axis are of importance. OCR Outputthat only the measurements of integrals of the magnetic field and its derivatives along the beamthe wavelength of the particle oscillations in the accelerator (betatron oscillations). This meansmethods must match these requirements. The length of the magnet is usually small compared topositioning in the accelerator. Construction techniques, measurement equipment and alignmentrequire very tight tolerances on their magnetic fields and therefore also on their geometric

Electromagnets used as beam guiding elements in particle accelerators or storage rings,

2 . 1 Accelerator Magnets

2 . MEASUREMENT REQUIREMENTS

[1, 2]. An interesting description of early measurement methods can be found in [3].methods, a more complete discussion can be found in the two classical bibliographical reviewsthe equipment is readily available from industry. For the many other existing measurementbe discussed. lt is noticeable that these methods are complementary and that a wide variety ofsubject to continual development In the following only the more commonly used methods willmethods have remained virtually unchanged for a very long period, the equipment has beenmeasurement methods may be the same. It is curious to note that while the measurementmeasurement requirements for each of these are quite different, whereas the appliedspecialities: namely that of beam guiding magnets and that of detector magnets. The

In the field of particle accelerator technology there are two major magnetic measurement

measurement technology.discovered electromagnetic induction, in 1831. This event marks the beginning of magnetalready formulated the quantitadve law of electromagnetism. Shortly after, Michael Faradayaffected the compass reading. By September of the same year André-Marie Ampere hadelectric current in a platinum wire, placed near and parallel to a magnetic compass needle

Hans Christian Oersted discovered electromagnetism in June 1820. He observed that an

1 . INTRODUCTION

(median plane and magnetic axis) are discussed.problems related to measurements and definition of field geometrythe more exotic methods are also briefly mentioned. Particularsensors and associated equipment are commercially available. A few ofmost of the needs for measurements in this area. It is mentioned whenare indicated. The described methods are complementary and coverReferences of historical nature as well as citations of more recent workresonance technique and the fluxgate magnetometer are given.descriptions of the fluxmeter method, the Hall generator, magneticwell as in spectrometer magnets used in particle physics. Shortmeasurements in beam- guidance magnets for particle accelerators asThe paper illustrates the most commonly used methods for magneticAbstract

CERN, Geneva, SwitzerlandK. N. Henrichsen

CLASSIFICATION OF MAGNETIC MEASUREMENT METHODS

70

lggmet s. OCR Outputobtaid in an absolute measurement as a function of the field level for a few commonly usedaccuracy all need to be considered. As a guide, Fig. 1 shows the accuracy which can bedetector magnets. The field strength, homogeneity and variation in time, as well as the requiredThe choice of measurement method depends on several factors both for beam—guidance and

2 . 3 . Choice of measurement method

model work is often useful and may save considerable time.measurement equipment and a clear idea of the way to present and judge the results. Somevolume. These requirements call for a detailed analysis of the task, careful design of theinstallation of detectors, vacuum chambers and other components within the magnetic fieldaddition, it is important that measurements are fully completed and certified before theaccelerator and the measurements can only be performed during shutdown periods. Inend of a construction period or, even worse, if the magnet has been installed into an existingtime is usually more limited, especially when the magnetic measurements are scheduled near thelarge detector magnets. The requirements for accuracy are less suingent. On the other hand,

The boundary conditions are slightly different in the case of magnetic measurements of

2 . 2 Detector Magnets

determining the absolute energy of the accelerated particles [4].In particular, the value of the total bending strength of the installed magnets can be used forfield cycling or for determining the particle acceleration procedures and for diagnostic purposes.operation of the accelerator. They will serve to define operational procedures, such as magnetic

All measured magnet parameters will continue to be useful during the commissioning and

the quality (or reducing the cost) of the accelerator.magnets. This sorting procedure can reduce the dispersion of bending strength, thus increasingvalues of field strength can be used to decide where to locate, or how to combine, individualthe accelerator according to the dispersion of their measured characteristics. For example, theand alignment in the accelerator. A problem related to alignment is that of locating magnets in

