Lattice correction and commissioning simulation of the Advanced Light Source upgrade storage ring

The ALS-U is the upgrade of the existing Lawrence Berkeley National Laboratory Advanced Light Source to a diffraction-limited soft x-ray light source. Here we present the lattice correction studies and commissioning simulations demonstrating that the proposed machine design can be expected to deliver the intended performance when realistic errors and perturbations are fully accounted for. Critical to this demonstration are the high-fidelity, realistic simulations of the beam-based alignment process (both in turn-by-turn mode during early commissioning and with stored beam) that are now made possible by the Toolkit for Simulated Commissioning. In addition to presenting a statistical performance analysis based on a large number of lattice error realizations, we also study the range of further improvements that can be obtained by fine-tuning the correction chain to individual error seeds, mimicking the approach one would follow once the machine is built.

Figure 1

Lattice and magnet layout in a normal (i.e., without hard bends) sector. Shown are the betatron and the dispersion functions (top), the aperture model, and the distribution of magnets (center) and the distribution of corrector magnets, skew quadrupole correctors, and beam-position monitors (bottom). The center figure emphasizes that all quadrupoles, except for the two pairs at each end, provide some degree of bending.

Figure 2

cad drawing of a normal arc sector including the four girders (or “rafts”) and their supports. The nine main bends are depicted in blue (B1 type), cyan (B2), and pink (B3). The eight sextupoles are in red. The focusing and defocusing quadrupoles are in green and yellow/light-green, respectively. In the non-normal sectors, normal bends no. 4 and 6 are replaced by permanent-magnet hard bends.

Figure 3

Illustration of how roll and offset errors stack up in the implementation of the SR misalignment error model. Note that each full sector is assigned an offset, girders in a sector are assigned offsets relative to their sector, and individual magnets are assigned offsets relative to the girder on which they are mounted. The girder yaw and pitch angles are derived from the specification of the offsets at the girder ends.

Figure 4

Lattice properties before correction for different scaling factors of the nominal error set. The plots are the fraction of lattice realizations at which the closed orbit exists (upper left), the rms dynamic aperture (upper right), and the rms closed orbit deviation (lower left) and beta beat (lower right). The calculations in the top images were done with (dashed) and without (solid) physical apertures, but the results are indistinguishable. Note that beta beat and orbit error are only calculated for the cases in which the closed orbit exists.

Figure 5

Beam transmission at two stages of commissioning as described later in Secs. 4a, 4b, 4c, 4d, 4e, after ramping up the sextupole magnets (left) and after rf commissioning (right), assuming various levels of BBA accuracy for the trajectory-based BBA procedure as indicated in the inset. Each curve is the CDF of 100 lattice realizations.

Figure 6

Correction chain failure rate vs assumed accuracy of the trajectory (left) and closed-orbit BBA (right). For trajectory, BBA failure is defined as not achieving 1000 turns beam transmission after rf commissioning; for closed-orbit BBA as nonconvergence of the linear-optics correction as described in Sec. 4h.

Figure 7

Illustration of trajectory BBA for the BPM-quadrupole pair BPM4-QF2: data and analysis. The $x$ axis shows the reading of the BPM targeted for BBA; the $y$ axis shows the index of the downstream BPMs; and the $z$ axis the difference in the trajectories as recorded at the downstream BPMs when changing the quadrupole strength from 95% to 105% of the nominal. A black dot represents the measurement for one of the ten steering offsets imparted to the injected beam; the black lines are linear fits. The red dots mark the zero crossing of these lines and the red diamond shows the weighted mean. In this example, the weighted mean is $19\mu \mathrm{m}$ off the actual quadrupole center, much less than the physical misalignment between BPM and quadrupole, about $-500\mu \mathrm{m}$. Note that after 12 BPMs downstream of the BBA-BPM, beam transmission decreases significantly when the injected beam is steered too much and only five out of the ten steered trajectories can be utilized; after 189 BPMs, no data could be used for BBA due to beam loss. This figure is conveniently created by switching on a plot flag in the SCBBA() routine.

