Superconducting multipole triplet field measurements

This paper presents magnetic field measurements for the Superconducting Multipole Triplets (SMT) prototypes of the Super Separator Spectrometer (S3). These advanced magnets, based on innovative concept design, generate magnetic fields of quadrupole, sextupole, octupole, and dipole. Magnetic field measurements have been conducted with a prototype mapping system to align the magnets and assess their performance. Moreover, detailed information on the experimental setup will be presented along with magnetic field analysis on the SMT’s multipoles.


Introduction
The Super Separator Spectrometer (S 3 ) is an experimental device dedicated to fundamental research in nuclear physics at the GANIL laboratory in France [1].It uses high-intensity ion beams from a linear accelerator (LINAC) to produce a secondary beam using fusionevaporation reactions [2,3].As its name suggests, S 3 serves as both a spectrometer (momentum achromat) and a separator, enabling to provide rejection of the primary beam and selection of the majority of the reaction products for further study [4].The spectrometer stage employs three superconductor multipole triplets (SMT), two magnetic dipoles, as well as an open magnet triplet combined with a beam dump to suppress background events outside charge-state acceptance [1].The separator stage features four SMTs completed by an electrostatic and a third magnetic dipole to achieve up to 65% transmission as well as a mass separation and can accommodate various reaction types [2].Indeed, S 3 offers flexible optical configurations achieved through versatile tuning of the various magnetic and electrostatic components [5].In fact, each SMT is composed of three singlets, each consisting of 3 quadrupole, 3 sextupole, 3 octupole, and 2 dipole magnets.The successful outcome of S 3 heavily relies on the precise alignment of these key magnetic elements and their fields' quality.Thus, ensuring the alignment of around 100 magnetic elements within 100 µm of their intended positions is necessary.

Experimental setup and procedure
When building the spectrometer, one of the main challenges is ensuring that the SMT's magnetic centreline position is correctly transferred to external references.This process, referred to as fiducialization, is crucial as it can significantly affect the overall alignment error.fiducialization, two measurements are required: one from the centre of the magnet to the mechanical centreline of the SMT and the other from the mechanical centreline to external references.This paper will present the first type of alignment along with field map measurements to evaluate the quality of the field gradient.

Coil winding choice
Since the SMT is constituted of superconductive coils that are not visible, the centre axis of the magnets is detected by measuring the magnetic field induced by these magnets.Moreover, using the same device, the real performances of a new coil design, referred to as Walstrom, could be evaluated.This particular configuration has never been used yet in a nuclear physics spectrometer application.Its concept is to specify the winding configuration of magnets to minimize the unwanted harmonics produced by the fringe field, resulting in a more stable particle trajectory [6,7].This design is based on the stream function expressed as: where n is the multipole index (n = 1 for the dipole magnet), θ is the angular position of the wire, N is the total number of wires, z represents the axial coordinate along the beam, and f(z) is referred to as the shape function.The Walstrom coil winding design selected for our coil which is described mathematically as where L S is the tip-to-tip length of the magnet and L E is the length of the coil end's region.Further detail can be found in reference [8].

Setup
Hence, in collaboration with Argonne National Laboratory, a magnetic field measuring prototype bench was designed using a SENIS-03C hall-probe sensor featuring virtually no planar Hall Effect.The 3 m long field-mapper device consists of a 3-axis magnetic sensor with a high resolution of 0.15×0.01×0.15mm 3 connected to a high-accuracy 32-bit teslameter.The hall probe is mounted on a cart positioned at 11 mm of an aluminum tube surface.Thanks to a translational stepper motor the probe can move transversally inside the SMT.Then, the aluminum tube can rotate by a stepper motor thus moving the probe in a rotational movement.This way, we can map the cylindrical inner surface at a fixed radius.Two encoders, placed on the extremity of the device, record the translational position of the sensor to ensure that no backlash problem appears, in addition to a rotational encoder to check the angle position value.The highresolution encoders are connected to a 12-bit AD Converter for precise position measurements.All motors, the teslameter, and the ADC interface are connected to a host computer to control the system using LabVIEW program, to provide automatic data acquisition, and to save the data for further analysis.The primary advantage of utilizing this method for realizing field maps is the absence of sag commonly observed in the wire [9,10] and motion arm techniques [11].We conducted measurements of the cylindrical field map along the beam z -axis, which involve detecting field components in the radial (B r ), azimuthal (B θ ), and beamline axis (B z ) directions. Figure 1 shows a picture of the field mapping bench, two-motion stage, device.The measurements were conducted by moving in the z -axis in steps of 2 mm and rotating the hall sensors in cylindrical coordinates at (∆θ =) 1-degree intervals.To prevent any potential backlash, the monitored movements were limited to the clockwise direction only.

Magnetic measurements
The angular accuracy of the hall probe was verified for B r and B θ components using the NMR Metrolab PT2025 as a reference sensor.The two teslameters were placed in a large dipole and a current variation generates a homogenous field up to 2 T. The detected fields for the two components of the Senis hall probe were compared to the NMR probe yielding an angular accuracy error lower than ±0.3°.
The superconducting singlets are mounted together to form one cold mass.Thus, to align this cold mass, it is essential to align the high-field quadrupole magnets to the mechanical axis of the SMT.Even though the center of the measuring bench was precisely placed in the center of the SMT using a laser tracker with a maximal error of measurement of ±17 µm, the adjustment of the remaining position offsets of the cart holding the hall sensor and traveling in the z -direction is still necessary.To do that, a permanent magnetic needle (cf. Figure 2) was mounted at the beginning and the end of the SMT.This technique is both, simple and effective for observing the system response in translational and rotational directions.The process entails identifying the point position where the magnetic needle generates the strongest magnetic field and then correlating this position to the coordination of the SMT external references.