Field geometry measurements are of great importance at the time of magnet installation

punches.production quality and will detect eventual wear of manufacturing tools such as laminationthe field strength and field quality. These series measurements act as a control on thereference targets. The dispersion of the measured parameters is of interest both in the case ofmeasured in order to monitor field dispersion and confirm or define the position of mechanical

During the series production of the magnets, the field strength and geometry must be

features and procedures needed to meet the production requirements are developed.magnet design in order to meet the requirements. It is during this phase that the special designstage the field quality is the most important parameter and modifications can be made to the

Magnet models are built at the time an accelerator is being studied and designed. At this

the median plane.defined and determines two critical parameters: the location of the beam axis and the angle ofstage for beam optics studies. The field geometry allows the mechanical reference targets to bedistribution in space and time, is of importance during the magnet design phase and at a laterwhich is of particular importance in low-field magnets. The field quality, that is the field

The magnet field strength (or excitation curve) includes that of the hysteresis curve,

characterised as field strength, quality and geometry.project: design, construction, installation and operation. The magnetic properties can be

Magnetic measurements are important throughout the various stages of an accelerator

area, and the wire is carefully glued to the core. Glass or ceramics with their low thermal OCR Outputwound on a core made from a mechanically stable material, in order to ensure a constant coilthe coil is chosen so as to link with selected field components [10]. The search coil is usuallymagnets with a wide horizontal aperture and limited gap height. In this case, the geometry ofis the main concem. Long rectangular coils were usually employed and are still used inmagnets [8, 9], where the precise measurement of the field integral along the particle trajectory

The coil method is particularly suited for measurements with long coils in beam—guidance

3.1.1 Induction coils

cylindrical symmetry.ranging from the simple flip-coil to the complex harmonic coil systems used in fields ofmeasurements, but with both coils moving. A wide variety of coil configurations are used,sensitivity when examining field quality. The same principle is applied in harmonic coilcompensating fluctuations in the magnet excitation current and providing a much highersearch coils connected in opposition, with one coil moving and the other fixed, thus

Very high accuracy may be reached in differential fluxrneter measurements using a pair of

fields.complex construction made it possible to perform point measurements in inhomogeneousoften chosen to suit a particular measurement. One striking example is the Flux ball [7] whosecontinuous rotation or simply a movement from one position to another. The coil geometry ismoving the coils in a static field. The coil movement may be a rotation through a given angle, aMeasurements are performed either by using fixed coils in a dynamic magnetic field, or bythe magnetic flux lines; this being of particular importance in accelerator magnets.particle accelerator magnets. It is also the most precise method for measuring the direction ofdirection of the earth's magnetic field. Nowadays it has become the most important method forWeber in the middle of the last century [6] when he studied the variations in strength andmethods for magnetic measurements, but it can be very precise [5]. It was used by Wilhelm

This method, which is based on the induction law, is the oldest of the currently used

3 . 1 The fluxmeter method

3 . MEASUREMENT METHODS

Fig. 1 Measurement methods: accuracies and ranges

nsw imxussr

10" 10* 1 10 10’ 10’ 10* 10*10*

uc HALL mrs*0’

Ac HALL PLATE

wzmuucmu METH00 ;

2:10

NMR

72

Miller integrator. It remained necessary, however, to employ difference techniques for OCR Outputaccuracy was further improved with the introduction of the classic electronic integrator, theof photoelectric fluxmeters [17] which were used for a long period of time. The measurementelaborate fluxmeters [16]. The coil method was improved considerably with the development

Induction coils were originally used with ballistic galvanometers and later with more

3.1.2 The flux measurement

are relatively slow.which is often complex, may be a disadvantage. Furthermore, the measurements in static fieldsother hand, the need for relatively large induction coils and their related mechanical apparatus,temperature, only a minor correction has to be applied for use at lower temperatures. On themeasurements at cryogenic temperatures. After calibration of the coils at liquid nitrogendynamic range also plays an important role. The technique can be easily adapted tocoil. The high stability of the effective coil surface is another asset. The linearity and the wide

