Vertical-longitudinal coupling induced by wakefields at the Cornell Electron-Positron Storage Ring Test Accelerator

Transverse vertical wakefields can increase vertical emittance and distort the phase space of a bunch in a storage ring. Here we report recent measurements and simulations of these effects from wakefields from movable scrapers at the Cornell electron-positron storage ring test accelerator. Charge-dependent vertical beam size growth was observed with a single scraper inserted through the top of the storage ring vacuum chamber. No change in the beam size was observed with top and bottom scrapers inserted symmetrically. The apparent growth in the vertical beam size was due in large part to the $yz$ coupling (vertical crabbing) induced by the transverse monopole wake of the asymmetric scraper configuration. We explored this $yz$ coupling and thus the orientation at the observation point by varying the vertical betatron phase advance between the vertical beam size monitor and the scrapers. In addition, we found that existing residual, current-independent $yz$ coupling, perhaps due to nonzero vertical dispersion in the rf cavities, could be compensated by the scraper wake. Predictions from tracking simulations are in good agreement with the measurements. Moreover, the vertical beam size as a function of vertical displacement at narrow-gap chambers (closed scrapers and undulator chamber) was measured. We found the transverse wakefield produced by the off-axis beam could also introduce a $yz$ tilt as well as dilute the beam emittance.

Figure 1

CESR layout showing the locations of rf cavities, undulators, scrapers, x-ray beam size monitors (xBSM) and visible-light beam size monitor (vBSM).

Figure 2

The vertical Twiss parameter ${\beta }_y$ and the dispersion ${\eta }_y$ of two lattices: ${\mathrm{lat}}^{+}(0)$ (blue line) and ${\mathrm{lat}}^{+}(-54)$ (red line). The bottom plot shows the vertical betatron phase difference in units of radians between ${\mathrm{lat}}^{+}(-54)$ and ${\mathrm{lat}}^{+}(0)$. Two dashed lines indicate the locations of the scraper ($s=336.5\mathrm{m}$) and the $e^{+}$ xBSM ($s=774.9\mathrm{m}$).

Figure 3

The $yz$ tilt angle ${\theta }_{yz}$ at the $e^{+}$ xBSM calculated from the one-turn matrix (red circles and green crosses) for 11 lattices, and from tracking simulations (black diamonds) for five lattices. $\mathrm{\Delta }{\varphi }_{\mathrm{so}}$ is the change of the vertical betatron phase difference between the scraper and the xBSM relative to ${\mathrm{lat}}^{+}(0)$.

Figure 4

(a) The vertical dispersion ${\eta }_y$ of the lattice ${\mathrm{lat}}^{-}(0)$ without (blue dashed line) and with (red line) the wake element. (b) ${\eta }_y$ of the lattice ${\mathrm{lat}}^{-}(0)$ with the coupling bump cp11 set at 0 (blue dashed line) and $+10\mathrm{k}$ (red line). All the ${\eta }_y$ shown are calculated from lattice models. The vertical dashed line indicates the location of the east rf cavity.

Figure 5

(a) cubit half model of the scrapers, including artificial tapers, with top scraper inserted and bottom scraper retracted. (b) Transverse wakes of the asymmetric scrapers: monopole (red), dipole (green), and quadrupolar (blue) term. The dipole and quadrupolar terms have been multiplied by a factor of $\mathrm{\Delta }y=0.5\mathrm{mm}$ to compare with the transverse monopole term. Dashed line: bunch distribution (${\sigma }_z=10\mathrm{mm}$).

Figure 6

Beam sizes as a function of the beam current for the $e^{-}$ lattice ${\mathrm{lat}}^{-}(0)$. The red dots are the data measured with both scrapers retracted and the black crosses are the data with top scraper fully inserted. Circles are from tracking simulations. The green line is calculated beam size growth due to IBS with both scrapers retracted.

Figure 7

(a) Measured vertical beam size ${\sigma }_y$ as a function of bunch current for ${\mathrm{lat}}^{-}(45)$ of electrons (circles: simulation). (b) Tilt angle ${\theta }_{yz}$ from tracking simulations for ${\mathrm{lat}}^{-}(0)$ and ${\mathrm{lat}}^{-}(45)$ with top scraper inserted (“in-out”).

Figure 8

The measured vertical beam size ${\sigma }_y$ as a function of bunch current with top scraper inserted (black crosses) or retracted (red dots) for two $e^{+}$ lattices: (a) ${\mathrm{lat}}^{+}(0)$ and (b) ${\mathrm{lat}}^{+}(-54)$. The simulated results are the diamonds and circles.

Figure 9

(a) Measured vertical beam size ${\sigma }_y$ as a function of bunch current with coupling bumps ($\mathrm{cp}11=\pm 10\mathrm{k}$) in ${\mathrm{lat}}^{-}(0)$ of electrons. (b) Measured vertical beam size contribution due to asymmetric scraper $\left(\sqrt{{\sigma }_{y,\mathrm{in}\text{−}\mathrm{out}}^2-{\sigma }_{y,\mathrm{out}\text{−}\mathrm{out}}^2}\right)$ as a function of bunch current.

Figure 10

Right: Particle distributions in the $yz$ plane from simulations for the $e^{-}$ lattice ${\mathrm{lat}}^{-}(0)$. Left: Cartoons showing the beam tilt in the $yz$ plane. Red: top scraper retracted. Black: Top scraper inserted. The coupling bump is set to (a) $\mathrm{cp}11=0$, (b) $\mathrm{cp}11=+10\mathrm{k}$, and (c) $\mathrm{cp}11=-10\mathrm{k}$ with a bunch current of 1 mA.

Figure 11

Measured vertical beam size ${\sigma }_y$ versus current for the $e^{-}$ lattice ${\mathrm{lat}}^{-}(0)$ with the coupling bump set at (a) $\mathrm{cp}11=0$ and (b) $\mathrm{cp}11=-10\mathrm{k}$. Small dots: data. Larger symbols with error bars: simulation. Red: both scrapers out (o-o). Black: top scraper inserted (i-o). Green: bottom scraper inserted (o-i). The cartoons indicate the beam tilts at 0.6 mA.

Figure 12

The measured vertical beam size ${\sigma }_y$ as a function of the beam vertical displacement $\mathrm{\Delta }y$ with respect to (a) the center of the scrapers and (b) the undulator chamber center at different $e^{-}$ bunch currents: 1 mA (black), 2 mA (red), 3 mA (green), and 4 mA (blue). The 2 mA data were not taken for the scrapers.