Assessment of a Translating Fluxmeter for Precision Measurements of Super-FRS Dipole Magnets

Abstract

In particle physics experiments, fragment separators utilize dipole magnets to distinguish and isolate specific isotopes based on their mass-to-charge ratio as particles traverse the dipole’s magnetic field. Accurate fragment selection relies on precise knowledge of the magnetic field generated by the dipole magnets, necessitating dedicated measurement instrumentation to characterize the field in the constructed magnets. This study presents measurements of the two first-of-series dipole magnets (Type II—11 degrees bending angle—and Type III—9.5 degrees bending angle) for the Superconducting Fragment Separator that is being built in Darmstadt, Germany. Stringent field quality requirements necessitated a novel measurement system—the so-called translating fluxmeter. It is based on a PCB coil array installed on a moving trolley that scans the field while passing through the magnet aperture. While previous publications have discussed the design of the moving fluxmeter and the characterization of its components, this article presents the results of a measurement campaign conducted using the new system. The testing campaign was supplemented with conventional methods, including integral field measurements using a single stretched wire system and three-dimensional field mapping with a Hall probe. We provide an overview of the working principle of the translating fluxmeter system and validate its performance by comparing the results with those obtained using conventional magnetic measurement methods.

1. Introduction

The facility for Antiproton and Ion Research (FAIR) is an international superconducting accelerator facility currently under construction at the Helmholtz Center for Heavy Ion Research (GSI) in Darmstadt, Germany [1]. The main part of the FAIR is the Superconducting Fragment Separator (Super-FRS)—a two-stage, large-acceptance, in-flight separator [2,3] made of 197 superferric magnets. Magnetic measurements of the magnets are performed at the European Organization for Nuclear Research (CERN) in a dedicated cryogenic facility [4]. The Super-FRS includes dipole magnets of Types II and III, the parameters of which are summarized in

Table 1. Main parameters of the Super-FRS dipole magnets.

	Unit	Dipole Type II	Dipole Type III
Number of magnets	-	3	21
Weight	kg	61,300	54,100
Bending angle	°	11	9.75
Curvature radius	m	12.5
Coil layers/turns	-	28/20
Coil Ampere-turn (for 233 A)	A	260,960
Inductance	H	18.2	15.8
Magnetic Stored Energy	kJ	651.9	591.6
Nominal central field	T	1.6
Nominal integral field	Tm	3.84	3.40
Good field region semi-major axis/semi-minor axis	mm	190/70
Aperture	mm	170
Integral field quality	-	$3\times {10}^{-4}$

. The first Type II dipole magnet was delivered at CERN at the beginning of 2022 and underwent extensive magnetic measurement testing, while the Type III magnet was delivered in February 2024.

The Super-FRS dipoles are superferric design, H-type magnets with superconducting racetrack coils. The coils are embedded in the cryostat and cooled to a cryogenic temperature of 4.5 Kelvin with liquid helium, while the yoke stays at room temperature. The magnets are about 2.5 m long and weigh about 60 tons.

Strict requirements and specific parameters of the dipole magnets for Super-FRS imply significant challenges for the measurements [5,6]. In particle beam physics, it is critical to know the magnet’s integral magnetic field as a function of current (commonly referred to as the load-line) to precisely control the beam bending path. The integral magnetic field is the line integral of the magnetic field B along the path that a particle travels through a magnet and as such represents the total bending power of a magnet. Particle beam physics also requires SuperFRS dipoles to have a high integral field quality $3\times {10}^{-4}$ (the spatial variation of the integrated field across the transverse plane of the beam) in a good field region (GFR) of 140 mm height by 380 mm width. Moreover, magnetic field measurements of three separate regions are required: the straight entry, the curved path on particle trajectory, and the straight exit. The three regions cover a total length of four meters, including the magnet’s homogeneous region as well as a large fraction of its fringe fields.

The most common techniques typically considered for dipole magnets measurements include the following:

