Spill ripple mitigation by bunched beam extraction with high frequency synchrotron motion

Slow extraction of bunched beams is widely used for mitigating the formation of temporal microstructures on the extracted beam due to ripples of the accelerator magnets power supplies. That helps in experiments with slow detectors or measurements with low event rates. Additionally, in ion cancer therapy machines, this technique is widely used for avoiding long gaps in the spill measured in ionization chambers which in turn would trigger interlocks. It is also well known that extraction of a bunched beam creates spill structures on time scales defined by the rf frequency which limits its usability for faster detectors. In this report, we show that further macroscopic spill structures of duration up to some hundred milliseconds can be created during bunched beam extraction for a sufficiently large synchrotron tune. The aim of this work is to study the influence of the synchrotron tune and its interplay with slow extraction settings on the slow extraction quality. Further dependencies on transverse emittance and longitudinal bunch area of the circulating beam are discussed.

Figure 1

Weighted duty factors according to Eq. (12) of spills obtained in simulations of the slow extraction of ${\mathrm{Ar}}^{18+}$ beams from SIS18 at the beam energy $E=500\mathrm{MeV}/\mathrm{u}$ as a function of the synchrotron tune according to the rf voltages $V_{\mathrm{rf}}=(0,1.2,6.2,12,70,200)\mathrm{kV}$, where $V_{\mathrm{rf}}=12\mathrm{kV}$ is the maximum which can be reached in SIS18. The rf voltage at the beginning of the simulations is switched off and slowly turned on during the first 50,000 turns. The initial maximum momentum deviation is ${\delta }_{\mathrm{m}}=5\times {10}^{-4}$ and is increased during the bunching process. Hence, also longitudinal dynamics with low rf voltages with particles captured and others not captured in the rf bucket are well described.

Figure 2

Upper graph: Schematic plot of the stable phase space area at instant $t$ and shrunk within a synchrotron period $T_{\mathrm{s}}$ by moving the machine tune $Q_{x,\mathrm{m}}$ toward the resonance tune $Q_{x,\mathrm{r}}$. Lower graph: Range of longitudinal coordinates of particles with certain horizontal emittance related to the distance of the separatrix from the beam center $X_{\mathrm{sep}}(t)$ at instant $t$ and shrunk within a synchrotron period $T_{\mathrm{s}}$ by $\mathrm{\Delta }{X}_{\mathrm{sep}}(T_{\mathrm{s}})$.

Figure 3

Intensity profiles as a function of the time difference to the synchronous particle of a circulating bunch and the sum of all bunches extracted during the whole extraction process. In doing so, an accumulated extracted bunch profile is obtained which represents the same particle number as the profile of the circulating bunch. The profiles are obtained in a simulation for conditions used in Fig. 1 with $h=5$ and $V_{\mathrm{rf}}=6.2\mathrm{kV}$.

Figure 4

Spill of an ${\mathrm{Ar}}^{18+}$ beam measured during slow extraction from SIS18 at the beam energy $E=500\mathrm{MeV}/\mathrm{u}$ bunched with the rf voltage of amplitude $V_{\mathrm{rf}}=12\mathrm{kV}$ and harmonic number $h=5$.

Figure 5

Spill of an ${\mathrm{Ar}}^{18+}$ beam obtained in a slow extraction simulation for SIS18 conditions at the beam energy $E=500\mathrm{MeV}/\mathrm{u}$, where $V_{\mathrm{rf}}=12\mathrm{kV}$, $h=5$, and quadrupole ripples of two different amplitudes are applied. The transverse beam emittances correspond to the machine acceptance at injection reduced by the factor of 0.2 and adiabatic shrinkage during acceleration afterward. Furthermore, the maximum momentum deviation in the bunches is ${\delta }_{\mathrm{m}}=5\times {10}^{-4}$. Both the transverse emittances and the maximum momentum deviation are lower than during the usual SIS18 operation. The dotted vertical lines mark the moments when the machine tune crosses a synchrobetatron resonance. The third integer resonance corresponding to $m=0$ in Eq. (20) is crossed at $t=0.41\mathrm{s}$.

Figure 6

Spills obtained for ${\mathrm{Ar}}^{18+}$ beam at beam energy $E=500\mathrm{MeV}/\mathrm{u}$ bunched with the rf voltage of harmonic number $h=5$ and amplitude $V_{\mathrm{rf}}=12\mathrm{kV}$ with varied horizontal emittance and momentum width. The black curve corresponds to the solid black curve in Fig. 5, where the initial horizontal tune is changed from $Q_{x,\mathrm{ini}}=4.329$ in the figure above to $Q_{x,\mathrm{ini}}=4.327$ in this figure in order to enable the application of increased horizontal emittance and momentum width.

Figure 7

Spills of the extraction of ${\mathrm{Ar}}^{18+}$ beams at beam energy $E=500\mathrm{MeV}/\mathrm{u}$ bunched with rf fields of the harmonic number $h=100$ obtained by particle tracking. Upper graph: The rf voltage $V_{\mathrm{rf}}=70\mathrm{kV}$ is applied and the horizontal tune is moved from $Q_{x,\mathrm{i}}=4.326$ to $Q_{x,\mathrm{f}}=4.334$. Lower graph: The rf voltage $V_{\mathrm{rf}}=5\mathrm{kV}$ is applied and the horizontal tune is moved from $Q_{x,\mathrm{i}}=4.329$ to $Q_{x,\mathrm{f}}=4.334$. The dotted lines mark the crossed synchrobetatron resonances.

Figure 8

Duty factors that correspond to the spills in Fig. 7 compared to that obtained with $V_{\mathrm{rf}}=0$, i.e., without bunching. The dashed curves represent the Poisson duty factors.