APS Storage Ring Parameters
M. Borland — August 27, 2024

The APS lattice [1] is a hybrid multi-bend achromat [2] with reverse bends [34]. There are 40 sectors in the ring, with 35 straight sections available for insertion devices.

There are seven main-direction bends per sector and six reverse-direction bends. Four of the main-direction bends have longitudinal gradients, while three have transverse gradients. All of the reverse bends have transverse gradients. In addition to the bends, there are eight ordinary quadrupoles and six sextupoles per sector.

Three straight sections each contain main four rf cavities at a frequency of 352 MHz, with nominal voltage of 4.5 MV total, going up to 6.5 MV when all gaps are closed. There is also a fourth-harmonic bunch-lengthening cavity [5] with a nominal voltage of 1.1 MV.

Injection uses on-axis swap-out [67] using a single pulsed septum and three stripline kickers in a single straight section. The kickers allow filling every third rf bucket. An emittance-exchange [89] system is incorporated into the transport line from the booster synchrotron to the ring, so that the horizontal emittance is much smaller than the vertical emittance for the injected beam.

The ring is designed to operate on or near the linear difference coupling resonance, allowing for equal emittances in the two planes. It also has a low-coupling mode, which is workable for many-bunch fills.


PIC

Figure 1: Design lattice for APS for a single sector.



Table 1: General storage ring parameters

General storage ring parameters

NotationModel Value
Beam energy E0 6.0 GeV
Nominal circulating current, multibunch Inmb 200.0 mA
Nominal stored electrons, multibunch N, q 4.6 × 1012, 736 electrons, nC
Nominal circulating current, single bunchInsb 4.17 mA
Nominal stored electrons, single bunch N, q 9.6 × 1010, 15.3electrons, nC
Number of periods Np 40


Table 2: Transverse parameters

Transverse parameters

Notation Value
Transverse tune νx, νy 95.12, 36.13
Natural chromaticityξx,n, ξy,n -135.16, -111.11
Dispersion function ηx,max, ηy,max 89.99, 0.00 mm
Beta function βx,min, βy,min 0.77, 1.87 m
βx,ave, βy,ave 4.07, 8.56 m
βx,max, βy,max13.17, 20.51 m


Table 3: Longitudinal parameters

Longitudinal parameters

NotationValue
Circumference C 1103.609 m
Revolution frequency f 0 271.647 kHz
Revolution time T0 3.681 μs
Harmonic number hrf 1296
Typical RF voltage V 0 4.5 MV
Typical synchronous phase ϕs 139.284 Deg
Momentum compaction factorαc 3.85 × 10-5
Longitudinal tune (at 4.5MV)νs 0.002


Table 4: Radiation parameters

Radiation parameters

NotationValue
Radiation energy loss (dipole) Ur,d 2.935 MeV
Damping Time τx 6.721 ms
τy 15.049 ms
τE 19.782 ms
Damping Partition Jx 2.239
Jy 1.000
JE 0.761
Equilibrium momentum spread (zero current)σδ 0.136
Equilibrium bunch length (zero current) σt 14.401 ps
σz 4.317 mm
Natural emittance ϵn 41.522 pm
Radiation integrals I1 0.042 m
I2 0.161 m-1
I3 4.256 × 10-3 m-2
I4 -1.994 × 10-1m-1
I5 2.831 × 10-7 m-1


Table 5: Nominal ID Source Parameters

Nominal ID Source Parameters

NotationValue
General
Horizontal beta function β x 5.258 m
Vertical beta function βy 2.379 m
Horizontal dispersion ηx 0.388 mm
Horizontal dispersion slope ηx 0.016 mrad
Vertical dispersion ηy 0.000 mm
Vertical dispersion slope ηy 0.000 mrad
Flat beam mode
Emittance ratio κ 0.100
Horizontal emittance at zero currentϵx 39.747pm
Vertical emittance at zero current ϵy 3.975 pm
Horizontal rms size σx 14.466μm
Horizontal rms divergence σx 2.749 μrad
Vertical rms size σy 3.075 μm
Vertical rms divergence σy 1.293 μrad
Round beam mode
Emittance ratio κ 1.000
Horizontal emittance at zero currentϵx 28.703pm
Vertical emittance at zero current ϵy 28.703pm
Horizontal rms size σx 12.296μm
Horizontal rms divergence σx 2.336 μrad
Vertical rms size σy 8.263 μm
Vertical rms divergence σy 3.474 μrad


Table 6: Nominal BM Source Parameters

Nominal BM Source Parameters

NotationValue
General
Horizontal beta function β x 0.773 m
Vertical beta function βy 4.709 m
Horizontal dispersion ηx 4.385 mm
Horizontal dispersion slope ηx 12.092mrad
Vertical dispersion ηy 0.000 mm
Vertical dispersion slope ηy 0.000 mrad
Flat beam mode
Emittance ratio κ 0.100
Horizontal emittance at zero currentϵx 39.747pm
Vertical emittance at zero current ϵy 3.975 pm
Horizontal rms size σx 8.128 μm
Horizontal rms divergence σx 7.170 μrad
Vertical rms size σy 4.326 μm
Vertical rms divergence σy 0.919 μrad
Round beam mode
Emittance ratio κ 1.000
Horizontal emittance at zero currentϵx 28.703pm
Vertical emittance at zero current ϵy 28.703pm
Horizontal rms size σx 7.585 μm
Horizontal rms divergence σx 6.093 μrad
Vertical rms size σy 11.626μm
Vertical rms divergence σy 2.469 μrad

References