Three-dipole kicker injection scheme for the Advanced Light Source upgrade accumulator ring

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I. INTRODUCTION
The ALS-U is the upgrade of theAdvanced Light Source to a 4th generation diffraction-limited soft xray light source [1].Achieving ALS-U's high brightness goal requires strong focusing-magnet gradients; the strong gradients necessitate strong chromatic sextupoles and these will shrink the dynamic aperture of the storage ring (SR) to about 0.5 mm radius once lattice imperfections are taken into account.
To inject into such a small dynamic aperture, ALS-U will implement on-axis single-train swap-out injection utilizing an accumulator ring (AR) housed along the inner wall of the SR tunnel.See Fig. 1 for an overview of the ALS-U accelerator complex.A small 2 nm-rad natural emittance, much smaller than the approximately 300 nm-rad emittance of the beam delivered by the existing booster, is required to inject into the storage ring with near-100% efficiency and sufficient margin.In addition to its function as a damping ring, the AR is intended to act as a beam-charge recycler in between swap-outs.The SR average current is 500 mA, distributed evenly over a 284-bunch beam consisting of eleven trains of 26 (or 25) bunches each.The AR is designed to carry a single train at a time; this is swapped with one of the SR trains once every about half-minute and replenished with top-off injection from the booster before the next swap-out.
The AR design has to fulfill two competing demands on the vacuum-chamber aperture: it should be wide enough to accept the large emittance beam from the booster, with a goal of 95% injection efficiency, but as narrow as possible to minimize the magnets' aperture and thus their weight and volume so that the AR can fit in the same tunnel as the SR.Consideration of these demands has guided the choice of injection scheme that recognizes that the AR can tolerate a significant injection transient.
Thus, an injection cycle leaves both the stored and injected beams with significant transients, both contained in the dynamic aperture of the machine.Such a technique is also referred to as aperture sharing.Fully exploiting the latitude offered by the latter observation, we  as does the ALS.The beam energy is increased from 1.9 117 GeV to 2.0 GeV to match that of the ALS-U storage ring.

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The AR emittance of 1.8 nm is comparable to that of the 119 ALS.
To preserve egress, the AR will be mounted close to  99.9 99.9 99.9 99.9 99.9 fined after considering short-range transverse wake fields.
Because of the non-zero injection transient, the stored beam generates wakes strong enough to sweep some of the injected particles into the vacuum chamber.This is described in more detail in Sec.VI.When taking short range wakes into account, it is found that a smaller perturbation to the stored beam improves the overall injection efficiency, even though the injected bunch has a larger initial offset and suffers slightly larger losses initially.
Mode B brings the injected beam closer to the septum as it enters from the BTA thus requiring a weaker main injection kick and allowing for a smaller stored beam transient at the expense of slightly reduced injection efficiency.The injected beam losses to the machine acceptance increase from 0.30% to 1.77%, while the losses due to wake fields decrease from 16.4% to 6.8%.BTA-side septum sheet losses also increase slightly from 0.80% to 1.05%.The white region is the acceptance in x-x space at the septum exit.The septum is drawn in black and is 1 mm thick with its inward edge 8 mm from the stored beam reference trajectory.The septum drawing was obtained by tracking.The parameters of the three modes are detailed in Table II.In a preliminary study we took a first cut at the pa-  The bottom-left picture in Fig. 7 is the cumulative den-  The short-range transverse wake fields have been cal-411 culated for each vacuum chamber element using a de-412 FIG. 9. Sensitivity of the injection efficiency to the nonuniformity of the injection kickers' pulse profile.The three data sets correspond to a 0%, 4%, and 10% sloping of the pulse profile.The simulation is conducted with a complete set of errors including shot-to-shot variation of the kick and septa strengths, as well as septum leakage fields.
tailed model of its geometry.Longitudinal wakes are not included in these results, however only the horizontal wakes have been observed to have a significant impact on the injection process.The wakes are applied close to the location of the impedance, although simulations are in good agreement with simpler calculations that use beta-function weighting to group together the impact of wake fields in every sector or even at a single location in the ring.The threshold for the Transverse Mode-Coupling Instability (TMCI) is 5.8 nC, about 8 times the nominal charge for a single bunch.Fig. 10 shows the beta-weighted wakefields from different components in both horizontal and vertical planes, along with their total.Wake fields are calculated for a Gaussian beam with rms bunch length of 1 mm, and serve as pseudo-Green functions in the following beam dynamics simulations.
The resulting transverse oscillations, especially of the stored bunch (because it contains about 90% of the charge), induce short-range wake fields.Despite the fact that the total bunch charge is expected to be far from the threshold for instabilities driven by short-range wakes, the wake fields do build up in intensity over a time scale of order 1 ms (roughly 1600 passes around the ring).Simulations show that the wake fields are strong enough to confine the stored bunch and delay phase decoherence, as shown in Fig. 11.At the same time, the more diffuse injected electrons increase in both oscillation amplitude and transverse width.
The 3DK 'balanced' configuration (Mode A) was chosen by optimizing for injection efficiency, but without considering the impact of wakes.Less than 1% beam losses are predicted in this case.However, when the expected wake fields are included, the injection efficiency drops to 83.6%.As shown in Fig. 12, most of the losses occur between 0.5 ms and 1 ms after injection, roughly between 1000 and 2000 passes around the ring.
An important aspect of the 3DK scheme is that it is flexible enough to allow for additional adjustments to   For the nominal wake fields, the goal of at least 95% injrection efficiency is not met even for Mode C. Thus, other strategies to mitigate the impact of short-range wake fields have been examined.The nominal chromaticity of 1 in both planes can easily be increased and will drive more rapid phase decoherence of the bunches.Both horizontal and vertical chromaticities contribute to this effect at high amplitudes.A small temporal offset of the injected bunch relative to the stored bunch directly reduces the wake field forces experienced by the injected electrons, as the injected particles experience the peak of the wake field for only brief periods during their syn-  13.Capture efficiency as a function of number of passes around the ring after injection, comparing Mode A, where the kicker settings are optimized without including wake field effects, to Mode C, which uses an alternative set of kicker strengths which is more tolerant to wake fields and also changes the injection beta function.Results are shown with and without wake fields, for enhanced wake fields, and for additional mitigations.conclude that while masking will significantly reduce the 603 damping obtained from the multibunch feedback system,