The main advantage of search coil techniques is the possibility of a very flexible design of

mm and a useful width of about 30 mm.has been developed for this purpose at LURE, Orsay [15]. It has a magnetic length of about 60may be necessary to examine the variation of the effective width. A hybrid permanent dipoletight tolerances on the width of the coil. If the field varies strongly over the length of the coil, itwinding imperfections. In the case of long measurement coils, it is important to ensure verymust be measured, but also its median plane which often differs from its geometric plane due tobe taken not to introduce thermal voltages. Not only the equivalent surface of the search coilhomogeneous magnetic field by reference to a nuclear magnetic resonance probe, but care mustThe coil-integrator assembly can be calibrated to an accuracy of a few tens of ppm in asensitivity of the fluxmeter method depends on the coil surface and the quality of the integrator.

The choice of geometry and method depends on the useful aperture of the magnet. The

fields and in particular to measurements in strong magnets with very small aperture.This method is well suited to geometry measurements, to the absolute calibration of quadrupolepositioning of the wire. Sensitivity is limited, but can be improved by using a multi-wire array.wire cannot be placed in a vertical position. The accuracy is determined by the mechanicalvarying the field and keeping the wire in a fixed position. Tungsten is often selected, if thethus integrating the flux cut by the wire. It is also possible to measure the flux change while

Another induction measurement consists of moving a stretched wire in the magnetic field,

[14].description of the general theory including detailed error analysis has recently been publishedand its related equipment is described in detail elsewhere in these proceedings. A thoroughwith a static coil linking to selected harmonics [13]. The harmonic coil measurement principlethe sensitivity of the system for measurements of field quality. Dynamic fields are measuredrotated with the main coil may be used to suppress the main field component and thus increasemeasurement of strength, quality and geometry. A compensating coil, connected in series andtypes of accelerator magnets. The method provides the additional advantage of simultaneousmeasurements have improved considerably and are now considered as the best choice for most

With the advent of modern digital integrators and angular encoders, harmonic coil

harmonic analysis.through slip rings to a frequency selective amplifier (frequency analyser), thus providing analogdeveloped since 1954 [11, 12]. The induced signal from the rotating coil was often transmittedcylindrical geometry. The coil support is usually a rotating cylinder. This method has been[3]. The harmonic coil method has now become very popular for use in magnets with circular

Continuously rotating coils with commutating polarity were already employed in 1880

its residual elasticity assures a well-defined geometry and mechanical stability of the coil.dilation are often used as core materials. During coil winding the wire must be stretched so that

73

period must be of the order of a second to obtain a reasonable resolution. OCR Outputthe flux since the input signal must never exceed the voltage level of the VFC. The rntegratron

This system is well adapted to digital control but imposes limits on the rate of change of

amplifier.linearity of 50 ppm. Its sensitivity is limited by the input amplifier, as in the case of the analogthe other is active. In this way no cumulative errors will build up. This integrator has a_provide instant readings of the integrator. One of the counters can then be read and reset whileof the VFC. Two counters are used in order to measure with continuously moving corls and tomeasurement. This offset is balanced by a 500 kHz signal which is subtracted from the outputavailable. The input of the VFC is given an offset of 5 V in order to provide a true bipolarcounter. The version shown in Fig. 3 was developed at CERN [19] and is now commerciallyon a high quality dc amplifier connected to a voltage-to-frequency converter (VFC) and a

In more recent years, a new type of digital integrator has been developed, which is based

integrators have been developed by industry and are commercially available.constant proved to be better than 50 ppm over a period of three months. A few electroniclchoice of cables and connectors. In tests at CERN the overall stability of the integrator timeterms of flux. Thermally induced voltages may cause a problem, so care must be taken rnthe0.5 |,tV which must be multiplied by the measurement time in order to express the sensitivity inis limited by the dc offset and low frequency input noise of the amplifier. A typical value rsand temperature characteristics matching those of the capacitor. The sensitivity of the mtegratorA suitable integrating resistor is much easier to fmd. Most metal-film resistors have stabrlrtres

The dielectric absorption of the integrating capacitor sets a limit to the integrator precision.

