Simulation and analysis of using deflecting cavities to produce short x-ray pulses with the Advanced Photon Source

We present detailed simulations and analysis of Zholents’s [A. Zholents, P. Heimann, M. Zolotorev, and J. Byrd, Nucl. Instrum. Methods Phys. Res., Sect. A 425, 385 (1999).] concept for using deflecting cavities in a synchrotron light source storage ring for the purpose of producing short x-ray pulses. In particular, we look at the optimization and performance of such a system for the Advanced Photon Source. We find the concept is practical and that x-ray pulse durations of about 1.5 ps FWHM should be achievable with more than 15% of the original intensity retained. Issues covered include lattice design, emittance degradation, lifetime, photon beam modeling, errors, and optimum choice of rf parameters.

Figure 1

Arrangement of components requiring minimal changes to the APS optics (after Sajaev [24]). In the first arrangement (a) chirped pulses are provided to a single undulator beam line and a single bending magnet beam line. In the second arrangement (b) chirped pulses are provided to three undulator beam lines (assuming canting of the middle pair [12]) and two bending magnet beam lines. The many quadrupoles and sextupoles that exist in the lattice are omitted from this drawing, for clarity.

Figure 2

Lattice functions corresponding to arrangement (b) from Fig. 1. The approximate locations of the cavities are marked with an “X”.

Figure 3

Arrangements of components requiring significant but manageable changes to the APS optics (after Sajaev [24]). These arrangements provide chirped pulses to more beam lines for the same cost compared those in Fig. 1. In the first arrangement (a) chirped pulses are provided to two undulator beam lines and one bending magnet beam line. In the second arrangement (b) chirped pulses are provided to four undulator beam lines and two bending magnet beam lines. The many quadrupoles and sextupoles that exist in the lattice are omitted from this drawing, for clarity.

Figure 4

Lattice functions corresponding to arrangement (b) from Fig. 3. The approximate locations of the cavities are marked with an X.

Figure 5

Projected rms vertical beam size for the APS with $h=1$ and $V=6\mathrm{MV}$, along with the ratio of the beam size to the vertical half-aperture.

Figure 6

Vertical emittance after a single pass through the system as a function of deflecting voltage for $h=8$. With interior sextupoles off, tracking with and without momentum spread illustrates the impact of the natural chromaticity.

Figure 7

Vertical emittance on successive passes in the ring for various vertical tunes, with 6 MV and $h=8$. Interior sextupoles are off.

Figure 8

Vertical emittance on successive passes in the ring, with 6 MV and $h=8$, showing the partial recovery of the emittance after a synchrotron oscillation (about 250 turns). Interior sextupoles and synchrotron radiation effects are off.

Figure 9

Eventual vertical emittance as a function of deflecting voltage for $h=8$, with interior sextupoles on and off, without synchrotron radiation effects.

Figure 10

Vertical emittance on subsequent turns for $V=2\mathrm{MV}$ and $h=8$, with interior sextupoles on and off, without synchrotron radiation effects.

Figure 11

Eventual horizontal emittance as a function of deflecting voltage for $h=8$, with interior sextupoles on and off, without synchrotron radiation effects.

Figure 12

Horizontal emittance vs pass including synchrotron radiation effects, with interior sextupoles on and off.

Figure 13

Vertical emittance vs pass including synchrotron radiation effects, with interior sextupoles on and off.

Figure 14

Vertical emittance as a function of deflecting voltage for various harmonic numbers, with interior sextupoles off and including synchrotron radiation effects.

Figure 15

Eventual vertical emittance as a function of beta-function difference between the two crab cavities, for $h=8$ and $V=4\mathrm{MV}$.

Figure 16

Eventual vertical emittance as a function of betatron phase advance between the two crab cavities, for $h=8$ and $V=4\mathrm{MV}$.

Figure 17

Eventual horizontal emittance as a function of cavity roll for $h=8$ and $V=4\mathrm{MV}$. The “CM” data is for common-mode roll while the “DM” data is for differential-mode roll.

Figure 18

Histograms of the increase in the eventual horizontal and vertical emittances for $h=8$ and $V=4\mathrm{MV}$ with 0.25 mrad rms rolls of quadrupoles and sextupoles between the crab cavities.

Figure 19

Variation of the vertical emittance for $h=8$ and $V=4\mathrm{MV}$ with voltage error in the second cavity.

Figure 20

Beam centroid normalized to beam size as a function of differential phase error between the crab cavities, for $h=8$ and $V=4\mathrm{MV}$.

Figure 21

Beam centroid normalized to beam size as a function of common phase error of the crab cavities, for $h=8$ and $V=4\mathrm{MV}$.

Figure 22

The sinc-function angular distribution compared to a Gaussian fit, for $1\AA$ radiation from a 2.4-m-long, 3.3-cm-period undulator in the APS.

Figure 23

Duration of the central 70% of the x-ray pulse as a function of the half-height of the slits, for various deflecting voltages and harmonic numbers of 4 and 8.

Figure 24

Transmission through the slits as a function of the obtained duration of the central 70% of the x-ray pulse, for various deflecting voltages and harmonic numbers of 4 and 8.

Figure 25

Emittance as a function of achievable pulse length for constant 50% transmission through the slits.