VII. MULTI-BUNCH STABILITY AND
the relatively large booster beam, and small enough emit-97 tance to inject with near-100% efficiency into the storage 98 ring.To that end, the existing ALS twelve-sector triple-99 bend acromat layout meets these needs.Such a layout is 100 well-understood, allowing R&D efforts to be focused on 101 the storage ring and transfer lines.With that, the ALS-U 102 AR is essentially a slightly smaller version of the existing 103 ALS twelve period triple-bend acromat.The AR's basic 104 parameters are compared with those of the existing ALS 105 in Table I.The optics and layout through one arc are 106 shown in Fig. 2. To adapt the ALS layout to the AR lay-107 out, the length of the straight sections was shrunk from 108 9.386 m to 8.762 m and the arcs were shrunk from 7.014 109 m to 6.415 m by reducing the magnet spacing.Nominal 110 bend, quadrupole, and sextupole magnet lengths are the 111 same between the ALS and AR.These adjustments bring 112 the total circumference down from 196.805 m to 182.122 113 m which makes the AR fit neatly along the inner tunnel 114 wall.The AR utilizes a non-swept gradient dipole design 115 (picture a geometry similar to a partially opened book), 116

FIG. 3 .
FIG. 2. Lattice and magnet distribution of an arc in the ALS-U AR.The ring is composed of 12 such arcs.Shown are the beta and the dispersion functions (top), the aperture model and the distribution of magnets (bottom).

Mode C has the
same kicker settings as Mode B but decreases β x to better fit the injected beam into the AR acceptance available after taking the septum sheet into account, similar to the technique applied in [4].This differs from Modes A and B where the beam distributions are matched to the ring.Reducing β x shrinks the injected beam horizontally, reducing losses along the septum sheet.After adjusting the septum strength to recenter the injected beam within the available machine acceptance, the centroid is brought closer to the septum, thereby reducing the injection transient.BTA-side septum sheet losses are reduced to 0.13%, and losses to the acceptance are reduced to 1.30%.

Fig. 5 FIG. 5 .
Fig.5shows the DA of the latter three modes viewed FIG. 6. Twiss functions (a) and layout (b) of the BTA transfer line.
FIG. 7. Top: particle losses in the injected (left) and stored (center and right) beam vs. kickers' angles for the ideal lattice.The pre-kickers' kick (vertical axis) is reported relative to Mode A settings (red lines).Bottom: for each one of 100 lattice-error realizations, a DK scan is carried out on a grid to identify the setting yielding the highest injection efficiency.The ensemble of the best DK settings is reported in the right figure.The left figure is the injection efficiency cumulative density function (CDF).

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rameter space by delimiting the region that exhibits no 359 or minimal losses in both injected and stored beam in 360 the absence of errors: see the top images in Fig. 7.In 361 the simulations the injected and stored bunches are rep-362 resented with 1000 particles and tracked for 1000 turns.