Fig. 2 Analog integrator

DC·AMPL

I.-.l;. JT .....

R I L {.1:} — +- 1;;}

A T < 0.1 ° C '?

resrstances.

components is therefore essential in order to reduce the voltages across the critical surfacethrough the capacitor and the resetting relay. Careful protection and shielding of thesemounted in a temperature-controlled oven. Another problem is the decay of the output signalintegrating capacitor is the most critical problem. The integrating components are thereforevery low input voltage offset and a very high open—loop gain. The thermal variation of the

Figure 2 shows an example of such an integrator. It is based on a dc amplifier with a

used in multi·coil systems.the development of solid state dc amplifiers, this integrator has become inexpensive and is oftenmeasurements possible and the Miller integrator has become the most popular fluxmeter. Withmeasurements of high precision [18]. Later, the advent of digital voltrneters made fast absolute

74

can be improved considerably by application of ac excitation [34, 35]. A good accuracy at low OCR OutputThis is mainly caused by thermally induced voltages in cables and connectors. The sensitivityresolution of the measurement, if conventional direct current excitation is applied to the probe.

The measurement of the Hall voltage sets a limit of about 20 [LT on the sensitivity and

are available on the market, but these show a lower sensitivity.strongly inhomogeneous fields. Special types, which have a smaller temperature dependence,magnetic centre is, therefore, better defined, so it is particularly well suited for measurements inshows a better linearity and has a smaller active surface than the usual rectangular generator. ItsHall coefficient is a function of the field level. The Hall generator of the cruciform type [33]

Last but not least is the problem of the non-linearity of the calibration curve, since the

all rather difficult to apply.determination of field geometry. Many possible remedies have been proposed [32] but they arethis plane. This effect limits the use in fields of unknown geometry and in particular its use forto the plane of the Hall generator problematic if a strong field component is present parallel toof the planar Hall effect [31], which makes the measurement of a weak field component normalfield [30], so relatively complex calibration tables are needed. Another complication can be thattemperature during measurements [30]. It depends, however, also on the level of the magnetictemperature coefficient may also be taken into account in the probe calibration by monitoring theorder to overcome this problem [29], but increases the size of the probe assembly. Thetemperature coefficient of the Hall voltage. Temperature stabilization is usually employed in

However, several factors set limits on the obtainable accuracy. The most serious is the

commercially available.operation are other attractive features. A large selection of this type of gaussmeter is nowmultiplexed voltage measurement [28]. The wide dynamic range and the possibility of statictime may be gained by mounting Hall generators in modular multi-probe arrays and applyingprobes can be mounted on relatively light positioning gear [27]. Considerable measurementmeasurement equipment and offers a compact probe, suitable for point measurements. The

The Hall- generator provides an instant measurement, uses very simple electronic

3.2.1 Hall probe measurements

and therefore the most commonly used in 1arge·scale field mapping [25-27].extensively. It is a simple and fast measurement method, providing relatively good accuracy,semiconductor materials were developed [22-24] and since then the method has been usedperformed using this effect [21]. It was, however, only around 1950 that suitableopposed the Lorentz force on the electrons [20]. In 1910 the first magnetic measurements wereand carrying a current developed a voltage mutually at right angles to the current and field that

E.H. Hall discovered in 1879 that a metal strip immersed in a transverse magnetic field