• The rotating coil magnetometer (or harmonic coil, described in [7]) enables high-precision measurements through signal compensation, or “bucking”, which removes the main field and isolates field errors. However, it is not well suited for dipole magnets with rectangular apertures of large width-to-height ratio, as it samples the magnetic field along a circular path. Furthermore, it is applicable only to relatively straight magnets.
• The single stretched wire (SSW), operated in static or pulsed mode [8,9] is a versatile technique that enables measurement of the integral field strength. In this method, a thin conductive wire is displaced within the field by precision stages (or the magnet current is pulsed during dynamic measurements). It can achieve high accuracy, as precise displacements are possible using translation stages. However, the SSW measures the integral field only along a straight line and thus cannot provide the field profile or resolve separate longitudinal regions.
• The Nuclear Magnetic Resonance (NMR) technique [10] offers highly accurate magnetic field measurements suitable for field mapping. However, it requires highly homogeneous field conditions and is unsuitable for measuring fringe field regions. Moreover, achieving high precision necessitates long acquisition times.
• A Hall Probe [11] mounted on a 3D mapper offers an alternative solution. Although it does not match the accuracy of NMR, it allows faster acquisition and operates effectively under varying field quality conditions, enabling full-length field mapping. It is also relatively cost-effective. Its disadvantages include sensitivity to electrical noise and temperature fluctuations, necessitating careful calibration.
• A static fluxmeter, operated in pulsed mode can be employed for integral field measurements in strongly bent dipole magnets [12,13]. In this technique, an induction coil (often an array of coils) is shaped to follow the magnet’s curvature. The time-varying field from the pulsed magnet induces a voltage in the coil, which, when integrated over time, yields the change in the integrated field. The signal strength (i.e., signal-to-noise ratio) depends on the ramp rate of the magnet current.

Due to the slow current ramp rate of the SuperFRS dipole magnets—2 A/s (i.e., 0.013 T/s)—it can, in practice, only be characterized in direct current excitation. To meet all measurement requirements, a new device concept—the translating fluxmeter—was proposed [14].

2. The Translating Fluxmeter Design

The translating fluxmeter is built on a 5-meter-long aluminum base plate with two rails, an encoder strip, and a carriage driven by a stainless steel wire of 1 mm diameter. The main sensing element is a printed circuit board (PCB) coil array covering 459 mm width (13 coils spaced every 38 mm). The coils have a length of 125 mm and a surface of 0.486 m². Details of the standard coil geometry are provided in

Table 2. Main parameters of the sensing element of the translating fluxmeter.

	Unit	Rectangular Coils	Graded Coils
Board width	mm	500
Board length	mm	150
Number of coils	-	13
Coils spacing	mm	38
Coil inner length	mm	120.9	6.13
Coil inner width	mm	23.6	13.4
Number of layers	-	12	14
Number of coil turns per layer	-	12
Nominal coil area	m2	0.486	0.1085

, along with additional coil configurations described in Section 3.4. The layout of the PCBs is shown in Figure 1. Spacers under the PCB allow the vertical change of the plane of measurement, thus performing a scan of the full magnet aperture. A drawing of the translating fluxmeter is shown on Figure 2 and the device installed in one of the Super-FRS dipole magnets is shown in Figure 3.

While the carriage moves through the magnet, the coils intercept the vertical component of magnetic flux density $B_y$. The change of the flux linked to the coil induces a voltage, which is recorded with an acquisition system. The carriage is equipped with an encoder head (Celera Motion Mercury II™ 6000) that reads its longitudinal position from an encoder strip installed on the support structure. The position read by the encoder is used to remove the dependency on the movement velocity by triggering measurement on equally spaced intervals. The induced coil voltage is integrated in time, with fast digital integrators [15] (FDI) between two trigger instances. This yields a set of flux increments $\Delta \Phi \left(z_k\right)$, which correspond to distinct longitudinal positions $z_k$ along the traced path. The movement velocity is optimized for noise reduction. The induced voltage is larger for faster velocities but so are the oscillations caused by mechanical vibrations. The optimum velocity and encoder step size are established at 0.3 m/s and 0.16 mm, respectively. The system acquisition consists of seven FDIs that allow the acquisition of 13 coils within two runs.

3. Calibration

3.1. Alignment

It is important to verify the proper positioning of the translating fluxmeter in the measured magnet to ensure the measurement path aligns with the magnet axis and to avoid systematic errors. The alignment of the base, as well as the carriage movement through the aperture, was performed using a laser tracker system. The PCB was aligned within 0.44 mm and 0.03 mm (vertical and horizontal absolute error, respectively) with irregularities during the move of ±0.25 mm and ±0.2 mm, which corresponds to an angular error below 0.05 mrad.

3.2. Coils Surface

With the precision of PCB manufacturing the effective surface is usually within few hundred ppm of the designed value. The surface of the induction coils can be calibrated in a known reference dipole field to mitigate possible defects. An alternative, relative calibration can be achieved “in situ”, where individual coils are cross calibrated against each other. To this end, the PCB is equipped with dowel pin holes, allowing it to be mounted with a shift in the x-axis that is exactly the distance between the coils (38 mm). The translating fluxmeter measurement is run three times with different PCB horizontal positions (offset in $x=\pm 38$ mm).Therefore, the same integral field is measured by three different coils, resulting in a system of equations that needs to be solved. To determine the cross-calibration coefficients, we fix one value and solve the system using the least-squares method. The coil surfaces vary within $\pm 200$ ppm. The calibration procedure was repeated periodically throughout the measurement campaign to confirm system stability. Calibration factors were stable within 50 ppm during the testing period.

