440
F. Bordry et al.
• Resistive/Inductive
These monitors make direct use of the image current flowing on the wall of
the vacuum chamber. A ceramic gap is used to force the image current through
external resistors, in the case of the resistive (wall current) monitor, or through
metallic rods fitted with transformers in the case of the inductive pick-up [122].
The position is calculated by comparing the output from suitably placed resistors
or rods.
• Magnetic
Such monitors are usually exploited for their relative insensitivity to stray
particles. In this case the two electrodes are replaced by two loops orthogonal
to the plane of measurement which couple to the magnetic field of the beam.
8.6.1.2 Beam Position Acquisition Systems
In order to extract an intensity independent position from all of these monitors a
normalised difference signal needs to be obtained, i.e. a difference signal which is
independent of the beam intensity [123]. In the case of the cavity this is simply
done by dividing the output of the dipole (difference) cavity with that of a separate
monopole (sum) cavity. In all the other cases one of the following methods is
employed (A and B being the signal from each electrode):
• Difference over sum (/)
The sum and difference are obtained either using a 0 ◦ /180 ◦ passive hybrid,
a differential amplifier or calculated by software after digitising the signal from
each electrode The resulting transfer function is highly linear with Normalised
Position = (A−B)/(A+B).
• Logarithmic ratio
The two input signals are converted into their logarithmic counterparts and
subtracted. In practice this is done using logarithmic amplifiers followed by a
differential amplifier. The transfer function is an S-shaped curve which becomes
highly non-linear when exceeding 70% of the normalised aperture: Normalised
Position = Log (A/B) = Log(A) − Log(B).
• Amplitude to Phase or Time
The two input signals are converted into signals of equal amplitude but
varying phase by combining them in a 90 ◦ passive hybrid. Normalised Position = ϕ = 2×arctan(A/B). The transfer function is again an S-shaped curve but
does not diverge for large excursions. In addition, the gradient is larger around
zero, making it more sensitive towards the middle of the pick-up.
The type of normalisation to be used will depend on the choice of processing
electronics, which in turn depends on the type of measurements to be performed
(single pass, single bunch, average orbit etc.). In all cases the non-linearity is taken
into account by calibration circuits and correction algorithms. Common acquisition
electronics include:
F. Bordry et al.
• Resistive/Inductive
These monitors make direct use of the image current flowing on the wall of
the vacuum chamber. A ceramic gap is used to force the image current through
external resistors, in the case of the resistive (wall current) monitor, or through
metallic rods fitted with transformers in the case of the inductive pick-up [122].
The position is calculated by comparing the output from suitably placed resistors
or rods.
• Magnetic
Such monitors are usually exploited for their relative insensitivity to stray
particles. In this case the two electrodes are replaced by two loops orthogonal
to the plane of measurement which couple to the magnetic field of the beam.
8.6.1.2 Beam Position Acquisition Systems
In order to extract an intensity independent position from all of these monitors a
normalised difference signal needs to be obtained, i.e. a difference signal which is
independent of the beam intensity [123]. In the case of the cavity this is simply
done by dividing the output of the dipole (difference) cavity with that of a separate
monopole (sum) cavity. In all the other cases one of the following methods is
employed (A and B being the signal from each electrode):
• Difference over sum (/)
The sum and difference are obtained either using a 0 ◦ /180 ◦ passive hybrid,
a differential amplifier or calculated by software after digitising the signal from
each electrode The resulting transfer function is highly linear with Normalised
Position = (A−B)/(A+B).
• Logarithmic ratio
The two input signals are converted into their logarithmic counterparts and
subtracted. In practice this is done using logarithmic amplifiers followed by a
differential amplifier. The transfer function is an S-shaped curve which becomes
highly non-linear when exceeding 70% of the normalised aperture: Normalised
Position = Log (A/B) = Log(A) − Log(B).
• Amplitude to Phase or Time
The two input signals are converted into signals of equal amplitude but
varying phase by combining them in a 90 ◦ passive hybrid. Normalised Position = ϕ = 2×arctan(A/B). The transfer function is again an S-shaped curve but
does not diverge for large excursions. In addition, the gradient is larger around
zero, making it more sensitive towards the middle of the pick-up.
The type of normalisation to be used will depend on the choice of processing
electronics, which in turn depends on the type of measurements to be performed
(single pass, single bunch, average orbit etc.). In all cases the non-linearity is taken
into account by calibration circuits and correction algorithms. Common acquisition
electronics include: