1. Tomography at Injection in the PSB
and related MDs
S. Hancock

2. Synchronous Phase at Injection in the PSB
The expression for the synchronous phase (at constant frequency) differs from the usual one (at constant radial position) solely by the factor γ 2 /( γ 2 − γ t 2 ), which at Booster injection evaluates to
sin φ s = 2πRρ V dB dt [dR/dt=0]
sin φ s = γ 2 ( γ 2 − γ t 2 ) 2πRρ V dB dt [df/dt=0]
See
S.Hancock, CERN-ACC-NOTE (2016)
R.Cappi and C.Steinbach, IEEE Transactions on Nuclear Science Vol. NS-28 No. 3 (1981)

3. Tomogram at Injection
Although injection involves a beam that is spiralling radially inwards with an rf frequency that is fixed despite a large (~0.5T/s) ramp rate, this can practically all be taken into account by the Tomoscope without modifying the tracking part of its reconstruction code. The trick is to force an appropriate decelerating bucket. This is not as counter-intuitive as it might seem. If there were no rf, the beam would still spiral inwards and the revolution frequency would therefore rise as the orbit length decreases. So, in order to keep the revolution frequency constant, an rf system would indeed need to slow the beam down to compensate.
T/s
T/s

4. Modified Distributor Timings
The total lack of synchronism at Booster injection results in a particle distribution whose initial phase fluctuates wildly from shot to shot with respect to the rf bucket into which it is subsequently captured. An alternative low-jitter injection into Ring3 was established by replacing the standard BIX.TPROT clock train used to pilot the injection warning pre-pulse BIX.WINJ by the genuine rf train BA3X.TREV. This was achieved in ppm by switching between external trains 1 and 2 once the Ring3 revolution train was distributed to the latter. The modification was completed by switching all BIXn.DIS distributor timings to count 40MHz ticks instead of BIX.TPROT ones.
BA3X.TREV 2
Ext2
40MHz
= 67 ticks per turn

5. Energy Matching wrt Linac2
With a reproducible phase at injection, it became possible (cf., a bunch-into-bucket transfer) to monitor the energy of the incoming beam and to adapt the injection frequency accordingly. Of course, no distinction can be made between a drift in Linac2 energy and any non-reproducibility of the Booster magnetic field itself.
See
Δfinj = -400Hz

6. Intensity Reproducibility
The asynchronous injection had long been suspected to be an ingredient in the intensity non-reproducibility observed for low-intensity beams, such as pilot beams for the LHC. Removing the jitter exposed a bug in the C16 blow-up which was finally fixed during the technical stop on 7 June 2016.
See

7. Dual-harmonic Capture
An “iso-adiabolical” process was developed based on constant-acceptance inner buckets to protect the core of the injected distribution whilst growing the outer bucket to capture the rest – and all this in such a way that the synchrotron frequency evolves iso-adiabatically. The result emulated the nominal 25ns beam, but with only 1.7 turns instead of the 2.6 turns for the operational user and hence a possible ~50% increase in brightness.
See

8. Fast Injection Losses
Gian Piero took up the challenge of reducing the fast losses and managed to increase the injection efficiency from 15-20% to 70-75%. This yielded an LHCINDIV-like beam with only 0.3 turns instead of 1.8 turns and with a much reduced transverse emittance.
See

9. Future Diagnostic?
Putting all the bunch-into-bucket injection-on-the-fly improvements together (and with a little offline tweaking and zooming), a first glimpse of the 200MHz structure of the incoming beam was revealed.