3.3. Flux Offset

The magnetic flux linked with the coil surface at longitudinal position $z_k$ is

$$\Phi \left(z_k\right)=\sum _{i=1}^k\Delta {\Phi }_i+\Phi \left(z_0\right),$$

(1)

where $\Phi \left(z_0\right)$ is the flux offset at the fluxmeter’s initial position $z_0$. Since $\Phi \left(z_0\right)$ is unknown, we must either make sure that $z_0$ is at zero field, i.e., $\Phi \left(z_0\right)=0$, or we correct the offset based on a known flux value. At the nominal current of 240 A, the Super-FRS dipoles are highly saturated and starting the fluxmeter outside of the fringe field is not possible (in one meter distance from the yoke edge the field is at a few millitesla). A Projekt Elektronik™ Hall sensor was used to measure the field in the starting position of the PCB. This was performed at multiple current levels to obtain the load-line as the fringe field extends with iron saturation. We also measured the central field using a nuclear magnetic resonance (NMR) probe to validate the offset correction. Both measurements agree within 200 ppm for the central field.

3.4. Convolution

The basic approach to reconstruct flux density $B_y\left(z\right)$ from measured flux $\Phi \left(z\right)$ is a simple division by coil area:

$$B_y\left(z\right)\approx {\displaystyle \frac{\Phi \left(z\right)}{A_c}}$$

(2)

where $A_c$ is the coil surface. More generally, the signal obtained by sliding the coil through a magnetic field can be described as a convolution between the flux density and coil sensitivity function $s\left(z\right)$, i.e., $\Delta \Phi \left(z\right)=(B_y\ast s)\left(z\right)$ (see [16]). The effect is an apparent field advance or lagging (on the profile rise and descend, respectively) and smoothing of the higher spatial frequencies of the field profile. The signal deconvolution can be computed in the frequency domain by dividing the signal spectrum $\Delta \Phi \left(f\right)$ by the coil sensitivity spectrum $s\left(f\right)$, i.e., $B_y\left(f\right)=\Delta \Phi \left(f\right)/s\left(f\right)$. It is then reversed to the spatial domain by inverse fast Fourier transformation. However, this approach leads to the amplification of measurement noise at frequencies for which the coil sensitivity function assumes small values, i.e., $s\left(f\right)\to 0$. This problem can be mitigated by using induction coils with optimized winding layout, so that $s\left(f\right)$ is non-vanishing in the relevant frequency range. One possibility is to use windings that gradually increase in length (namely graded coil [16]). The systematic error in $B_y\left(z\right)$ for the basic approach and the effect of the deconvolution for a standard (rectangular) coil is seen by the oscillations shown in Figure 4a. One drawback for the graded coil is that the effective surface for the same number of windings and layers is reduced. This may affect the signal-to-noise performance (we used a graded coil with an effective surface of 0.1085 m² that is about five times less than standard coils). Another drawback is that the calibrated effective surface of the graded coil shows higher variations from the design values (in the 1000 ppm range) than the standard coil, due to its more complicated shape. The calibrated coil surface is used to compute a correction factor which is applied to the sensitivity function $s\left(f\right)$. Finally it is noted that the deconvolution is irrelevant for the integral field, as through Fubini’s theorem [17] the integral field is independent on the sensitivity function.

4. Magnetic Field Measurement Applications

The first of Series (FoS) Type II and Type III dipole magnets passed through an extended testing program, with the magnetic field characterized using the translating fluxmeter, and results verified using a Metrolab™ NMR teslameter PT2025, and a single stretched wire (SSW) [8,9]. The FoS Type III dipole magnet was additionally measured using a 3D Hall probe mapper [18]. The goal of the extensive testing program was to confirm the magnetic design and validate the use of the translating fluxmeter for the magnet series testing. A comparison to established measurement methods was performed to assess the confidence in the translating fluxmeter results. Because of the wide range of magnetic field properties it can evaluate, multiple measurement methods have to be used for the verification. An illustrative comparison of the methods is presented in

Table 3. Comparison of translating fluxmeter with established measurement methods [19].

