Magnetic field measurements of printed-circuit quadrupoles and dipoles

Abstract

Printed-Circuit (PC) quadrupoles and dipoles have been designed
and developed for focusing and bending a space-charge dominated electron
beam in the University of Maryland Electron Ring (UMER), currently under
development. Due to the rather small aspect ratio (length/diameter
<1) of the magnets, the field quality, especially the nonlinear
fringe field, has been a concern for the success of the UMER project.
Extensive theoretical and experimental studies of the field structure of
the magnets have been performed. Simple and precise methods for the
magnetic field measurements of the PC magnets have been developed. In
this paper, we present the various techniques and results of the
measurements. The magnetic multipole components of quadrupoles and
dipoles are determined from measurements with a long rotating coil. In
addition, the integrated field of quadrupoles is obtained with the
pulsed, taut-wire method. A comparison between the experimental results,
theoretical analysis and calculation with a magnetics code, MAG-PC, is
presented

Full text

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MAGNETIC FIELD MEASUREMENTS OF
PRINTED-CIRCUIT QUADRUPOLES AND DIPOLES∗ ∗
W.W. Zhang#, S. Bernal, P. Chin, R. Kishek, M. Reiser, M.Venturini, J.G. Wang, V. Yun
University of Maryland, College Park, MD 20742

