446
F. Bordry et al.
where Q is the change in tune, p/p the momentum spread (or relative change in
momentum), R/R the relative change in average radius, f /f the relative change
in RF frequency and ξ the chromaticity. Please note that the chromaticity, ξ , is
often expressed as Q’ = Qξ , where Q is the total betatron tune including the integer
part. A typical chromaticity measurement therefore consists of performing a tune
measurement for several different RF frequency settings. What is usually measured
is the average change in closed orbit, due to dispersion, from which the relative
change in radius, and hence momentum change can be calculated. The chromaticity
is then simply the measured tune change divided by the applied momentum change.
In order to obtain a continuous chromaticity measurement the technique of RF
modulation can be combined with PLL tune measurement [131].
8.6.3.3 Coupling Measurement
The control of coupling (the degree to which horizontal and vertical betatron motion
is linked) is also important for circular accelerators. Excessive coupling will make
tune and chromaticity measurements almost impossible, as the information from
both planes are mixed-up in the observed signal. A direct measure for the total
coupling coefficient |C - | can be obtained by the “closest tune approach” method.
Both betatron tunes are measured during a linear quadrupole power converter ramp
which crosses the values of the horizontal and vertical tunes. Any coupling present
in the machine will introduce a forbidden band through which the tune cannot cross,
instead jumping from one side to the other. The width of this band is given by the
total coupling coefficient |C - |.
In order to obtain a continuous measurement of coupling the PLL tune measurement can again be used, comparing the amplitude of the tune response in the plane
of excitation with that of the other plane [132].
8.6.4 Beam Profile Measurements
Transverse beam distribution measurements are performed in all accelerators. As
well as providing a direct measure of the beam quality, they can be used verify
accelerator lattice functions and to calculate the emittance of particle beams. There
are many ways to measure the beam size with the most commonly used techniques
described in this section.
8.6.4.1 Secondary Emission Grids
Secondary Emission (SEM) Grids, also known as harps, consist of ribbons or
wires which are placed in the beam [133]. See Fig. 8.63. As the beam intercepts
the grid, secondary emission occurs leading to a current in each strip which is
F. Bordry et al.
where Q is the change in tune, p/p the momentum spread (or relative change in
momentum), R/R the relative change in average radius, f /f the relative change
in RF frequency and ξ the chromaticity. Please note that the chromaticity, ξ , is
often expressed as Q’ = Qξ , where Q is the total betatron tune including the integer
part. A typical chromaticity measurement therefore consists of performing a tune
measurement for several different RF frequency settings. What is usually measured
is the average change in closed orbit, due to dispersion, from which the relative
change in radius, and hence momentum change can be calculated. The chromaticity
is then simply the measured tune change divided by the applied momentum change.
In order to obtain a continuous chromaticity measurement the technique of RF
modulation can be combined with PLL tune measurement [131].
8.6.3.3 Coupling Measurement
The control of coupling (the degree to which horizontal and vertical betatron motion
is linked) is also important for circular accelerators. Excessive coupling will make
tune and chromaticity measurements almost impossible, as the information from
both planes are mixed-up in the observed signal. A direct measure for the total
coupling coefficient |C - | can be obtained by the “closest tune approach” method.
Both betatron tunes are measured during a linear quadrupole power converter ramp
which crosses the values of the horizontal and vertical tunes. Any coupling present
in the machine will introduce a forbidden band through which the tune cannot cross,
instead jumping from one side to the other. The width of this band is given by the
total coupling coefficient |C - |.
In order to obtain a continuous measurement of coupling the PLL tune measurement can again be used, comparing the amplitude of the tune response in the plane
of excitation with that of the other plane [132].
8.6.4 Beam Profile Measurements
Transverse beam distribution measurements are performed in all accelerators. As
well as providing a direct measure of the beam quality, they can be used verify
accelerator lattice functions and to calculate the emittance of particle beams. There
are many ways to measure the beam size with the most commonly used techniques
described in this section.
8.6.4.1 Secondary Emission Grids
Secondary Emission (SEM) Grids, also known as harps, consist of ribbons or
wires which are placed in the beam [133]. See Fig. 8.63. As the beam intercepts
the grid, secondary emission occurs leading to a current in each strip which is