Operational aspects of experimental accelerator physics Page: 15 of 28
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13
A real-time difference of two button signals (say top
and bottom) would have all of the spectral characteristics
of the bunch structure, in addition to the betatron side-
bands caused by the time-dependent kicker. One typically
sees enormous spectral lines at revolution harmonics, and
the kicker strength must be turned up enough to bring the
betatron sidebands up above the noise threshold of the
system. A measurement of the frequency of these sidebands
yields the fractional part of the tune according to
v = w/wo [10]
where Ac is the distance from a sideband to the nearest
(v<1/2) or second-nearest (v>1/2) harmonic of the
revolution frequency co. The ambiguity v<1-/2 or v>l/2 can
be resolved by changing quadrupole strengths and paying
close attention to the sign of the resulting change in
tune. For example, increasing a horizontally focussing
quad (QF) or string of quads is known to increase the
horizontal tune. In this situation, the horizontal
betatron sidebands will move outward from their associated
revolution harmonic, i.e., vH must increase. A similar
procedure can be used vertically. The only fly in the
ointment is when the machine is fully coupled and both
horizontal and vertical sidebands vH and vv appear in equal
strengths, regardless of which plane is being driven. For
this, one can use the fact that the horizontal tune moves
up more than the vertical tune moves down when the
horizontal focussing is increased. More commonly, a
software knob is used to vary focusing and defocusing quads
QF and QD simultaneously so that the horizontal and
vertical tunes can be varied independently in an orthogonal
manner.
If the integer part of the tune is desired, it can be
found by observing the orbit distortion caused by changing
a single steering corrector and counting the number of
oscillations.
3.2 Betatron Tune Measurement Instrumentation
To measure the tune, a transverse drive system, a real-
time beam position sensor, and a device for measuring
transfer function are required. The drive system consists
of a drive element and an amplifier. If striplines are
used, the system will operate at rf frequencies up to
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Decker, G.A. Operational aspects of experimental accelerator physics, report, July 1, 1995; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc792469/m1/15/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.