∗ Research supported by the U. S. Department of Energy
# Email: wwz@glue.umd.edu
Abstract
Printed-Circuit (PC) quadrupoles and dipoles have been
designed and developed for focusing and bending a space-
charge dominated electron beam in the University of
Maryland Electron Ring (UMER) [1], currently under
development. Due to the rather small aspect ratio
(length/diameter < 1) of the magnets, the field quality,
especially the nonlinear fringe field, has been a concern for
the success of the UMER project. Extensive theoretical
and experimental studies of the field structure of the
magnets have been performed. Simple and precise
methods for the magnetic field measurements of the PC
magnets have been developed. In this paper, we present
the various techniques and results of the measurements.
The magnetic multipole components of quadrupoles and
dipoles are determined from measurements with a long
rotating coil. In addition, the integrated field of
quadrupoles is obtained with the pulsed, taut-wire method.
A comparison between the experimental
theoretical analysis and calculation with a magnetics code,
MAG-PC, is presented.
results,
1 INTRODUCTION
A compact Electron Ring is being developed at the
University of Maryland to study space charge effects and
collective behavior of beams in a circular lattice [2]. The
UMER has been designed to transport an electron beam of
10 keV, 100 mA, and 50 ns in a circular lattice of 11.5 m
in circumference. The key components of the electron ring
lattice are Printed Circuit (PC) quadrupoles and dipoles.
The electron beam is focused by 72 PC quadrupoles and
deflected by 36 PC dipoles. Table 1. lists the physical
parameters of the PC quadrupoles and dipoles. These very
short, air core magnets are made of current loops on
flexible printed circuits [3]. This approach can meet not
only the demand for beam transport in the electron ring,
but also a significant reduction in cost. Nevertheless, the
challenging problem is that the magnets have a rather
small aspect ratio, resulting in highly nonlinear fringe
fields. This concern has been addressed by extensive
study of the field structure of the magnets in both theory
and experiments.
Table 1: Physical parameters of PC magnets
Quadrupole
2.79 cm
4.65 cm
0.833
4.14 G/cm-A
dipole
2.872 cm
4.437 cm
0.772
5.22 G/A
Radius R
Length L
L/2R
Grad (B Field)
2 SPATIAL HARMONICS
MEASUREMENT
An accurate, widely used method of measurement of
harmonics content in magnetic quadrupoles is the
rotating coil [4]. A rectangular coil with dimensions 2.54
cm by 12.7 cm has been built [5]. It is used in such a way
that one side of the coil is always positioned along the
axis of the magnets, so the only relevant component of
the magnetic field is Bφ. The voltage waveform induced
in the rotating coil, spinning at 6±0.001 Hz, is digitized
and fast-Fourier transformed in a scope. The oscilloscope
is triggered by a synchronous signal related to the
angular position of the rotating coil. Figure 1 is a photo
of the basic setup.
Figure 1: Rotating coil setup (without µ-metal shield).
The PC quadrupole is the block labeled "Q4"
in the photo.
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The Earth's field and environmental noise are carefully
compensated, since otherwise they produce a dipole term
and other harmonic terms that affect the accuracy of
measurement. To shield the effect of the Earth's field, a µ-
metal box is employed; the residual field is about 5 mG.
The effect of random noise is reduced by averaging more
than ten measurements. The first step is to adjust the PC
magnet relative to the rotating coil to minimize the dipole
component (for the quad), or the quadrupole component
(for the dipole); a 3-axis support fitted with non-magnetic
micrometer screws is used for this purpose, which makes
quadrupole magnetic axis corresponding to the mechanical
axis of the coil. In this way, the rotating coil allows us to
determine the magnetic axis of each quadrupole relative to
its mechanical axis to within 0.025 mm. Figure 2 shows a
typical spectrum from one quadrupole (with µ -metal
shield).
95
80
65
50
35
20
08 162432 40
dbV
Frequency (Hz)
Dip
Q
S
O
DeDu
Figure 2: Harmonic spectrum of PC quadrupole:
Dip(ole), Q(uadrupole), S(extupole), O(ctupole),
De(capole) and Du(odecapole).
Both theoretical analysis [6] and MAG-PC calculations
show that the only high order harmonic term allowed in
the UMER PC quadrupole is the duodecapole; for the PC
dipole, the sextupole and decapole terms occur. The
unexpected measured high order harmonic terms in both
PC magnets can be traced to machining errors in the metal
mandrels, small errors in assembly, and possible
distortions of the printed circuit. The dipole term in the
quad spectrum is due mostly to the residual Earth's field.
Table 2 lists the measured harmonic multipole terms
relative to the main component in both PC quadrupoles
and dipoles. Each number is the average of thirty-two
measurements.
Theoretical analysis [6] yields a duodecapole term for the
PC quadrupole equal to 0.098 %, while MAG-PC
calculations give 0.12 %, both in agreement with the
measured value, within experimental error. The measured
multipole terms have been used in single-particle studies
and error analysis of the University of Maryland Electron
Ring [7]. They also provide important information for the
mechanical alignment of the UMER.
Table 2: Measurement results
Magnet
HarmonicDipole(%)
Dipole
Quadrupole
Sextupole
Octupole
Decapole
Duodecapole
Quadrupole (%)
0.3
100
0.3
0.2
0.19
0.15
100
0.37
0.51
0.14
0.11
------
3 MAGNETIC FIELD MEASUREMENT
Because of the small size of the PC magnets, direct
measurements with, for example, a
gaussmeter is impractical. An alternative is to derive the
field from integrated-field measurements using the
pulsed taut-wire method [8,9]. Figure 3 shows the
experiment setup.
Hall-probe
Figure 3: Setup for integrated magnetic field
measurement with a pulsed taut-wire.
A current pulse (about 4 A, 300 µs at 0.2 Hz) is applied
to a long straight wire parallel to and some distance from
the PC magnet axis. The Lorentz force on the wire
produces a mechanical vibration that a photogate sensor
turns into a voltage. The amplitude of the voltage
waveform is proportional to the integral of the transverse
magnetic field. In order to reduce the effects of room
vibration and noise, the waveforms are averaged over at
least 100 pulses. Since the Earth's magnetic field affects
the motion of the wire, the waveform produced by the
Earth's field alone is first obtained and then subtracted
from the measurements. Figure 4 shows the result of a
typical waveform after subtracting the Earth's field
signal.
I (t)
Detector
Weight
Taut - wire
100cm
l
Trigger
Delay
High current
Pulser
HP54540
Oscilloscope
Amplifier
Printer
HP - VEE
HP586
Computer
HPIB
z - l
d
z
d
PC magnets
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To obtain an accurate value of the integrated magnetic
field, a calibration is required. The simplest calibration
method uses a set of small Helmholtz coils: the integrated
magnetic field of the coils is carefully determined from
measurements with both a gaussmeter and the taut-wire;
thus the correspondence between amplitude of measured
waveform and integrated field (i.e. number of volts per
G×cm) is established. Since the optical sensor has a limited
linear area, the calibration is performed with care taken to
avoid changing the sensor and taut-wire relative
positioning used during the magnet measurements.
Figure 4: Typical signal from photogate sensor in the taut-
wire method.
After differentiation and normalization of a waveform
similar to Figure 4, the normalized field profile of Figure 5
is obtained. The difference between experimental results
and calculations is more pronounced in the tails, where the
sensitivity of the taut-wire apparatus becomes a problem.
Figure 5: Normalized field profile of a PC quadrupole at
r=0.45×quad radius and θ=45
is the result of MAG-PC calculations.
o. The solid line
An obvious improvement is to increase the peak current
(without changing the pulse width) applied to the wire or
the DC current applied to the magnet. This latter option,
however, results in quadrupole heating.
The taut-wire method is also suitable for measuring the
integrated magnetic field of pulsed magnets like the
Panofsky quadrupole and the injector/extractor dipole
intended for the Maryland Electron Ring [10].
4 SUMMARY
A rotating coil and a pulsed taut-wire apparatus have
been used to measure the harmonic content and
integrated magnetic field, respectively, of the PC
magnets for the University of Maryland Electron Ring.
These complementary measurements provide detailed
information on the field quality of the small aspect ratio
lenses, important for simulations of the beam dynamics
as well as a realistic design of the mechanical lattice. The
measurements are also significant on their own right,
since the magnets are possibly the shortest (relative to
their aperture), in existence.
The results of both the rotating coil and the pulsed-taut
wire measurements are consistent with calculations with
the iron-free magnetics code MAG-PC. The rotating coil
results are also in fair agreement with theoretical
predictions.
Studies similar to the ones reported here for DC magnets
are planned for the pulsed elements of the UMER.
5 REFERENCES
[1] M. Reiser et al., these Proceedings
[2] M. Reiser et al, Fusion Engineering and Design, 32-33,293 (1996);
J. G. Wang et al., Particle Accelerator Conf., 1997, p. ????.
[3] T.F. Godlove, S. Bernal and M. Reiser, Particle Accelerator Conf.,
1995, p. 2117.
[4] W.G. Davies, Nucl. Instr. and Meth. Phys. Res. A311, 399-436
(1992).
[5] Rawson-Lush Instruments Co., Inc. Acton, Massachusetts.
[6] M. Venturini, Ph.D. dissertation, University of Maryland, July,
1998.
[7] L.G. Vorobiev, X. Wu and R.C. York, Michigan State University
unpublished Report, October, 1998.
[8] O. Shahal et al., Nucl. Instr. and Meth. Phys. Res. A259, 299-302
(1989).
[9] H.Nishihara and M.Terada, Journal of Appl. Phys. 41, 8, 3322-
3324, (1970).
[10] Y. Li et al., these Proceedings.
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t (ms)
10mV
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0.25
0.5
0.75
1
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Proceedings of the 1999 Particle Accelerator Conference, New York, 1999