Instrumentation & Measurement Magazine 24-9 - 23

Fig. 2. Operation principle of a BPM. (a) A " button-style " electromagnetic BPM pickup; (b) LHC button feedthrough; (c) Beam bunch and image charges resulting a
BPM pickup signal; (d) Frequency domain behavior of the BPM signal; and (e) BPM difference signal.
Fig. 2e illustrates the BPM operational principle for a single
plane, often horizontal or vertical, with a pair of symmetrically
arranged BPM electrodes A and B in a beam pipe of aperture
2R. While the pulse-like signal waveforms out of each BPM
electrode have identical shape, the signal amplitudes are inverse
proportional to the distance between BPM electrodes
and beam, R−pos, and therefore proportional to the beam position
(pos) with reference to the beam pipe center and to the
beam intensity (int), but as of the symmetry with different
signs for electrodes A and B:
vv 
pos int ;
AB pos int
 
(1)
It seems obvious to subtract the two voltage signals of the
symmetrically arranged BPM electrodes, to get a signal proportional
to the beam position (pos), and while this is true, the
signal of each BPM electrode remains proportional to the beam
intensity velec
∝ int, and due to this so-called common-mode signal
the difference signal vΔ of the BPM electrodes still contains
the beam intensity:
vΔ vv  
AB pos int
(2)
A normalization procedure is required to extract a pure,
beam intensity independent position signal from the BPM
electrodes:
v Δ
v
December 2021
int

pos int
int

= pos
Typically, the intensity signal required for the normalization
is derived from the BPM electrodes as well, e.g.,
vint
v vv
v vv
Δ
Σ
=
AB
AB


 pos
(3)
however, several other methods for the beam intensity normalization
also exist.
The BPM pickup
There exist a variety of types on BPM pickups with different
characteristics, e.g.,
◗ " Button-style " or electrostatic BPM: Based on capacitive
coupling electrodes. Acts as high-pass filter together
with the load impedance (typical 3-dB cut-off frequency
100-1000 MHz). Compact, robust, low-cost mechanics.
Develops some unwanted eigen-resonances at
higher frequencies, typically >1 GHz. Very popular in
all electron accelerator BPM systems, but also in hadron
machines with reasonable short bunches [3].
◗ Stripline BPM: Directional coupler based on λ/4 TEM striptransmission-line
electrodes with 50 Ω characteristic
impedance [4]. Can be " tuned " to a specific
operating frequency range by choosing the appropriate
length of the stripline electrodes. Offers broadband characteristics-therefore
also suitable for intra-bunch beam
observation-can have a 50 Ω source impedance, and
IEEE Instrumentation & Measurement Magazine
23
= vΣ = vA + vB ∝ int, which leads to the well-known method
of beam position signal normalization:

Instrumentation & Measurement Magazine 24-9

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