All numbers are obtained from the DIMAD-style input file. The gradients are computed from the energy gains there, corrected for speed-of-light transit time factors. The solenoid fields are computed using momentum which are found by integrating through the cavities in 1 cm steps using the given phase, where the zero-crossing of the phase corresponds to zero energy gain through the cavity.
To get the correctly matched lattice, one must include the edge focusing in the cavities. One must also include edge focusing in the solenoids by adding additional cylindrically-symmetric focusing on the ends. The kick on each end is B2ar/[8(pc/q)2], where B is the solenoid field, a is the aperture radius of the solenoid, r is the particle radius, p is the particle momentum, c is the speed of light, and q is the particle charge. Note this is a defocusing kick, which arises from the fact that the solenoid length times the integral of B2 is less than the integral of B, squared.
This lattice breaks up into three types of cells: 12 short cells (3 m long), 18 medium cells (5 m long), and 22 long cells (8 m long). The short cells have a = 19.5 cm for their solenoids and one single-cell cavity. The medium cells have a = 19.5 cm for their solenoids and one two-cell cavity. The long cells have a = 15 cm for their solenoids and two two-cell cavities. All the cavity apertures are 46 cm diameter, and the nominal gradient is 15 MV/m (despite the pillbox numbers below).
This description should exactly match the ICOOL input file.
This table gives the lattice:
Type | Length (m) | Bz (T) | Ez (MV/m) | RF Frequency (MHz) | Phase (°) |
---|---|---|---|---|---|
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.280258543135198 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -73.3386 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.295108707051999 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -72.4792 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.310710385332338 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -71.6770 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.327009807772755 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -70.8176 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.34405325605815 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -69.9581 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.361837575676156 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -69.0987 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.380359228531087 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -68.2966 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.399566300276945 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -67.4371 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.419503495128384 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -66.5777 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.440166650091075 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -65.7183 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | -1.48833970197267 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -64.8588 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.205174 | ||||
Solenoid | 1 | 1.161585480681157 | |||
Drift | 0.5 | ||||
Cavity | 0.744826 | 23.56196654152332 | 201.25 | -64.0567 | |
Drift | 0.3 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.244832878465834 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -62.7962 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -62.7962 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.148406007034057 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -61.4211 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -61.4211 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.185889409746292 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -59.9887 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -59.9887 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.225097958873612 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -58.5563 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -58.5563 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.266003266619797 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -57.1468 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -57.1468 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.308556446045105 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -55.7316 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -55.7316 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.352735457456626 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -54.3164 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -54.3164 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.398515445898499 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -52.9069 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -52.9069 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.445858958173241 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -51.5032 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -51.5032 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.494730073340989 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -50.1052 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -50.1052 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.545098096441989 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -48.7129 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -48.7129 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.596923187393087 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -47.3206 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -47.3206 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.650170130928767 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -45.9398 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -45.9398 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.704804144480872 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -44.5647 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -44.5647 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.760783551580789 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -43.1953 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -43.1953 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.818069225896601 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -41.8374 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -41.8374 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | -1.678688009298644 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -40.4852 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -40.4852 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.460348 | ||||
Solenoid | 1 | 1.454189254234557 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -39.1445 | |
Cavity | 0.744825 | 23.57409296988061 | 201.25 | -39.1445 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 1.542544635313145 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -37.3511 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -37.3511 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -37.3511 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -37.3511 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 1.697849671094697 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -35.2426 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -35.2426 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -35.2426 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -35.2426 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -1.77111869641457 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -33.1685 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -33.1685 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -33.1685 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -33.1685 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 1.874687691265038 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -31.1173 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -31.1173 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -31.1173 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -31.1173 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -1.980615160584863 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -29.1005 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -29.1005 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -29.1005 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -29.1005 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 2.08873386902708 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -27.1181 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -27.1181 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -27.1181 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -27.1181 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -2.198872643534033 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -25.1700 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -25.1700 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -25.1700 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -25.1700 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 2.31087102675717 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -23.2564 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -23.2564 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -23.2564 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -23.2564 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -2.424563071303099 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -21.3828 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -21.3828 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -21.3828 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -21.3828 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 2.539795403712444 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -19.5436 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -19.5436 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -19.5436 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -19.5436 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -2.656420357053925 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -17.7445 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -17.7445 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -17.7445 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -17.7445 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 2.774285959351801 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -15.9855 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -15.9855 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -15.9855 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -15.9855 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -2.893260514475263 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -14.2724 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -14.2724 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -14.2724 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -14.2724 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 3.013196063750335 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -12.5936 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -12.5936 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -12.5936 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -12.5936 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -3.133979219409849 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -10.9664 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -10.9664 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -10.9664 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -10.9664 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 3.255473682418484 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -9.37932 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -9.37932 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -9.37932 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -9.37932 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -3.377579090324824 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -7.83233 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -7.83233 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -7.83233 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -7.83233 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 3.500187021200664 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -6.33691 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -6.33691 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -6.33691 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -6.33691 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -3.623192801532467 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -4.88332 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -4.88332 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -4.88332 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -4.88332 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 3.746501834695975 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -3.47613 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -3.47613 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -3.47613 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -3.47613 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | -3.870034854513243 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -2.11479 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -2.11479 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -2.11479 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -2.11479 | |
Drift | 0.8 | ||||
Drift | 0.25 | ||||
Drift | 0.470696 | ||||
Solenoid | 1 | 3.993711339272642 | |||
Drift | 1 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -0.799849 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -0.799849 | |
Drift | 1.5 | ||||
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -0.799849 | |
Cavity | 0.744825 | 23.56196654157389 | 201.25 | -0.799849 | |
Drift | 0.8 |
J. Scott Berg <jsberg@bnl.gov> 13 September 2005. |
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