	Translating Fluxmeter	NMR	SSW	3D Hall Probe Mapper	Static Fluxmeter
Magnet powering mode	DC	DC	DC/AC	DC	AC
Local/integral field	Local and Integral	Local	Integral on a straight line	Local	Integral
Measurement speed	Fast	Very Slow	Slow	Slow	Fast
Measured field component	$B_y$	$B_y$	$B_y$ and $B_x$	$B_y$  $B_x$  $B_z$	$B_y$
Horizontal/vertical resolution	38 mm/24 mm semi-flexible	up to 1 mm (NMR mapper)	∼5 mm (for usable signal strength in moderate field)	Unlimited	Typically few tens of mm
Longitudinal resolution	0.16 mm	up to 1 mm (NMR mapper)	None	Unlimited	None
Absolute measurement accuracy	100 ppm (needs calibration)	up to 1 ppm	∼100 ppm	up to 100 ppm (needs calibration)	up to 10 ppm (needs calibration)

.

4.1. Main Field Loadline on Particle Trajectory

We express the correlation between the applied excitation current and the resulting integral field as the loadline. In Figure 5, we present the ratio between the integral field on particle trajectory and the excitation current as a function of the current (the so-called transfer function). For the Type II dipole, the measured integral field on the particle trajectory was 3.83 Tm, which is 0.13% below the required 3.84 Tm, and for the Type III, the integral was 3.38 Tm, which is 0.66% below the required 3.40 Tm. The magnets start to saturate at about 100 A for the nominal, and the saturation reaches about 25% for Type III and 24% for Type II. Gradual change of the longitudinal field profile as the magnet saturates can be observed (Figure 6).

4.2. Field Quality

The field quality in the GFR is obtained by interpolating the data from a mesh grid on the nominal particle trajectory. The hard-edge model is used to approximate the beam path (the magnetic field is assumed to be zero until the particle enters the magnet, where the field instantaneously jumps to a constant value and drops to zero when the particle exits the magnet).

The dipole magnet needs to bend the beam path by equal angle regardless of the beam’s horizontal entry point. This implies that a beam traveling along a larger radius must be subjected to a higher integral magnetic field. To achieve this, Super -FRS dipole magnets have a trapezoidal shape (in top view), as shown in Figure 7. As a result, the integral magnetic field increases for trajectories shifted toward the longer edge and decreases toward the shorter edge of the magnet. It can be described as a field gradient—or quadrupole component—of about 80 ppm/mm. For homogeneity considerations we exclude it by removing the linear best-fit component of the field.

Solid chamfers are mounted on the edges of the yoke to shape the magnetic field. They are removable, allowing for their redesign if measurements indicate the field quality does not meet requirements. Each chamfer is laterally divided into three separate parts for easy manual handling. They are shown in Figure 8. After the first measurements of the Type II FoS magnet, it was discovered that the chamfer blocks were not sufficiently retained, which caused them to move significantly from their position during the powering. This led to the deterioration of the integral field homogeneity. After the chamfers’ installation was temporarily reinforced, repeated measurements showed considerable improvement in field quality (Figure 9a,b). Another observation made from the field profile is the presence of two ‘dips’ located at longitudinal positions of around ±600 mm and ±500 mm for the Type II and Type III magnets, respectively. The laminated half-yoke is, in fact, built of 3 parts, and this is the junction position between them.

Besides the integral field quality on the particle trajectory, the field map obtained by the translating fluxmeter allows for the analysis of field quality at each z position. The pseudo-multipoles (i.e., Fourier–Basel series coefficients) can be derived by polynomial series expansion on a horizontal plane [20]. For the quantitative analysis of the effect of the new chamfers fixation, we show the change of the polynomial 3rd degree and the polynomial 4th degree along the z-axis (Figure 10) (it is a purely numerical approximation of the magnetic field without physical correspondence to a classical multipole expansion).

4.3. Local Field—Evaluation Against NMR

The local (central) field load line, as well as the homogeneity and the central part of the longitudinal field profile, were verified with an NMR magnetometer. The central field absolute value measured with the translating fluxmeter is strictly dependent on the accuracy of the offset correction. For the central homogeneity, seven horizontal (x-axis) positions were scanned in the magnet center (about 1.5 m longitudinally) using the translating fluxmeter moving system with sensing element replaced with the NMR probe. Central field homogeneity results are within 50 ppm between the coils and the NMR. It confirmed that the central field quality is better than expected by the magnetostatic finite element simulation (see Figure 11b). The magnetic 3D model has been developed and solved with Opera^®18R2 by J. Lucas (Elytt Energy S. L.). A quarter of the yoke has been modeled, with the rest replaced by boundary conditions.

