Beam dynamics and expected performance of Sweden’s new storage-ring light source: MAX IV

MAX IV will be Sweden’s next-generation high-performance synchrotron radiation source. The project has recently been granted funding and construction is scheduled to begin in 2010. User operation for a broad and international user community should commence in 2015. The facility is comprised of two storage rings optimized for different wavelength ranges, a linac-based short-pulse facility and a free-electron laser for the production of coherent radiation. The main radiation source of MAX IV will be a 528 m ultralow emittance storage ring operated at 3 GeV for the generation of high-brightness hard x rays. This storage ring was designed to meet the requirements of state-of-the-art insertion devices which will be installed in nineteen 5 m long dispersion-free straight sections. The storage ring is based on a novel multibend achromat design delivering an unprecedented horizontal bare lattice emittance of 0.33 nm rad and a vertical emittance below the 8 pm rad diffraction limit for 1 Å radiation. In this paper we present the beam dynamics considerations behind this storage-ring design and detail its expected unique performance.

Figure 1

Schematic of one of the 20 achromats in the 3 GeV storage ring. Magnets indicated are gradient dipoles (blue), focusing quadrupoles (red), sextupoles (green), and octupoles (brown).

Figure 2

Beta functions ${\beta }_x$, ${\beta }_y$ and dispersion ${\eta }_x$ for one achromat of the 3 GeV storage ring. The position of the dipoles, quadrupoles, and sextupoles are indicated at the bottom.

Figure 3

Amplitude-dependent tune shifts for the 3 GeV storage-ring bare lattice. Sextupoles and octupoles have been included in this calculation.

Figure 4

Chromaticity for the 3 GeV storage-ring bare lattice. Sextupoles and octupoles have been included in this calculation. The linear chromaticity has been corrected to $+1.0$ in both planes.

Figure 5

Dependence of the beta functions (at the center of the long straight section) on momentum deviation for the bare lattice. Sextupoles and octupoles have been included in this calculation.

Figure 6

Illustration of the unit cell dipole magnet block. The common iron block integrates the unit cell dipole and the two flanking defocusing sextupoles. Further integration of the unit cell focusing quadrupoles and focusing sextupole is presently under consideration.

Figure 7

Illustration of the matching cell magnet block. The common block integrates the 1.5° soft-end dipole, the final focusing quadrupole doublet, three octupoles, and two BPM/corrector pairs.

Figure 8

Dynamic aperture at the center of the 5 m long straight section for the 3 GeV storage ring with four PMDWs installed. The data results from 6D tracking in Tracy-3 for one synchrotron period ($\approx 500$ turns).

Figure 9

On-momentum dynamic aperture at the center of the 5 m long straight section for the 3 GeV storage ring with four PMDWs installed. The crosses show dynamic aperture results for 20 seeds with random error distributions (misalignments and higher-order multipole errors assigned to quadrupoles and sextupoles) and applied orbit correction. While the dynamic aperture is reduced when the errors are included, it still substantially exceeds the requirements.

Figure 10

Diffusion map (2000 turns) at the center of the 5 m long straight section for the 3 GeV storage ring with four PMDWs installed. The scale is logarithmic in tune shift from low (blue) to high (red).

Figure 11

Diffusion map (top) and corresponding frequency map (bottom) for on-momentum particles in the 3 GeV storage ring with four PMDWs installed (2000 turns). The scale is logarithmic in tune shift from low (blue) to high (red). Note that compared to the diffusion map given in Fig. 10 the scale here has been shifted to lower diffusion rates by an order of magnitude.

Figure 12

Diffusion map taken at the center of the long straight section for off-momentum particles in the 3 GeV storage ring with four PMDWs installed. The scale is logarithmic in tune shift from low (blue) to high (red).

Figure 13

Diffusion map (top) and frequency map (bottom) for off-momentum particles in the 3 GeV storage ring with four PMDWs installed. The scale is logarithmic in tune shift from low (blue) to high (red). The linear chromaticity has been adjusted to $+1.0$ in both planes. The “wrap up” of the chromatic tune shift around the working point is clearly recognized.

Figure 14

Momentum acceptance for one achromat of the error-free MAX IV 3 GeV storage ring calculated with Tracy-3 in 6D. Three configurations of the storage ring are displayed: the bare lattice ($V_{\mathrm{cav}}=1.5\mathrm{MV}\to {\delta }_{\mathrm{rf}}=6.2\%$), a lattice with four PMDWs ($V_{\mathrm{cav}}=1.5\mathrm{MV}\to {\delta }_{\mathrm{rf}}=5.3\%$), as well as a lattice containing four PMDWs and ten IVUs ($V_{\mathrm{cav}}=2.0\mathrm{MV}\to {\delta }_{\mathrm{rf}}=5.8\%$). The position of the dipoles, quadrupoles, and sextupoles are indicated at the center.

Figure 15

The trend line shows Touschek lifetime for the bare lattice (IBS neglected) if it were possible to vary the lattice emittance while keeping the energy spread constant. Specific configurations (bare lattice, four PMDWs, and four PMDWs plus ten IVUs; all including LCs) are indicated by crosses and dots. Crosses indicate IBS neglected, dots indicate IBS included. The enlarged segment illustrates the effect of IBS for the bare lattice configuration: while the IBS emittance growth ($+{\epsilon }_x$) leads to a decrease of Touschek lifetime, the IBS energy spread growth ($+{\sigma }_{\delta }$) leads to an increase of Touschek lifetime.

Figure 16

Touschek lifetime vs horizontal emittance for different configurations of the MAX IV 3 GeV storage ring: bare lattice, lattice with four PMDWs, lattice with four PMDWs and ten IVUs. Where indicated, the effect of the Landau cavities (LC) has been included (with bunch lengthening to ${\sigma }_s=50\mathrm{mm}$ assumed). The vertical emittance ${\epsilon }_y=8\mathrm{pm}\mathrm{rad}$ and rf acceptance ${\delta }_{\mathrm{rf}}=4.5\%$ were kept constant. The effect of IBS is indicated by arrows. Crosses indicate IBS neglected, dots indicate IBS included.

Figure 17

Brilliance limit for the MAX IV 3 GeV storage ring for in-vacuum permanent-magnet undulators (PMU), cryogenically cooled in-vacuum undulators (CPMU), and superconducting undulators (SCU). The undulator parameters are given in Table .