3 . 2 The Hall generator method

Fig. 3 Digital integrator

SOO kHz+ 5 V

ENTR 2

AMPL 0-,0,, >——| VFCAMPW Ei! Icwtni

0 - 1

75

[50]. OCR Outputfield is modulated with a low-frequency signal in order to determine the resonance frequencycoefficients of 4257.608 Hz/G for protons and 653.569 Hz/G for deuterons. The magneticmeasured frequency is directly proportional to the strength of the magnetic field withnuclear induction (coupling into a detecting coil) or as resonance absorption [49]. Thefrequency oscillator. The precession frequency of the nuclei in the sample is measured either as

In practice, a sample of water is placed inside an excitation coil, powered from a radio

accuracy better than 10 ppm.Commercially available instruments measure fields in the range from .045 T up to 13 T with aneasy and precise frequency measurement it is independent of temperature variations.very high precision. It is now considered as a primary standard for calibration. Based on anSince then, the method has become the most important way of measuring magnetic fields withlater the phenomenon was observed in solids by two independent research teams [46-48].[44, 45] for measurements of the nuclear magnetic moment in molecular beams. A few yearsbut also for high precision field mapping. This measurement method was first used in 1938

The magnetic resonance technique is frequently used, not only for calibration purposes,

3 . 3 Magnetic resonance techniques

be maintained over a period of several months [43].ppm. By keeping the Hall generator permanently powered, an accuracy better than 30 ppm canpoints. A well designed Hall-probe assembly can be calibrated to a long term accuracy of 100the calibration function can be verified from field values measured between the calibrationmicroprocessor device [29] and the subsequent field calculations are very fast. The quality offor the bipolar calibration of a cruciform Hall generator) can be easily stored in aconsuming but need only be done once at calibration time. The coefficients (typically about 60in the literature [42]. The calculation of the polynomial coefficients may be somewhat timederivative of the function is continuous at these points. Very efficient algorithms can be founda piecewise polynomial of third degree passing through the calibration points such that theis very well suited to interpolation from tables of experimental data. The function is defined asapproximation" properties [41]. The function adjusts itself easily to non-analytic functions andThe advantage of the spline function comes from its minimum curvature and its "bestdone in the form of a simple Lagrange interpolation or even better with a cubic spline function.sufficient number of calibration points which were measured with high precision. This can be

A physically better representation is the use of a piecewise cubic interpolation through a

simple computation of the magnetic induction from a relatively small table of coefficients.a sufficiently large number of calibration points. This representation has the advantage of acommonly represented in the form of a polynomial of relatively high order (9 or more) fitted tosimultaneously using the nuclear magnetic resonance technique. The calibration curve is most

Hall generators are usually calibrated in a magnet in which the field is measured

3.2.3 Calibration

less important at cryogenic temperatures and are discussed in detail in [40].generator in a heated anticryostat [39]. 'I'he complications related to the planar Hall effect areadds a serious complication to the calibration. The problem may be solved by locating the Hallcent at high fields, depending on the type of semiconductor used for the Hall generator. Thisa field dependent oscillatory effect of the Hall coefficient which may amount to about one perproblem at low temperatmes. The so-called "de Haas-Schubnikov effect" [37, 38] shows up asAlthough they show a very low temperature coefficient, they unfortunately reveal an additional

Special Hall generators for use at cryogenic temperatures are also commercially available.

measurement of the Hall voltage [36].fields can then be achieved by employing synchronous detection techniques for the

76

particles, subject to the field. OCR Outputbe obtained by observing the light transmission through a colloidal suspension of diamagnetrcstudies of the variations in the direction of the earth's magnetic field. Another visual effect mayneedle. This compass method was applied, long before the discovery of electromagnetism, forcompass needle at different points in the volume to be examined and note the direction of thelines. Another very classical way of observing flux—line pattems is to place a free-movingsurface placed near a magnetic source, thus providing a simple picture of the disuibution of flux

The best known visual field mapper is made by spreading iron powder on a horizontal

3 . 6 Visual field mapping

for field monitoring was implemented in one of the large LEP spectrometers [58].came on the market and were used also for magnetic measurements [57]. A recent applicationbecame available that the method tumed into a success. Then inexpensive magneto-resistorsmeasurement method. As with the Hall generator, it was only when semiconductor materialsand problems with electrical connections, caused a general lack of reliability in thisDependence on temperature and mechanical stress, combined with difficulties of manufacturealready existed at the end of last century. Technical problems were, however, important [56].

