Longitudinal bunch profile and electron beam energy spread

Longitudinal bunch profile depends mainly on the single bunch charge (or single bunch current). Every APS operating mode has different single bunch current and therefore has different bunch length. The plot below shows measured bunch length dependence on the single bunch current between 1 mA and 18 mA and the fit that uses the formula shown below the plot. The bunch length in this plot is shorter than it was quoted before. Earlier numbers were obtained using a Gaussian fit, present numbers are calculated as true standard deviation.

The following formula obtained by fitting the log of the data above can be used to calculate the bunch length at any current in the range between 1 and 18 mA (it is equivalent to the formula given on the figure above):

$\sigma_t (ps) = 25.1 I^{0.1484+0.0346 \ln I}$

The table below gives bunch length at single bunch currents used at APS:

Current	Operating mode	Bunch length
4.25 mA	24 singlets	33.5 ps
16 mA	Hybrid, main bunch	50 ps
1.5 mA	Hybrid, multiplets	27 ps
0.31 mA	324 bunches	22 ps

Bunch profiles were measured with the streak camera on July 22, 2008. Figures below show bunch profiles for 4 mA and for 16 mA and Gaussian profiles calculated using bunch lengths from the table above. One can see that the measured bunch profiles slightly deviate from the Gaussian.

Electron beam energy spread

Rms energy spread of the electron beam is $0.96 \cdot 10^{-3}$, and it stays constant for single bunch currents up to 6mA. After that, the energy spread increases approximately linear with the single bunch current and reaches $1.2 \cdot 10^{-3}$ at 20 mA. The plot below shows the energy spread vs single bunch current. It was measured using 3-point beam size measurement in June 2005.