Figure 8

Scatter plots of DA (top) and Touschek lifetime (bottom) vs rms closed-orbit distortion (COD) in the chromatic sextupole magnets. Left and right plots show the horizontal and vertical CODs, respectively. DA and lifetime are calculated after performing LOCO-based linear optics correction (see Secs. 4a–4h) for various sets of BBA accuracy assumptions between 0 and $100\mu \mathrm{m}$ identified by colored circles. The black crosses are calculated with $0\text{−}\mu \mathrm{m}$ BBA accuracy and $10\mu \mathrm{m}$ magnet and girder offsets. Each data point corresponds to one lattice and appears in all four plots. The average lifetime is below the 0.5 h requirement above $60\mu \mathrm{m}$ COD. Note that only cases where LOCO converged are shown (see also Fig. 6).

Figure 9

Final BBA accuracy at combined function quadrupoles as a function of the HCM calibration error for the horizontal (left) and vertical (right) planes. The upper plots show the BPM offset w.r.t. the magnet centers for all BPMs at QF [4–6] (see Table 2) for 200 error realizations in the commissioning simulation after three iterations of BBA (see Sec. 4g), when no CM or BPM calibration correction is applied. A clear correlation between the HCM calibration error and the BBA error is noticeable. The lower plots show the conditional CDFs of the BBA error for various HCM calibration error intervals. The effect is negligible for the vertical plane.

Figure 10

Beam transmission at various steps of the correction chain. The left-hand plot shows that on day 1 of commissioning without any correction, the beam will almost certainly get lost within the first two arcs. The colored lines in the right-hand plot indicate the beam transmission after performing the correction steps detailed in the inset.

Figure 11

BBA results after completing two trajectories and three closed-orbit correction iterations, as indicated in the insets. The figures show the statistical distributions of the BPM alignment errors for BBA conducted on the BPMs adjacent to quadrupole (top) and sextupole (middle) magnets. The bottom images report the rms of the distributions shown above at the various correction stages ($\mathrm{Index}=1$ corresponds to the initial BPM mechanical misalignment errors; $\mathrm{Index}=2$ to the errors after the first trajectory-correction iteration, and so on). Left (right) pictures are for alignment errors in the horizontal (vertical) plane. Note that BBA on sextupoles (red curves) is done only on stored-beam BBA, and hence $\mathrm{Index}\ge 3$ (see Sec. 4g).

Figure 12

Results of the rf commissioning procedure. Shown is the difference between the closed orbit energy (left) and phase (right) with respect to the injected beam, both initially (blue) and after each of the three iterations. The rms values are shown in the inset.

Figure 13

Machine status after applying final orbit correction. The lower plots show the CDFs of the number of required beam injections (right) and the required corrector strength (left) of all CMs of all error seeds. The upper plots show the rms value of the BPM readings (solid) and COD in SF/SD magnets (dashed) before and after applying three iterations of Secs, 4f, 4g, 4h (rms over each error seed).

Figure 14

Visualization of LOCO results. Cumulative distribution functions (CDF) of beta beat, dispersion error, and emittance each before (dashed) and after (solid) optics correction in the upper four plots.. The lower two plots show the final relative quadrupole set-point deviation from the design value (left) and the required skew quadrupole strength (right).

Figure 15

DA (top and center) and lifetime (bottom). The comparison is between before (blue) and after (red) performing optics correction, and after including and compensating for the IDs (yellow). In the upper images, the solid curve is the ideal lattice DA, and the purple ellipses indicate the injected beam size ($3\sigma$). In the bottom image, the dashed curves are the CDF for the Touschek lifetime only; the solid curves are the CDF for the total beam lifetime (Touschek and vacuum).

Figure 16

Lifetime optimization using LOCO dispersion weights. The histogram in the right plots shows the value of horizontal and vertical dispersion weight yielding the best lifetime without IDs (upper row) and after ID compensation (lower row). The black lines in the left and center plots show the lifetime for each pair of dispersion weights, the red lines indicate the lifetime when for each error realization the best value is chosen. The optimum dispersion weights with and without IDs differ.

Figure 17

Touschek lifetime optimization by harmonic-sextupole scans following the dispersion-weight optimization. The left plot shows the lifetime as a function of the SHH and SHH2 set points for one choice of error seed. In this example, the lifetime can be increased from 0.94 to 1.12 h. The right plot shows the distribution of Touschek lifetime after regular ID compensation in blue for the selected error seeds (gray curve shows the distribution of all error seeds, see Sec. 4i), after optimizing the post-ID lifetime using LOCO dispersion weights (red curve, see Sec. 5a) and after tuning the sextupole magnets (yellow curve).