Transverse beam splitting made operational: Key features of the multiturn extraction at the CERN Proton Synchrotron

Following a successful commissioning period, the multiturn extraction (MTE) at the CERN Proton Synchrotron (PS) has been applied for the fixed-target physics programme at the Super Proton Synchrotron (SPS) since September 2015. This exceptional extraction technique was proposed to replace the long-serving continuous transfer (CT) extraction, which has the drawback of inducing high activation in the ring. MTE exploits the principles of nonlinear beam dynamics to perform loss-free beam splitting in the horizontal phase space. Over multiple turns, the resulting beamlets are then transferred to the downstream accelerator. The operational deployment of MTE was rendered possible by the full understanding and mitigation of different hardware limitations and by redesigning the extraction trajectories and nonlinear optics, which was required due to the installation of a dummy septum to reduce the activation of the magnetic extraction septum. This paper focuses on these key features including the use of the transverse damper and the septum shadowing, which allowed a transition from the MTE study to a mature operational extraction scheme.

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Figure 1

Layout of the PS ring including the combined-function main magnets (red and blue rectangles for the focusing and defocusing parts, respectively) and the location of the key elements for MTE. The ten different sectors of the PS are indicated by the numbers and the radial offset between the rectangles accounts for the four different magnet types (see [7] for more detailed information).

Figure 2

Top: rf voltage program and magnetic cycle of the PS. Injection occurs at $2.14\mathrm{Gev}/c$ and extraction at $14\mathrm{GeV}/c$. Bottom: Operational functions of the octupoles and sextupoles applied to perform the transverse splitting. ${\mathrm{O}}_{\mathrm{NLC}}$ represents the family of octupoles dedicated to the correction of nonlinear coupling. The grey area corresponds to the time during which the transverse dipolar excitation is active.

Figure 3

Top: Comparison between good and bad splitting efficiency based on horizontal profiles measured with WS54. Bottom: Waterfall representation of multiple measured horizontal profiles, with the color scale corresponding to the amplitude of the data shown in the image at the top. Each measurement was recorded on a different cycle and clear oscillations of the beamlets’ intensities are visible.

Figure 4

Top: Tune measurement along an argon ion cycle. The average value over 900 cycles is shown. Sidebands are visible in both planes. Bottom: Distance of the sidebands from the horizontal tune. The dashed line corresponds to the expected distance of the sideband frequency $f_{\mathrm{SB}}=5\mathrm{kHz}$ from the main tune peak along the cycle.

Figure 5

Top: The FFT of $\dot{B}$ measured on an argon cycle reveals an important peak at 5 kHz. Bottom: The amplitude of the peak at 5 kHz shown in the top figure oscillates in the same way as the amplitude of the sideband of the horizontal tune discussed in Fig. 4.

Figure 6

Comparison between the time evolutions of the measured profile amplitude of the outermost island and the amplitude of the 5 kHz current ripple of the PFWs.

Figure 7

Waterfall representation of multiple measured horizontal profiles after an intervention aimed at damping the current ripple of the PFWs at 5 kHz. Significantly improved stability with respect to the measurements shown in Fig. 3 is clearly visible.

Figure 8

Reconstructed two-dimensional probability distribution function for ${\eta }_{\mathrm{MTE}}$ and programmed tune offset with respect to the nominal settings. A parabolic shape of the level lines of the probability distribution function is clearly visible.

Figure 9

Simulated horizontal phase space at the location of WS54 (top) and measured profile (bottom), which corresponds to an average value over 100 measurements. The grey band represents the one sigma standard deviation and the colored lines the Gaussian fits for the different beamlets, with the only constraint being the equal integral of the functions corresponding to the four islands. Excellent agreement between the predicted positions of the SFP and the actual measurement is obtained, which is indicated by the dashed lines.

Figure 10

WS54 measurements of the evolution of the transverse splitting along the cycle, with the simulated positions of the core (circle) and the islands indicated by the respective markers. In this case, the resonance was crossed at 760 ms and the rotation of the phase space started around 808 ms (indicated by the white solid line). Note the apparent discontinuity in the islands’ positions at this moment, which is due to the projection effect from phase space to horizontal space.

Figure 11

Simulated horizontal phase space portraits in SS01 at the end of the splitting process in the absence of a tune ripple (top) and with a ripple amplitude corresponding to the maximum measured current ripple on the PFWs circuits (bottom). To quantify the effect on ${\eta }_{\mathrm{MTE}}$, particles inside the red boundary (drawn at $\pm 3.5{\sigma }_{\mathrm{core}}$ in $x$ and $x^{\prime }$) are considered core particles. The efficiency of the splitting process is clearly reduced by the presence of a tune ripple.

Figure 12

Dependency of the splitting efficiency on the amplitude (top) and frequency (bottom) of the external perturbation. The ripple amplitude is expressed in terms of the amplitude of the sinusoidal perturbation of the horizontal tune. A low-frequency ripple significantly perturbs the splitting process.

Figure 13

Dependence of ${\eta }_{\mathrm{MTE}}$ on the amplitude (top) and frequency (bottom) of the excitation generated by the transverse damper. The color scale provides the information on the extraction losses as measured by the BLM in SS16.

