[FFA_CEBAF_Collab] [EXTERNAL] Magnets for recent single-FFA lattice (Sep'22)

[Brooks, Stephen]

Attached are pictures of somewhat feasible magnets that go with our one-turn FFA lattice.  I had to do some tweaking:

1.  Energies used to define the aperture range are after synchrotron radiation emission, which reduces the apertures a bit (helps).

2.  Rectangular magnets are broken into 6 longitudinal segments and displaced by
dx, -0.2*dx, -0.8*dx, -0.8*dx, -0.2*dx, dx
respectively, with dx being a value for each magnet around -1.5mm.  This allows the peak magnetic field to follow the particle trajectory better and gives improved magnetic efficiency, for example reducing |B|_max from 1.706 to 1.573T in the hardest magnet.

3.  Overall gradient has been scaled to 0.6 of its original value.  This means orbit excursions are larger by 1/0.6 and cell length is longer by sqrt(1/0.6).  But tunes stay constant in this scaling, as does packing factor (bonus: drifts also go up from 8cm to 10.3cm).

Design rules are +/-8mm (16mm total) vertical aperture in the beam region, +/-3mm (6mm total) vertical minimum vertical gap for synchrotron radiation escape.  (This is small but +/-4mm doesn't work well at the moment, I may need to mess with the magnet geometry some more).  And +/-12 degrees opening angle for the external vacuum chamber for synchrotron radiation (makes it mechanically a lot stronger).

B_r in the model is 1.248T not 1.3T.  This is to compensate magnetic interactions, which in the case of my prototype magnet, reduced the magnetisation to 96% of the simple mu_r=1 prediction.  (That's why I have a 1.536T magnet not a 1.6T magnet).  It is also consistent with mu_r being slightly above 1 in the B-H curve.

     -Stephen
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