The magnetic design of the ALBA storage ring (SR) is based on a modified Chasman-Green (Double Bend) lattice. The basic unit cell (repetitive structure) is an arrangement of two bending magnets accompanied by quadrupoles that produce non-zero dispersion in the straight lines between cells. Despite dispersion contributes to the radiation apparent beam size, the ALBA lattice design minimizes it while maximizing the available space in the straight sections.

The straight sections at ALBA are called LSS (long), MSS (medium) and SSS (short). The unit cell has MSS with small beta values which has very good properties to allow the installation of insertion devices, however they are not long enough to accommodate the injection straight. So, modified cells, called matching cells, are used to accommodate LSS. The following table summarizes the main parameters of the ALBA storage ring.


Nominal energy (GeV) E 3.0
Circumference (m) C 268.8003
Revolution period (ns) / frequency  (MHz) 896.62 / 1.1153
Nb of cells ; nb of superperiods
Nb x straight section length (m)
16 ; 4
4 x 8.0m + 12 x 4.2m + 8 x 3.1m
Betatron tunes Vx ; Vy 18.155 , 8.362
Momentum compaction a1
Energy dispersion E/E 1.1·10-3
Damping time (ms) 3.2
Emittance (nm·rad) 4.58
Radiation loss per turn (keV) 1024
Total power loss (200 mA) (kW) 223
Bunch length (Max RF voltage) (ps) 15.8
(m) minimum / maximum value 0.4 / 18.0
(m) minimum / maximum value 1.3 / 25.0
Dispersion function minimum / maximum value (m) nx 0.02 / 0.23
Vacuum vessel aperture except IDs (mm) H x V 72 x 28


The periodicity of the ALBA lattice can be noticed in the variation of the beta functions along the ring. One quadrant of the ring is plotted in the next plot. Also the straight sections and the cells distribution within the quadrant are highlighted.


The ALBA lattice design focuses the beam to a relatively small size and divergence. This achievement has the drawback of producing high-chromatic aberrations (very negative chromaticity). Chromaticity is corrected to produce positive values by the use of strong sextupole magnets. At 120 mA, the chromaticity is corrected to [2, 4]. Sextupoles have non-linear magnetic fields which make the tune change with the oscillation amplitude and eventually limit the region of dynamical stability: the so called dynamical aperture. The following table summarizes the non-linear properties of the ALBA lattice:

Nb of sextupoles/nb of families 120 / 9
Natural chromaticity -40 ; -27
Corrected chromaticity (120 mA) +2 ; +4
Tune shifts amplitude (rad-1m-1) 2300
Half on-momentum dynamic aperture (H) -22 ; +30
Half on-momentum dynamic aperture (V) +- 13

It is usual to evaluate the dynamical region of stability, called dynamical aperture, without taking into account the physical limitations. This calculation allows the quantitive evaluation of  the effect of the sextupoles. A large dynamical aperture when compared to the physical aperture of the vacuum chamber ensures good injection efficiency. To keep the scattered particles stable, off-momentum dynamical apertures are considered. The next plot shows both on and off momentum dynamical apertures while considering only transverse motion (no longitudinal motion is considered) during 300 turns.


The information in the dynamical aperture is somewhat limited. More information is achieved if the particles are tracked for even more turns. Tracking for 2000 turns allows the calculation of the tune and the regularity of the motion at every launching point. The map that links the position in the x-y transverse plane with the nx-ny tunes plane is called a frequency map. Usually the frequency map is plotted against the diffusion (how the tune varies along the tracking). In the next plot the transverse plane and tune planes are plotted against a logarithmic scale. Small value areas represent very stable areas (blue), usually close to the closed orbit tune. Large diffusion values (red) represent unstable motions as those areas closed to resonance crossings in the tune diagram.