Correction of unevenness in recycler beam profile Page: 4 of 4
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In the present example, Veff 32 V at the tail of the beam
and -9.2 V at the head. Amplification from the LLRF to
the cavity gap is 2000. Feedback at the LLRF is therefore
-16 mV at tail and +4.6 mV at head. To avoid phase-
space increase, the feedback has to be applied slower than
one synchrotron period of the beam, ~1.7 s here at 1 a-,.
Thus the feedback has to be applied in many small steps
(more than 10) in practice.
At the rf fan-back, 1.6 V out of the +2 kV barrier voltage
is only 0.08%, pretty small, and the signal-to-noise ratio is
therefore very low. In practice, we need to average over
200 to 500 data samples in order to sort out the signals.
With a 1 GHz oscilloscope, the time required is typically
~1 min, including data storage and processing.
Another compensating method is to employ the beam
profile unevenness picked up at wall-gap monitor as feed-
back input. Because the profile unevenness is very much
larger than the rf imperfection, the signal-to-noise ratio is
relatively very much higher, so that an average of ~20 sets
of readout will be enough. But there are other disadvan-
tages. The Haissinski equation can be expanded as
r e#E Z - 1
p(T)~ p(0) I- jVeff(T')dT' .
Thus profile unevenness is
Ap(T) = p(T) - P(0) = eTO2 0 P(0)j Veff(T')dT',
and is proportional to rf potential-well unevenness, a prop-
erty we noticed earlier. The compensation voltage is
behind a slanting profile. This is because the rf pulses are
ac-coupled to the beam and f VeffdT A 0 between the bar-
riers. Further voltage fine adjustment was then made to
ensure f VgrdT = 0 and the beam profile became flat.
Figure 5: (Color)
The signals at 2 ns
interval was low-
pass filtered, and
then decimated to fit
the 18.936-ns LLRF
time resolution ta-
Time ( s)
Figure 6: (Color) A proton beam with profiles before (left) and
after (right) profile-unevenness compensation.
Vcop -- eI/32Eo p(0)
The compensation procedure involves a differentiation and
a multiplication with a constant which depends on the
energy-offset distribution. For a distribution with a smooth
spread at both ends, the dependency should be small. This
method also involves an expansion by omitting all higher-
order terms. However, this last concern can be eliminated
by solving the Haissinski equation exactly with the solution
given by Eq. (1) but with p(0) replaced by p(T).
The fan-back voltage was recorded with a Tektronix
TDS 3054B digital oscilloscope, with time resolution 2 ns.
The data were averaged for 500 samples to further improve
signal-to-noise ratio. The noisy data were first low-pass fil-
tered to remove high-frequency noises. A decimation was
made to fit the 18.936-ns time resolution of the input table
to be applied to the LLRE The correction pulse was then
sent to the LLRF in small steps.
As a test, a proton beam with modest intensity 1 x 1011
and aE ~2 MeV is stored in a barrier bucket of length 2 s.
The profiles before and after correction are shown in Fig. 6.
In another example shown in Fig. 7, the first compensa-
tion removed the curvature of the beam profile but leaving
Figure 7: (Color) First com-
pensation removed beam profile
curvature leaving behind a slant-
ing profile, since f VeffdT - 0.
Fine adjustment of the barrier
voltage was required to totally
flatten the uneven profile.
The connection between the uneven beam profile and rf
imperfection and beam-loading has been given. The com-
pensation of beam-profile unevenness has been success-
fully performed. Although compensation is straight for-
ward, it is rather tedious because the compensation has
to be applied in many small steps to avoid phase-space
increase. When the area under the fan-back voltage is
nonzero, fine-adjustment of the barrier wave must be per-
formed. To guarantee a correction pulse free of any dc
component, a simple solution is to compute the difference
between l4f and the reference voltage over the entire rev-
olution period (not just between the barriers) when deter-
mining the feedback to the LLRE An automation of the
compensation procedure has been designed and is being
built, hoping that the compensation could be performed in
the future by just pushing a button.
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Crisp, J.; Hu, M.; Ng, K.Y. & /Fermilab. Correction of unevenness in recycler beam profile, article, May 1, 2006; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc874878/m1/4/: accessed November 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.