Figure 14

Dependence of ${\eta }_{\mathrm{MTE}}$ on the timing (top) and duration (bottom) of the excitation generated by the transverse damper. In both cases the scanned quantities are provided with respect to the nominal value used for MTE operation. The color scale provides the information on the extraction losses as measured by the BLM in SS16.

Figure 15

Dependence of ${\eta }_{\mathrm{MTE}}$ on the slope (top) and initial value (bottom) of the excitation frequency generated by the transverse damper. The color scale provides the information on the extraction losses as measured by the BLM in SS16.

Figure 16

Simulated horizontal phase space portraits in SS01 during a nonadiabatic final rotation. Once the beamlets are sufficiently separated (see Fig. 7), the rotation occurs within 2000 turns. The top figure shows an intermediate situation after 1000 turns and the phase space in the bottom corresponds to the end of the rotation process. Due to the nonadiabatic rotation de-trapping has occurred, leading to particles captured between the core and the islands, and filamentation inside the islands is ongoing. The respective cycle times are indicated in the bottom left corners of the plots.

Figure 17

Time-independent PTC simulation results to demonstrate the behavior of the external island at the entrance to SMH16 during the final rotation. Top: Horizontal phase space. As indicated by the time-dependent simulation results, the island is actually rotated and squeezed before it expands again. The legend indicates the different instances along the cycle. Bottom: Evolution of ${\beta }_x$-function. To reduce losses at SMH16, the optimum position of the external beamlet would correspond to the situation at 809 ms. The colored markers correspond to the situations shown in the top figure.

Figure 18

Simulated dependency of the position of the SFP (top) and of the ${\beta }_x$-function (bottom) on the current of X55. In both cases the figures describe the situation for the external island at the location of SMH16. The initial values are indicated by the stars.

Figure 19

Simulated horizontal phase space portraits in SS01 showing the evolution of an improved final rotation, which takes about six times longer than the one illustrated in Fig. 16. ${\eta }_{\mathrm{MTE}}$ is conserved during the process and the final surface of the islands, which is shown in the bottom plot, is significantly reduced. Note that the SFP of the external island is located at $x^{\prime }\approx -1\mathrm{mrad}$, which is required to properly position the beamlet in SS15 and SS16. The respective cycle times are indicated in the bottom left corners of the plots.

Figure 20

Horizontal phase space portraits at TPS15 (top) and SMH16 (bottom) during the fast extraction bump. The shown surfaces of the islands represent single particle 2D tracking results, for a particle situated close to the separatrix. The optimization of the rotation has to consider the phase advance of $\approx 22.5°$ between the two locations.

Figure 21

During the rise time of the fast extraction kickers, the beam is swept from the internal to the external side of both TPS15 and SMH16. Proper adjustment of the positions (and angles) of both septa allows to put SMH16 in the shadow of TPS15, and, therefore, reduce the losses in SS16. In the shown configuration the black rectangles indicate the septa at properly adjusted positions to provide shadowing. The efficiency of the shadowing might, however, be different between the core and the islands.

Figure 22

Simulated horizontal orbit of a core particle at maximum amplitude of the slow extraction bump (black). This orbit is achieved as superposition of the red and blue curves, which represent the two $\pi$-bumps created by the dedicated magnets in SS12 and 20, and SS14 and 22, respectively. The locations of TPS15 and SMH16 are indicated by the dashed lines.

Figure 23

Simulated horizontal orbits of the islands with the amplitude of the slow bump being at its maximum. The envelopes represent a beam size with extension of $3{\sigma }_x$ and $2{\sigma }_s$, based on Gaussian distributions in both planes (${ϵ}_{x(1\sigma )}^n=5\mathrm{mm}\mathrm{mrad}$, $\mathrm{\Delta }p/p_{(1\sigma )}=5\times {10}^{-4}$). The horizontal mechanical aperture is represented in gray. The two septa are closely approached and the actual aperture limitation is caused by the proximity of the beam to the vacuum chamber inside MU19.

Figure 24

Top: Signal of the fast BLM16. The grey area indicates a duration of five turns, with the dashed lines being separated by one turn. The red and the blue circles correspond to the maximum beam loss occurring during the extraction of the islands and the core, respectively. Bottom: Dependency of beam loss on the position of SMH16 for an angle of 0 mrad. Red and blue circles correspond to the losses of the islands and the core, respectively, and the black circles represent their sum. Error bars describe the standard deviation obtained over 10 consecutive measurements. The dashed line and the grey band indicate mean value and standard deviation of losses for the nominal septa settings.

Figure 25

Integrated beam loss measured after extraction on the MTE cycle using TPS15 and SMH16 in shadowing configuration. Only BLM15 is saturated, and beam loss at the adjacent SMH16 is significantly reduced. For comparison, the MTE case without TPS15 and the CT case are shown. Error bars for the case of MTE with shadowing correspond to the standard deviation of 500 consecutive measurements.

Figure 26

Correlation between the signal of the slow BLM16 and the amplitude variation of the 5 kHz component of the main magnetic field using TPS15 and SMH16 in shadowing configuration.