities for each case are listed in Tab. 4. Tunes and chromaticities for the case with errors are corrected to the full ring case.

Figure 18

Energy acceptance for four cases: the full ring layout (including eight SSs), a lattice without long straight sections (“U-D cells only” in legend corresponds to perfect ring), a full ring coupled layout including SSs and random skew quadrupoles to produce full coupling and a full ring with errors. The limits are determined using 6D tracking simulations of 2048 SR turns with rf and radiation. The figure concerns the first 35 m of ARC-U in every case. Tunes and chromaticities for each case are listed in Table 4. Tunes and chromaticities for the case with errors are corrected to the full ring case.

Figure 19

Frequency map analysis for full ring with errors. Configuration space is shown on the top, tune space on the bottom. The diffusion rates are computed based on 6D tracking performed over 2048 turns without radiation.

Figure 20

Bunch length and Touschek lifetime vs rf voltage for a full ring lattice.

Figure 21

Injected and stored beam (not to scale) at injection. The beta at injection for this lattice is ${\beta }_{x,y}=(42.0\mathrm{m},6.05\mathrm{m})$.

Figure 22

Trajectory of electrons injected (center of the injected beam) and horizontal apertures. Only the first 1 km is shown for display purposes.

Figure 23

Location of lost particles during 1000 turns tracking of a 6D beam composed of 2048 $e^{-}$ injected: at the optimal injection position (top), with a too large horizontal position (bottom). All particles are intercepted by the protection scrapers.

Figure 24

EBS cell assembled.