# Hall sensor angle error and relative position calibrations for cryogenic permanent magnet undulator of high energy photon source test facility (HEPS-TF)

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## Abstract

### Purpose

A new in-vacuum three-dimensional Hall probe magnetic measurement system is under fabrication for characterizing the magnetic performance of the Cryogenic Permanent Magnet Undulator (CPMU). In order to fit the small gap (5 mm) of magnetic structure and vacuum environment, a small three-dimensional Hall probe has been manufactured. The angular and positional misalignment errors of the Hall sensors play an important role in the measurement accuracy of the CPMU. In order to minimize the misalignment errors, a method of calibrating angle error and relative assembly displacements of a three-dimensional Hall probe is carried out.

### Methods

The angle error of Hall sensors will be calibrated by a standard dipole magnet and a five-dimensional Hall bench. The standard dipole magnet will generate a single direction and uniform magnetic field. And the five-dimensional Hall bench is used to rotate the Hall probe which is put in the center of magnet. Based on the relationship between angle and magnetic field strength, the angle error of each Hall sensor will be obtained. The relative position between the sensitive areas of the Hall sensors will be calibrated by a two-dimensional magnetic field undulator section. Based on Maxwell’s equations, through the calculation of measurement magnetic field strength, the relative assembly displacements of the three Hall sensors can be derived.

### Results

The details of the calibration methods and the data processing of angle error and relative assembly displacements of a three-dimensional Hall probe are presented. The three-dimensional magnetic fields of a cryogenic permanent magnet undulator can be received accurately by correcting these angle errors and position errors of Hall sensors.

### Conclusions

This paper illustrates the relative position and angle calibration procedures and the data processing of a three-dimensional Hall probe. Now the design of a smaller Hall probe is in process. The calibration of the angle errors and position errors will be carried out after the fabrication of the standard dipole magnet.

## Keywords

Magnetic measurement system Cryogenic permanent magnet undulator Three-dimensional Hall probe Calibration of Hall probe## PACS

07.85.Qe 41.60.Ap 52.59.Px## Introduction

Chinese High Energy Photon Source Test Facility (HEPS-TF) is a 6 GeV third-generation synchrotron radiation facility with ultralow emittance and extremely high brightness [1, 2]. A Cryogenic Permanent Magnet Undulator (CPMU) will be installed to deliver a high-performance X-ray [1, 3, 4]. The CPMU is a full-scale in-vacuum undulator with a period of 13.5 mm and a magnetic length of 2 m. By adopting a gap of 5 mm and cryogenic temperatures of 85 K, the target peak field achieved will be 1 T with the RMS of Phase errors less than \(3{^{\circ }}\) and the first field integrals less than \(100\mathrm{Gs}\cdot \mathrm{cm}\) [5, 6].

Since the RMS phase error and the field integrals of CPMU have a strong influence on the spectral flux and the closed orbit, the precise measurement of the magnetic quantities is essential to characterize magnetic errors [7]. A new in-vacuum Hall probe measurement system which is used to measure the CPMU magnetic field is under development [6].

## Hall sensors angle error calibrations

*B*is the real magnetic field. The angle error \({\theta }\) will lead to a relative magnetic measurement error:

*B*of a Hall sensor placed in a one-dimensional magnetic field space. However, in the measurement application, the output voltage of the Hall sensor is a collection of the three magnetic field components where there exist angle errors between Hall sensors and magnetic fields. The relationship between the measured magnetic fields and the real ones can be indicated as:

The main parameters of standard dipole magnet which is used to implement the angular calibration of Hall probe

Parameter | Value |
---|---|

Gap | 82 mm |

Maximum field | 1.3 T |

Good field region from vertical and horizontal plane | \(\pm 15\,\hbox {mm}\) |

Quality of good field | \(5\times 10^{-4}\) |

*T*:

*B*is the magnetic field of dipole magnet. The angle errors, \(a_{12},a_{22}\) and \(a_{32}\) can be obtained by:

*T*is obtained through the above calibration method. After finishing the measurement of the CPMU, the real magnetic field of CPMU is calculated by the measured magnetic field with the formula:

## Hall sensors relative position calibrations

*Z*axis. There are spacing, \({\delta }_{\mathrm{{z}^{\prime }}(\mathrm{H}1-\mathrm{H}2)} \) (H1, H2 = HX, HY, HZ), among three Hall sensors. Owing to the manual welding error, there are small distances, \({\delta }_{\mathrm{{x}^{\prime }}(\mathrm{H}1-\mathrm{H}2)} \) and \({\delta }_{\mathrm{{y}^{\prime }}(\mathrm{H}1-\mathrm{H}2)} \), among three Hall sensors. Figure 4 shows the relative position between sensitive areas of the Hall sensors, which will be calibrated on a two-dimensional magnetic fields undulator section as shown in Fig. 5.

*S*) as shown in Fig. 5 should meet the following equation:

*S*). Due to the position errors \({\delta }_{{{\mathrm{y}}^{\prime }}({\mathrm{HZ}}-{\mathrm{HY}}) }\) and \({\delta }_{\mathrm{{z}^{\prime }}({\mathrm{HZ}}-\mathrm{HY})} \), the \({\tau }\) is unequal to zero. By moving the coordinate of \({ {B}}_\mathrm{mz}\), a set of solutions \( (\delta _1,\delta _2 )\) will meet the formulas (26) and (27) to minimize the function \({\tau }\).

The three-dimensional magnetic fields of CPMU can be received accurately by corrected these position errors of Hall sensors. After the field calibration of Hall sensors, the position errors calibration can be carried out immediately.

## Conclusions

HEPS is developing a high-performance CPMU. In order to test its performance, a high precision vacuum hall measurement system is required. To adjust to the vacuum and the small gap conditions, we manufacture a new three-dimensional Hall probe. This paper illustrates the relative position and angle calibration procedures and the data processing of a three-dimensional Hall probe. Now the design of a smaller Hall probe is in process. The calibration of the angle errors and position errors will be carried out after the fabrication of the standard dipole magnet.

## Notes

### Acknowledgements

The authors would like to acknowledge Dr. Shu Guan, Dr. Wu Lei, Dr. Gu Kuixiang and Dr. Tang Zheng for great helpful discussion and suggestion.

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