The magneto-resistivity of bismuth was exploited quite early and a commercial instrument

3.5 Magneto-resistivity effect

other practical applications, for example for navigation purposes.mT and a resolution of l nT are commercially available from several sources. They have manyby applying water cooling to the bias coil. Fluxgate magnetometers with a typical range of llimit of the measurement range is usually of the order of a few tens of mT, but can be extendedhas increased the sensitivity to about 20 pT and can assure a wide dynamic range. The upperhave taken place over the last decade [53-55]. The use of modern materials for magnetic coresinteresting application is now in space research and important developments of this techniqueand in cases where the measured field should not be distorted by the probe. The mostapplications. Much more complex coil configiuations are applied for precision measurementsaround accelerator or detector magnets. lts fine time resolution also makes it ideal for timingdirectional device with very high sensitivity, it is suitable for studies of weak stray fieldsadvantage of offering a linear measurement and is well suited for static operation. As amaintains the zero field [52]. The method is restricted to use with low fields, but has thecoil, a detection coil that indicates the zero field condition and a dc bias coil that creates andrectangular hysteresis curve. ln its basic version it contains three windings: an ac excitationstrip". The core is made up from a fine wire of Mumetal or a similar material that has an almostexcitation coils are wound. It was introduced in the l930's and was also named "peaking

The fluxgate magnetometer is based on a ferromagnetic core on which detection and

3.4 Fluxgate magnetometer

which were not so readily available in the past.applications. However, the related signal processing requires powerful computing facilities,measurements [51]. It is a very promising technique which has proven its quality in other

Magnetic resonance imaging (MRI) has been proposed for accelerator magnet

be noted that cryogenic probes are not yet commercially available.sensitivity and dynamic range also set limits to the suitability of this method. Finally, it shouldinhomogeneous field. A correction of the order of 0.2 T/m may be obtained [50]. The limitedproviding a field gradient, is often placed around the probe when used in a slightlyhomogeneous field in order to obtain a sufficiently coherent signal. A small compensation coiloperation of the system. The most important disadvantage is the need for a rather

The advantages of the method are its very high accuracy, its linearity and the static

is also obtained in this case by turning the measurement cylinder l80° around its vertical axis. OCR Outputincludes the feature of a precise median plane measurement. Correction for coil geometry errorshave the advantage of providing a direct reference to gravity. A good harmonic coil systemstrong static field. Pendulum coils have also been employed with success in static fields andor a single stretched wire can be moved in the plane perpendicular to the median plane in alimited only by the mechanical support of the coil. A set of stretched wires may replace the coil,repeating the measurement. An accuracy of about 0.02 mrad is commonly obtained and isinduction coil, which can be compensated (and measured) by rotating the coil l80° andvariation of flux, an angle can be calculated. This angle includes the geometric error of theWhen changing the magnetic field between two known levels and measuring the correspondingto the median plane and equipped with an inclinometer for the determination of the angle.simplest solution is to mount a fixed induction coil with a large magnetic surface perpendicularinclinometers. Precise magnetic measurements are best obtained by the fluxmeter method. The

The mechanical measurement is very simple to perform using commercially available

position of conductors, the tilt of the plane must always be measured by magnetic sensors.structures. In superconducting magnets, where the field geometry is determined mainly by themagnetic saturation of an asymmetric steel core or by influence from surrounding ferromagneticcaused by an elastic deformation of the yoke due to magnetic forces, or it may occur due tomay prove necessary to verify it by magnetic measurements. A tilt of the median plane can bevariation along the particle path [62]. This angle can, however, depend on field strength, so itangle is often defined after a precise mechanical measurement of the gap geometry and itspossible, for subsequent periodic surveys. In classical steel-core magnets the median planetargets are placed in positions, that are easily accessible during installation, alignment and, ifit must be known to an accuracy of 0.1 mrad. A mechanical reference surface or alignment