The measurements also allowed us to compare field profiles in the central homogeneous field region, as shown in Figure 12a and Figure 12b for the dipoles Type II and Type III, respectively.

4.4. Integral Field—Evaluation Against Single Stretched Wire

For the straight line integral field quality, the measurements were compared to the SSW method. The integral field homogeneity is in agreement within 100 ppm with respect to the translating fluxmeter over the entire SSW measuring range (i.e., $\pm 200$ mm) as shown in Figure 11. Additional measurements with SSW were performed on the rectangular boundary and the field reconstructed using boundary element method (BEM) [21]. The advantages of this approach are reduced time of the measurements, effective attenuation of random errors, and reduction of systematic errors. This method resolves the field in the middle; however, the accuracy decreases significantly near the measured boundary due to the non-convergence of the computation as detailed in reference [18] and depicted in Figure 11a where BEM results deviate from direct SSW and translating fluxmeter at $x=200$ mm. The integral field quality scan results are presented in Figure 13. For comparison, the map obtained with translating fluxmeter (Figure 13c) has the disadvantage of a lower spacial resolution (23 mm vertical and 38 mm horizontal).

4.5. Field Map—Evaluation Against 3D Hall Probe Mapper

The FoS Type III magnet was measured using a 3D mapper (produced by Axist S.r.L., Rivoli, Italy). The mapper is equipped with a 3D Hall sensor from Projekt Elektronik™ (Berlin, Germany) model AS-N3DC, which is mounted on a 3000 mm length carbon shaft and moved by a 3-axis alignment stage with a range of 1000 mm in the horizontal and vertical directions (x-axis and y-axis, respectively) and 3000 mm in the longitudinal direction (z-axis). The measurement points are taken on the fly without motion discontinuity. Due to the bench and the magnet configuration, the available mapper range was limited to the upper half of the aperture. It corresponds from the midplane ($y=0$ mm) to $y=+67$ mm vertically, and $z=-1900$ mm to $z=+1100$ mm longitudinally. Local field measurements in the close vicinity of the upper pole are desired to characterize the effects of junctions between the half yoke segments in the magnetic field. However, due to large mapper arm diameter of 45 mm, the sensor head could not reach the same vertical position as the translating fluxmeter. This implies a measured field difference of about 20 mT at the peak on the magnet edges (i.e., about $z=\pm 950$ mm). This field difference vanishes in the magnets longitudinal center (Figure 14). Finally, with the high spatial resolution of the mapper, field fluctuations in the yoke segments junction areas (i.e., at about $z=\pm 500$ mm) were measured. These fluctuations are attributed to welds on the yoke as shown in Figure 15.

The mapper system offers more flexibility than the translating fluxmeter; however it is not ideal for the measurement of magnets in large series. The scan of single line takes approximately 150 s with nominal velocity. That means for the mapper, it takes 30 min for the measurement set of 13 tracks, while using a translating fluxmeter, it is less than 1 min. The mapper also requires complex alignment installation, setup, and calibration procedures (approximately 5 days) and does not cover the full required length. Lastly, the Hall probe installed on the mapper did not have a temperature–compensation feature, implying a sensitivity to temperature variations that cannot be controlled in the measuring hall (measurement error caused by that can be seen in Figure 15a at $x=-125$ mm as apparent field discontinuity).

5. Conclusions

In this work, we presented the results of the magnetic measurement study carried out using a novel instrument—the translating fluxmeter. It is one of the first practical applications of the device in magnet testing. This work is a culmination of the collective efforts put in by a number of people involved in the development of the translating fluxmeter, which dates back to 2015 [14,22] with last development iteration described in [23]. The extended magnetic measurement program was performed on the two types of the Super-FRS main dipole magnets. We were able to qualify magnet design and production and validate the measurement system to be used in the series testing. It has been compared against well-established measurement methods: single stretched wire, NMR, as well as 3D Hall mapper. We showed that the translating fluxmeter is able to accurately assess the magnetic field quality of the Super-FRS dipoles with the precision of 50 ppm, measure the magnetic flux density on particle trajectory, and simultaneously provide a reconstruction of a longitudinal field profile. The only other system capable of providing this set of data together is a 3D Hall probe mapper. While the mapper might be more flexible, the big advantage of the translating fluxmeter is that it allows us to perform a scan in a much shorter time. The translating fluxmeter is also quite robust, demonstrating stability in non-controlled conditions of the test facility hall. In conclusion, the translating fluxmeter proved to be an effective tool for verifying magnets subjected to stringent requirements, allowing detailed measurements during the series production, which are usually reserved for extended prototype testing programs.