APS Storage Ring Parameters
M. Borland — August 27, 2024
The APS lattice [1] is a hybrid multi-bend achromat [2] with reverse bends [3, 4]. 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 [6, 7] 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 [8, 9] 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.
General storage ring parameters
Notation | Model 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 bunch | Insb | 4.17 | mA |
Nominal stored electrons, single bunch | N, q | 9.6 × 1010, 15.3 | electrons, nC |
Number of periods | Np | 40 | |
Transverse parameters
Notation | Value | ||
Transverse tune | νx, νy | 95.12, 36.13 | |
Natural chromaticity | ξx,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,max | 13.17, 20.51 | m | |
Longitudinal parameters
Notation | Value | ||
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 factor | αc | 3.85 × 10-5 | |
Longitudinal tune (at 4.5MV) | νs | 0.002 | |
Radiation parameters
Notation | Value | ||
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 × 10-1 | m-1 | |
I5 | 2.831 × 10-7 | m-1 | |
Nominal ID Source Parameters
Notation | Value | ||
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 current | ϵx | 39.747 | pm |
Vertical emittance at zero current | ϵy | 3.975 | pm |
Horizontal rms size | σx | 14.466 | μm |
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 current | ϵx | 28.703 | pm |
Vertical emittance at zero current | ϵy | 28.703 | pm |
Horizontal rms size | σx | 12.296 | μm |
Horizontal rms divergence | σx′ | 2.336 | μrad |
Vertical rms size | σy | 8.263 | μm |
Vertical rms divergence | σy′ | 3.474 | μrad |
Nominal BM Source Parameters
Notation | Value | ||
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′ | 12.092 | 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 current | ϵx | 39.747 | pm |
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 current | ϵx | 28.703 | pm |
Vertical emittance at zero current | ϵy | 28.703 | pm |
Horizontal rms size | σx | 7.585 | μm |
Horizontal rms divergence | σx′ | 6.093 | μrad |
Vertical rms size | σy | 11.626 | μm |
Vertical rms divergence | σy′ | 2.469 | μrad |