The critical parameter for the alignment of a dipole is its median plane. As a general rule

4 . 1 Dipole geometry

alignment of quadrupoles.installing and aligning the magnets. Very tight tolerances are required, in particular for thesynchrouons is the positioning and verification of mechanical reference targets for use when

One of the main purposes of the magnetic measurements of beam-guidance magnets for

4 . DEFINITION OF FIELD GEOMETRY

field mapping and simulation of particle trajectories by computer programs.reduce effects of stiffness and gravity. This method has now been entirely replaced by precisemechanical tension in the wire. A flexible, annealed, aluminium wire was used in order todescribe the path of a charged particle with a momentum corresponding to the current and theconductor is stretched in a magnetic field, it will curve subject to the electromagnetic force and

Floating wire measurements [60, 61] were quite popular in the past. If a current-carrying

3.6.2 Floating wire method

image processing techniques might improve the method substantially.convincing when applied to the precise determination of magnet geometry, even though modemprinciple has proved useful for measurements of transient magnetic fields [59]. It is lesspolarizing medium. This can give a certain indication of the field geometry. This measurementmagnet. The rotation of the plane is proportional to the field strength and the length of thefield pattem in a quadrupole by observation through polarization filters placed at each end of thefilled with a polarizing liquid and placed inside the magnet gap may visualize for example theeffect) is a classical method for the visualization of magnetic fields. A transparent container

The magneto-optical rotation of the plane of polarization of polarized light (Faraday

3.6.1 Faraday effect

78

become an interesting alternative as an absolute standard and for measurements of weak fields. OCR OutputAlso the use of superconducting quantum interference devices (SQUIDS) might in the long runMagnet resonance imaging is a promising technique which could find a lasting application.

In the field of new technologies, there are two methods which merit consideration.

drawn to definitions of geometry and the future alignment considerations.requirements. Already at an early stage of the system design, particular attention must becomplementary and the use of a combination of two or more of these will certainly meet mostof a more exotic measurement method. The measurement methods described above aretherefore prudent to examine existing possibilities carefully before launching the developmentmeasurement tasks related to beam-guidance magnets as well as for spectrometer magnets. It is

Proven measurement methods and powerful equipment is readily available for most of the

S . CONCLUSION

improves accuracy and measurement speed, when reference targets are put in place.the classical alignment methods based on telescopes and optical targets. This considerably

The use of laser beams and position detecting photoelectric diodes [63] has now replaced

precision cameras and image processing equipment may improve this situation.inferior to that obtained by the harmonic coil measurement. Perhaps the development ofparticles have been employed in the past. The accuracies obtained are, however, very muchFaraday effect and the transmission of light through colloidal suspensions of diamagneticmultipole magnets. They provide a spectacular illustration of the field distribution. Both the

Observations of optical effects have been used for the determination of geometry of

has also proved quite suitable for this measurement.targets remains, so the required Hnal precision is not easily reached. The stretched wire methodcan be observed with an accuracy of a few um, but the problem of transfer to the referenceobservations of field-dependent phenomena can be done with high accuracy. The magnetic axisharmonic coil method provides a very precise measurement of the magnet geometry, so evena precise mechanical measurement of the gap geometry and its variation along the magnet. Themagnets the measurement was often, as for the median plane measurement in dipoles, based onaxis must be known and represented to an accuracy of 0.1 mm or better. In classical steelangle of its median plane. The typical requirement for a quadrupole is that the position of its

For multipole magnets the positioning of the magnetic axis is more important than the

4 . 2 Multipole geometry

is essential and is obtained by tumin g the measurement probe 180° as in the other cases.geometry error. For the compass and Hall generator measurements correction for sensor errorsare not ideal for this measurement due to the planar Hall effect which adds a iield dependentpresence of the magnetometer may distort the field in the magnet gap. Equally, Hall generatorsmechanical force on the compass needle is zero at equilibrium condition and secondly themagnet, but for precision measurements this method suffers from two drawbacks. Firstly the

Compass magnetometers may give an indication of the directions of flux-lines in a

[19] P. Galbraith, private communication. OCR Output

Sci. Instr., 24 (1953) 743-754.18] G.K. Green, R.R. Kassner, W.H. Moore, L.W. Smith, "Magnetic measurements", Rev.

