Measurement of coherent beam-beam tune shift under crabbing collision at KEKB

Effective head-on collision and improvement in specific luminosity were established by the installation of crab cavities in KEKB. Tune spectra of a colliding bunch in a crabbing collision were observed by using a spectrum analyzer. The beam-beam spectrum showed strong nonlinear resonance. By taking into account this nonlinearity, the coherent beam-beam tune shift was measured as a function of the bunch current. The vertical beam-beam parameter estimated from the coherent beam-beam tune shift was found to agree with that observed by using a bunch-by-bunch luminosity monitor. The estimated vertical beam-beam parameter is saturated at approximately 0.05; this value is the beam-beam limit. Further, the bunch current corresponding to the beam-beam limit was found to be considerably lower than that used in usual operations. The horizontal beam-beam parameter was not saturated over 0.15. The horizontal beam-beam parameter estimated from the coherent beam-beam tune shift approximately agrees with a calculated beam-beam parameter considering the dynamic beam-beam effect.

Figure 1

Relative beam-beam kick as a function of the horizontal position shift at the IP; the dashed red line indicates the relative beam-beam kick in the case of a head-on collision, and the solid green line indicates the relative beam-beam kick in the case of a horizontal crossing angle of 22 mrad under identical beam conditions.

Figure 2

Sum of coherent beam-beam parameters as a function of the coherent beam-beam tune shift. Part (a) shows the horizontal plane calculated with unperturbed fractional tunes ${\nu }_{x0}^{+}=0.506$ and ${\nu }_{x0}^{-}=0.512$, and (b) shows the vertical plane calculated with unperturbed fractional tunes ${\nu }_{y0}^{+}=0.571$ and ${\nu }_{y0}^{-}=0.589$, assuming ${\Xi }_q^{+}={\Xi }_q^{-}$.

Figure 3

Schematic gated tune monitor.

Figure 4

Vertical tune spectra of a colliding positron bunch denoted by the green curve. The blue line is a resonance curve fitted to a single peak. The left peak represents the $L$ mode and the right side spectrum represents the $H$ mode. The upper and lower excitation levels are $-28$ and $-25\mathrm{dB}$, respectively. In the vertical axis, 0 dBm corresponds to an oscillation amplitude of 0.3 mm. An amplitude of $-20\mathrm{dBm}$ at the detector corresponds to an amplitude of less than $1\mu \mathrm{m}$ at the IP.

Figure 5

Horizontal tune spectra of an electron bunch denoted by the green curve. The blue line is a resonant curve fitted to a single peak. The peak corresponds to the $H$ mode. The excitation level changes from $-39\mathrm{dB}$ (upper) to $-30\mathrm{dB}$ (lower). The $L$ mode appears as a second peak that is located around a tune of 0.509 in the lower panel. An amplitude of $-20\mathrm{dBm}$ at the detector corresponds to an amplitude of $6\mu \mathrm{m}$ at the IP.

Figure 6

Vertical tune spectra of a positron bunch while increasing the electron bunch current denoted by the green curve. The positron bunch current is 0.82 mA, while the electron bunch current is changed from 0.38 mA (upper) to 0.58 mA (lower). The blue line is a resonance curve fitted to a single peak.

Figure 7

Vertical tune spectra of a positron bunch at bucket number 0 (upper) and 4753 (lower). The bunch currents of the positron and electron are 0.93 and 0.45 mA, respectively. The total currents of the positron and electron are 1600 and 850 mA, respectively. An amplitude of 1.0 in the vertical scale corresponds to an oscillation amplitude of 0.3 mm.

Figure 8

Vertical average beam-beam parameter as a function of the product of bunch currents. The red dots represent the average coherent beam-beam parameter estimated from the tune shift, and the blue squares represent the beam-beam parameter estimated from the luminosity measurement.

Figure 9

Horizontal coherent beam-beam tune shift as a function of the product of bunch currents.

Figure 10

The red dots represent horizontal average beam-beam parameter as a function of the product of the bunch currents. The blue solid line represents the horizontal average beam-beam parameter calculated using the beam size considering the dynamic beam-beam effect. The green dashed line is the beam-beam parameter calculated using the nominal beam size. The tune of the $H$ mode is used in the calculation of the dynamic beam size.

Figure 11

The red dots represent horizontal average beam-beam parameter as a function of the product of bunch currents with low emittances of ${ϵ}_{x0}^{+}=15\mathrm{nmrad}$ and ${ϵ}_{x0}^{-}=18\mathrm{nmrad}$. The blue line represents the horizontal beam-beam parameter calculated using the beam size considering the dynamic beam-beam effect. The green dashed line is the beam-beam parameter calculated using the nominal beam size. The tune of the $H$ mode is used in the calculation of the dynamic beam size.

Figure 12

Specific luminosity per bunch as a function of the product of bunch currents. The red dots and blue dots represent the specific luminosity at ${ϵ}_{x0}^{+}+{ϵ}_{x0}^{-}=18+24\mathrm{nmrad}$ and ${ϵ}_{x0}^{+}+{ϵ}_{x0}^{-}=15+18\mathrm{nmrad}$, respectively, measured with a fixed betatron function at the IP.

Figure 13

The red dots represent a beam-beam kick as a function of the horizontal position, measured at a bunch current product of $0.4{\mathrm{mA}}^2$. The dashed green line represents a beam-beam kick with an effective size of $162\mu \mathrm{m}$ considering the dynamic beam-beam effect. The solid black line represents a beam-beam kick with an effective nominal size of $196\mu \mathrm{m}$. The kicks were calculated, assuming a Gaussian profile.