Lattice optimization of a fourth-generation synchrotron radiation light source in Novosibirsk

We discuss the choice of the magnetic lattice and parameter optimization of the fourth-generation light source SKIF (Russian acronym for Siberian Circular Photon Source) under construction in Novosibirsk. The study compares several basic lattice cells to procure one with low emittance and large dynamic aperture. The result is a developed lattice of SKIF with 72 pm natural emittance (at zero beam current and absent betatron coupling) at 3 GeV beam energy and 476 m circumference. Only two families of sextupoles provide horizontal and vertical dynamic apertures of 12 mm and 3.5 mm, respectively, and energy acceptance more than 5%. To check the potential of the found solution, we used slightly modified SKIF lattice to design 6 GeV light source and reached 33 pm natural emittance for 1075 m circumference with 40 straight sections. Again, only two sextupole families ensure sufficient dynamic aperture (7 mm horizontal and 4 mm vertical) and energy acceptance more than 5% for simple efficient injection and sufficient beam lifetime.

Figure 1

Low emittance cell layout.

Figure 2

Four periodic optical solutions for the cell from Fig. 1. F and D stand for focusing and defocusing quadrupole, respectively. Solution 4 provides minimum emittance (TME).

Figure 3

Stability area of the cell in the form of tune ${\nu }_x$ (left) and integrated strength $p_1$ of the first quadrupole (right) on integrated strengths $p_2$ of the second quadrupole.

Figure 4

Horizontal and vertical chromaticity vs second quadrupole strength.

Figure 5

The sextupole strengths of the four solutions vs the second quadrupole strength.

Figure 6

Horizontal emittance as a function of the second quadrupole’s strength (left) and as a function of tune (right).

Figure 7

Exact and approximate mTME emittance (left) as a function of tune. The mTME emittance for different ratios of the magnet and cell lengths (right). The red curve is FODO emittance.

Figure 8

Quadrupoles’ strengths of mTME cell as a function of horizontal tune.

Figure 9

Sextupoles’ strengths of mTME cell as a function of horizontal tune.

Figure 10

TME cell emittance for different u. The red line indicates minimum emittance equal to 75 pm with parameters from Table 1.

Figure 11

Optical functions for model cells mTME (left) and TME (right).

Figure 12

Normalized to ${\beta }_x=15\mathrm{m}$, ${\beta }_y=5\mathrm{m}$ dynamic apertures of mTME (left) and TME (right).

Figure 13

Optical functions of SKIF base cell (left) and cell with high field dipole (right).

Figure 14

Optical functions of SKIF super period ($1/16$th of the ring), beginning and ending at the center of the straight section.

Figure 15

Positioning of chromatic sextupoles.

Figure 16

Transverse dynamic aperture without (left) and with (right) synchrotron oscillations.

Figure 17

Horizontal (left) and vertical (right) phase trajectories up to the last stable particle from Fig. 16 (rf is OFF).

Figure 18

Frequency map analysis for $\delta =-3\%$ (top), $\delta =0\%$ (middle), and $\delta =3\%$ (bottom). The color represents the difference of the tunes calculated on the first (1024 turns) and the second halves of the tracking time (2048 turns). The blue corresponds to identical tunes, which means regular motion, the red corresponds to large tunes difference and means chaotic motion.

Figure 19

Tune dependance on initial amplitudes: the tune ${\nu }_x({\nu }_y)$ is plotted along the vertical axis, one of the initial coordinate $x(y)$ is plotted along the horizontal axis, while the colors represent the other coordinate $y(x)$.

Figure 20

Energy acceptance with $Y_0={\sigma }_y=4.243\mu \mathrm{m}$ (left) and bandwidth (right) of SKIF with RF OFF.

Figure 21

Elements (top) and local energy aperture (bottom) over the super period with parameters from Table 4.

Figure 22

Transverse dynamic aperture (rf ON) with corrected alignment errors (24 samples) for $\delta =-3\%$ (top), $\delta =0\%$ (middle), and $\delta =+3\%$ (bottom).

Figure 23

Normalized brightness versus horizontal and vertical beta functions. Lighter color means higher brightness.

Figure 24

Optical functions of SKIF super period ($1/8$th of the ring), beginning and ending at the center of the straight section.

Figure 25

Transverse dynamic aperture with synchrotron oscillations (left) and energy acceptance ($Y_0={\sigma }_y=4.243\mu \mathrm{m}$ and rf is OFF) (right) for alternative optics.

Figure 26

Optical functions of scaled mTME SKIF cell on the left ($E=6\mathrm{GeV}$, ${ϵ}_x=30\mathrm{pm}$, $L_c=3.27\mathrm{m}$) and cell with longitudinal field gradient dipole on the right ($E=6\mathrm{GeV}$, ${ϵ}_x=30\mathrm{pm}$, $L_c=4.78\mathrm{m}$).

Figure 27

Distribution of the dipole field (left, black), the gradient (left, red) and the sextupole gradient (right) in the cell with the longitudinal gradient dipole.

Figure 28

Superperiod of the light source with 6 GeV beam energy and 33.5 pm emittance.

Figure 29

Dynamic aperture of 6 GeV light source for three values of under-compensated chromaticity.

Figure 30

Energy acceptance with $Y_0={\sigma }_y$ (left) and bandwidth (right) of 6 GeV light source.