(1937) 805-809.[17] R.F. Edgar, "A new photoelectric hysteresigraph", Trans. Amer. Inst. Elect. Eng., 56

[16] M.E. Grassot, "Fluxmetre", J. de Phys., 4 (1904) 696-700.

A. Daél, private communication.[15]

coil magnetometers", Nucl. Instr. and Meth., A 311, (1992) 399-436.[14] W.G. Davies, "The theory of the measurement of magnetic multipole fields with rotating

Upton, USA (1972) 787-790.magnets", Proc. 4th Int. Conf. on Magnet Technology, Brookhaven National Lab.,

[13] G.H. Morgan, "Stationary coil for measuring the harmonics in pulsed transport

Part H: Study of a quadrupole magnet", Rev. Sci. Instr., 25, (1954) 485-489.I.E. Dayton, F.C. Shoemaker, R.F. Mozley, "Measurement of two-dimensional fields,[12]

Rev. Sci. Instr., 25, (1954) 480-485.[11] W.C. Elmore, M.W. Garrett, "Measurement of two-dimensional fields, Part I: Theory",

fields", Thesis, Delft (1958) 55-67.B. de Raad, "Dynamic and static measurements of strongly inhomogeneous magnetic[10

Brookhaven National Lab., Upton, USA (May 1986) 297-301.experience", Proc. of the ICFA Workshop on Superconducting Magnets and Cryogenics,B.C. Brown, "Fundamentals of magnetic measurements with illustrations from Fermilab[9]

synchrotron magnets", J. Sci. Instr., 27 (1950) 264-270.E.A. Finlay, J.F. Fowler, J.F. Smee, "Field measurements on model betatron and[8]

W.F. Brown, J.H. Sweer, "The Fluxball", Rev. Sci. Instr., 16 (1945) 276-279.[7]

Inclination mit dem Magnetometer", Ann. der Physik, 2 (1853) 209-247.W. Weber, "Ueber die Anwendung der magnetischen Induction auf Messung der[6]

field", IEEE Trans. on Magn., MAG-17 (1981) 1851-1854.[5] J .H. Coupland, T.C. Randle, M.J. Watson, "A magnetic spectrometer with gradient

Francisco, USA (May 1991) 2122-2124.LEP from precise magnet measurements", 1991 Particle Accelerator Conference, San

[4] J. Billan, J .P. Gourber, K.N. Henrichsen, "Determination of the particle momentum in

(1929) 213-242.L.W. McKeehan, "The measurement of magnetic quantities", J. Opt. Soc. Amer., 19[3]

Nucl. Instr. and Meth., 21 (1963) 17-46.[2] C. Germain, "Bibliographical review of the methods of measuring magnetic fields",

(1955) 83-126.[1] J.L. Symonds, "Methods of measuring strong magnetic fields", Rep. Progr. Phys., 18

REFERENCES

80

arsenide", Phys. Rev., 110 (1958) 880-883. OCR OutputH.P.R. Frederikse, W.R. Hosler, "Oscillatory galvanomagnetic effects in n—type indium[38]

longitudinal magnetic fields", Phys. Rev., 107 (1957) 981-992.J. Babiskin, "Oscillatory galvanomagnetic properties of bismuth single crystals in[37]

[36] K.R. Dickson, P. Galbraith, "A digital micro-teslameter", CERN 85-13 (1985).

[35] C.D. Cox, "An a.c. Hall effect gaussmeter", J. Sci. Instr., 41 (1964) 695-691.

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83