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FIG. 8. Temporal and spatial profiles of the thin-septum leakage field as included in the injection efficiency studies.The left plot shows the integrated kick at various horizontal coordinates as a function of turns.Conversely, the right plot shows the integrated kick at various times as a function of a particle horizontal coordinate.

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sity function (CDF) of this set, showing that about half 378 of the lattices have injection efficiency larger than 98.5%.379We then proceeded by refining the simulations to 380 include a more complete set of errors and perturba-381 tions.Specifically, to the AR lattice errors we added: 382 septa and kickers shot-to-shot variations (Table III), non-383 uniformity of the kicker-pulse temporal profile, and sep-384 tum leakage fields.385 The non-uniformity of the kicker pulse is simulated by 386 assigning a linear slope to the pulse profile.The slope 387 is defined as the difference between the kicks on the first 388 and last bunch of the bunch train relative to the nominal 389 kick.The simulation of the leakage fields is done by calcu-390 lating the kick map associated with the field accounting 391 for both the temporal and spatial field extension, to be 392 applied at every turn before the field has died off, Fig. 8. 393 A result from these more complete simulations is shown 394 in Fig. 9 demonstrating the sensitivity of injection effi-395 ciency to the sloping of the kickers' pulse.As before, 396 for each lattice-error realization, the injection efficiency 397 was determined after performing a 2D scan of the kicker's 398 amplitude to identify the optimum.Among other things, 399 from these results we concluded that a 4% slope would 400 During injection both the electrons from the booster 404 and the stored bunch onto which they are added undergo 405 several millimeter transverse oscillations and this has the 406 potential to induce potentially harmful transverse collec-407 tive effects.The investigation of these effects is the topic 408 of this section.These investigations were conducted us-409 ing the Elegant accelerator code[8]. 410

FIG. 10 .
FIG.10.Transverse short-range wakefields in the AR from individual components and their combined total.The wake potentials are calculated for a Gaussian beam with rms bunch length of 1 mm and serve as pseudo-Green functions in beam dynamics simulations.Left: horizontal plane, right: vertical plane

461-FIG. 11 .
FIG. 11.Horizontal phase space of the stored (orange) and injected (blue) bunches after 2000 turns, without wakes (above) and with nominal wakes (below).The left figures show the results for Mode A, the right for Mode C.

Figure 12
Figure12shows the evolution of the size and horizontal offset of the injected bunch when short-range wake fields are either included or ignored.Results for Mode A are shown on the left-side plots, and for Mode C on the rightside plots.In Mode A, the width of the injected bunch steadily decays without wake fields, while with the nominal wakes the width of the bunch grows until it peaks after 1800 turns around the ring with an rms of 3.5 mm, up from 2.2 mm.The centroid motion rapidly damps from 1.5 mm without wakes, but with the nominal wakes it increases to 3.5 mm amplitude, followed by envelope oscillations which slowly decay over thousands of passes around the ring.For Mode C, there is similar behavior in the width of the injected bunch but the amplitude of the centroid motion starts out at 2 mm and only grows to 3.0 mm.The centroid motion again has continued envelope oscillations in the presence of wakes, but at a lower amplitude than for Mode A.
FIG.12.Comparison of the evolution of the size (top) and centroid motion (bottom) of the injection bunch for the cases without wake fields (red) and with nominal wake fields (green).The left figures show results for the 3DK settings referred to as Mode A ('balanced'), and right figures show Mode C, which is tuned for better performance in the presence of wake fields.The corresponding injection efficiencies for the two cases are 83.6% and 93.1%.

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FIG.13.Capture efficiency as a function of number of passes around the ring after injection, comparing Mode A, where the kicker settings are optimized without including wake field effects, to Mode C, which uses an alternative set of kicker strengths which is more tolerant to wake fields and also changes the injection beta function.Results are shown with and without wake fields, for enhanced wake fields, and for additional mitigations.
FIG.14.Per-mode growth rates of a 25 bunch train in the accumulator ring determined by multi-bunch macro-particle tracking with resistive wall wake fields.During steady-state, all RW modes are safely damped with a total growth rate of about −2.5 ms −1 .During the injection transient the effectiveness of the TFB is significantly diminished by the necessity of masking the 4 buckets into which charge is injected, though all modes remain damped.

TABLE I .
Parameter list of the ALS-U Accumulator Ring and existing ALS.

TABLE II .
Injection modes achieved by adjusting kickers and septum strength.Mode A achieves a high injection efficiency with a small stored beam transient.Mode B reduces the stored beam transient to mitigate short range wake fields, at the expense of greater losses on the BTA-side septum sheet and due to injected particles exceeding the acceptance.Mode C recovers high injection efficiency by shrinking (mismatching) the horizontal β of the injected beam.Short-range wake fields were not studied for the on-axis injection and closed stored-beam bump modes.