Transcript Longitudinal Painting

Longitudinal Painting
S. Hancock p.p. G. Feldbauer
Synchrotron Tune at Injection
For the sake of aperture we now consider both LHC-type and fixed-target proton beams to
have the same smaller emittance at injection and that controlled longitudinal blow-up will
provide what is required starting from 0.4eVs. Long bunches to avoid space charge imply
low synchrotron frequencies and make it difficult to paint a uniform distribution by
synchrotron motion alone.
40 MHz rf voltage (left) at which matched bunches of 0.4 eVs occupy 70% of a stationary bucket length
at PS2 injection energy and corresponding synchrotron period (right) for real (solid lines) and imaginary
(dashed lines) values of γtr.
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Energy Offset
The energy spread of the SPL bunches was assumed to be a free parameter adjusted by a
debuncher, but simulations with both fixed and alternating energy offsets invariably produced
distributions that were either badly inhomogeneous or too short or both.
352.2MHz
ΔE = 3–6.5MeV
σE = 1–3MeV
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Moving Chopping Window (1)
Sawtooth period
4.264 turns
Inner window
0.45º
Outer chopping boundary +0.7º
Outer chopping boundary -0.7º
To obtain reasonable results it was necessary to go beyond the present performance of the
chopper to one that is capable of removing single SPL bunches and of operating with a
chopping factor of 0.5 or less (cf., 0.625). Instead of rapidly modulating the energy offset of
the incoming bunches, the idea is to modulate the portion of the bucket length that gets
populated on each turn.
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Moving Chopping Window (2)
The best bunch obtained exhibits a bunching factor of ~0.5 for a bucket length filling of 72%
(4σ). The chopping factor was 0.5, meaning that 163 turns would be required to inject
4.2×1011 protons assuming an SPL peak current of 32mA.
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Acceleration at Constant Acceptance (1)
Assuming dB/dt increases linearly to a maximum of 1.5T/s in a time 50, 75, 100 or 150ms, it
is straightforward to choose a voltage programme during the early part of the ramp such that
the acceptance remains constant at the value which matches 0.4eVs bunches to 70% of the
initial (stationary) bucket length. More voltage always increases the bucket height, but the
question is: would more voltage reduce the synchronous phase sufficiently to make the
bunches longer or would the increase in bucket height win making them shorter? In fact,
more voltage would shorten the bunch so such a programme yields the longest bunch for
given acceptance margin, which is good from the space charge standpoint.
Ignoring any transverse blow-up, relative space charge detuning is readily inferred from the
voltage programme. Very roughly speaking, the area under each of this second set of curves
is the penalty associated with the corresponding ramp.
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Acceleration at Constant Acceptance (2)
Taking the case of a 100ms parabolic ramp, the best-case bunch simulation was extended to
include acceleration (up to the maximum of the voltage programme).
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Conclusions
I quote Gregor verbatim:
“The results of the simulations done during this study show that with the changed parameters
compared to the previous studies only the injection scheme with the Moving Inner Chopping
Window is able to generate PS2 bunches with acceptable features. Schemes only working
with energy offsets and simple chopping variants are not capable of obtaining such bunches.
But consequently, ‘passive’ longitudinal painting is still in reach for the PS2.”
Thesis Project Reports (Vienna University of Technology)
V. Knuenz, “Study of longitudinal aspects of an H- charge exchange injection into PS2”,
(2008).
I. Vonderhaid, “Study of longitudinal filling schemes for the PS2 injection”, (2008).
G. Feldbauer, “Study of longitudinal painting schemes for H- charge exchange injection into
the PS2”, (2009).
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