Characterization of beam position monitors for measurement of second moment Page: 3 of 5
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Characterization of Beam Position Monitors for Measurement of Second Moment
S. J. Russell, J. D. Gilpatrick, J. F. Power and R. B Shurter, Los Alamos National Laboratory, Los Alamos,
NM 87545 USAA dual-axis beam position monitor (BPM) consists of four
electrodes placed at 90 intervals around the probe aperture.
The response signals of these lobes can be expressed as a sum
of moments. The first order moment gives the centroid of the
beam. The second order moment contains information about
the rms size of the beam. It has been shown previously that the
second order moment can be used to determine beam emit-
tance [1]. To make this measurement, we must characterize the
BPM appropriately. Our approach to this problem is to use a
pulsed wire test fixture. By using the principle of superposi-
tion, we can build up a diffuse beam by taking the signals from
different wire positions and summing them. This is done two
ways: first by physically moving a wire about the aperture and
building individual distributions, and, second, by taking a two
dimensional grid of wire positions versus signal and using a
computer to interpolate between the grid points to get arbitrary
wire positions and, therefore, distributions. We present the
current results of this effort.
I. Introduction
Here at Los Alamos, we have two photoinjector driven
electron linacs. The first is an 8 MeV machine originally built
to drive the APEX free electron laser. It has since been moved
from its original location and is currently being employed in
experiments investigating sub-picosecond bunching of an elec-
tron beam. The second is the 20 MeV accelerator for the
Advanced Free Electron Laser experiment and has been oper-
ating since the summer of 1992.
Photoinjector driven electron accelerators are at the fore-
front of electron beam technology. They produce beams of
unparalleled quality. However, measuring second moment
properties of these beams, such as the rms emittance, is very
difficult [2]. This is due to their generally non-Gaussian beam
distributions. In order to measure the rms emittance, we need
an approach that does not require prior knowledge of the beam
distribution. Beam position monitors (BPMs) offer such a
technique [3].
For us to be able to use BPMs for emittance measurements,
we need a method of calibration for measuring the second
moment of the BPM signal. Our approach is presented here.
II. Calibration Theory
The BPMs that we will be using for this measurement were
originally built for the AFEL beamline [4]. These are capaci-
tive, or button-style, probes that differentiate the beam bunch
* Work performed under the auspices of the U. S. Department
of Energy.charge distribution that is induced on the probe electrodes.
A. BPM Signal
For the square electrodes, or lobes, of our BPMs, the signal
induced by a relativistic beam on the lobe at angular position $
is proportional to
simt
{2(+4- (xcos +ysin$)
sin2c 2
+ 2 { [ (X-ar ) + (x -2)] cos2$
a+2(xy)sin2$ } +O(- ) }
a(1)
The radius of the BPM apeture is a, the angle subtended by the
BPM lobe is a, i and f give the centroid position of the beam
and the angled brackets indicate an rms average over the beam
distribution. The term 02- a2 is what we are trying to mea-
sure. oX is equal to the rms average (x2) in the coordinate
system centered on the beam distribution, and similarly for aY.
B. Calibration equation
We are interested in extracting the quantity
2 2) + 2 2
(o6 -a) + (x2-Y2)
xy
from our BPM signals. For a perfect BPM, with four identical
lobes at 0, 90, 180 and 270 degrees around the apeture, this
term is given by
2 2 + 2 _2 SR+SL-STSB
(X-Y) + (x y k SR+SL+S S (2)
where SR, SL, S, and SB are the signals from the right, left, top
and bottom BPM lobes respectively (see Fig. 1) and k is a con-
stant to be determined. However, the lobes of a real BPM will
not be identical in general. Each will have a unique subtended
angle, c, and a unique apeture radius a. Therefore, equation
(2) must be modified to
2 2) + (2 2
xycl+c2S+c3x(1-S) +c4y (1+S)
1+ c5S
where S is defined by
SR+SL-ST-SB
S R + SL+ S + SB(3)
(4)and the cis are constants that need to be determined. This is the
goal of our calibration procedure.- ..-t-- -,---r-"rzr ,,flt.Z' rfl---~'~'--,--~~, - - -- --
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Russell, Steven J.; Gilpatrick, John D.; Power, John F. & Shurter, R. Brad. Characterization of beam position monitors for measurement of second moment, report, May 1, 1995; New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc709923/m1/3/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.