Effect of the yokes
Iron yokes, consisting of cylindrical shells surrounding the cryostat, were incorporated into the original design to improve the field performance of the quadrupole magnets, resulting in a modest increase of 6.5% in gradient and 1.6% in effective length.The alignment of these yokes was carried out using the laser tracker but encountered challenges which are primarily due to the shape of the SMT provided by the manufacturer.The SMT was not cylindrical as per our design, but rather almond-shaped, due to the fabrication process and lack of design's specifications, which left insufficient space for adjusting the iron yokes' positions.As a result, the center of the iron yoke could not be better aligned than 200 µm from the center of the cryostat.

SMT magnets alignment
Measurements of the quadrupole's radial field, B r , for one revolution, are performed to evaluate the shift of the cold mass's center axis position.The final step consists of adjusting the mechanical tie rods, which control the cold mass position of the SMT, accordingly to the result.This process is relatively straightforward when using low static currents in the coil.With a current below 200 A, the magnetic measured center of the quadrupole's field was no more than 50 µm shifted compared to the theoretical center.However, at a higher electrical current (>250 A), the cold mass begins to be steered by the iron yokes due to the strong magnetic force that is now guided by the iron yokes, which causes a brutal shift of the cold mass of around 2 mm.The non-linear behavior observed at a higher field was provoked by the misalignment of the iron shells which caused the forces applied by the 8 tie rods to be insufficient for stabilizing the cold mass in its position.This phenomenon induces undesirable harmonics of the field due to saturation [12].

Field Analysis
Field map measurements for the SMT's magnets were performed.We can deduce the effective magnetic length and the field gradient of the magnets from the detected field along the path of the z -axis.The effective magnetic length is determined from: As for the field derivative, it can be expressed by: Table 1 shows the measured values of the F D and the L ef f at a reference radius of r 0 = 139 mm.In addition, a comparison to the extracted values from the computed field maps is shown for the quadrupole, sextupole, and octupole magnets for a current of 465 A, 365 A, and 260 A, respectively.The result shows a very good match except for the field derivative of the octupole magnet, where a difference of 8% is noticed.Fortunately, this difference is not problematic, since the octupole corrector coil does not generate a high field when compared to the quadrupole's field.We also analyzed the field harmonics of the quadrupole magnet to assess its quality.By using Fourier analysis, we were able to extract the strength of the multipole components as a function of the multipole order, n, for the normal and skew fields [13].The normal, B N ormal r,n , and skew, A Skew r,n , fields yield: B r (r 0 , θ, z) cos(nθ)dθ.Figure 3 shows an example of the harmonics analysis of the quadrupole field at a static current of 180 A. Different scales were used to plot fields to display both absolute and relative multipole components, which are represented by the right and left vertical axes, respectively.The quadrupole field term (n = 2) was removed from the graph to ensure visibility as its strength outweighs the harmonics.The same analysis was conducted for the skew fields in the lower panel.The measured relative harmonics of the normal terms were found to have a lower strength (<1.3%) compared to the maximum error allowed by the design, which is 3% of the quadrupole field.Nonetheless, the relative field error caused by the skew term, which is expressed by: 0.017 0.462 = 3.67%, exceeds the 0.1% requirement.It is worth mentioning that some forbidden multipoles appear in our measurements (e.g., n = 1, 3).Using COMSOL software, simulations have revealed that this is due to radial misalignment of the iron yoke rather than being intrinsic to the Walstrom design.
A further study using ion optic modeling software (LISE++) [14] has shown that in the event of a 2 mm misalignment of the cold mass center axis (as previously seen) for 7 of the 21 existing quadrupole magnets (chosen arbitrarily), the transmission will experience a loss of 12%.This value seems to be unsatisfactory and the reduction of the misalignment of the iron yoke with the mechanical SMT axis is impractical, rendering its removal as the only viable solution for the time being.This decision was made following an analysis of the theoretical field map, which indicated that the expected field integral reduces by only 7.41% when the iron shell is removed.

Conclusion
We have developed and qualified a prototype mapping system to assess the performance of 7 Superconducting Multipole Triplets (SMT) and the effectiveness of the Walstrom coil design.Our initial results demonstrated that the mapping system could accurately align the magnets.However, we observed non-linear behavior at high currents due to the misalignment of the iron shells.Thus, we conducted magnetic field mapping measurements for a quadrupole magnet and analyzed the field harmonics using Fourier analysis.While the relative harmonics of the normal terms were satisfactory, there were some undesirable multipoles.An electromagnetic model suggests that prohibited multipoles emerge due to the radial misalignment of the iron yokes corresponding to the SMT cryostat.Hence, after estimating that the iron yokes contribution will not affect considerably the optical calculation performances, we decided to remove them.Our plan includes repeating the field quality measurement without the iron yokes to verify the model and fully investigate and qualify the promising Walstrom coil design.

Figure 2 .
Figure 2. Schematic of the permanent magnetic needle that is used to identify and calibrate the position of the card holding the hall probe sensing element.

Figure 3 .
Figure 3. Schematic of the permanent magnetic needle that is used to identify and calibrate the position of the card holding the hall probe sensing element.

Table 1 .
Comparison between the measured and computed values of the field derivative and the effective length of the quadrupole, sextupole, and octupole magnets.