# NMR Magnetometer Based on Dynamic Nuclear-Polarization for Low-Strength Magnetic Field Measurement

^{*}

## Abstract

**:**

## 1. Introduction

_{0}= (γ/2π) B

_{0}, for

^{1}H nuclei, (γ/2π) = 42.57747892 MHz/T, the magnetic field value exhibits a linear correlation with the frequency, wherein the constant of proportionality is the gyromagnetic ratio (γ). Thus, the magnetic field value strictly depends on the frequency and is unaffected by factors such as temperature [21].

- Proposed a method that combines pulsed NMR with dynamic nuclear polarization (DNP), which extends the measurement lower limit, improves measurement speed, and ensures measurement accuracy;
- Proposed a new magnetometer structure and simulated the measurement process, analyzing the influence of different factors on the signal-to-noise ratio;
- Constructed a complete measurement system and verified its accuracy, as well as improved the SNR of the magnetometer in low magnetic field measurements through experiments at different magnetic field strengths.

## 2. Simulation Computation and Methods

#### 2.1. NMR Magnetometer Structure

- Polarization

_{p}to induce polarization of the hydrogen protons.

_{p}, there is no transverse magnetization vector due to the inconsistent proton precession phases. However, in the direction parallel to B

_{p}, a macroscopic magnetization vector M

_{0}is established:

_{p}value, the more evident the level splitting, and the greater the intensity of the M

_{p}. The process of the macroscopic magnetization vector (reaching Boltzmann equilibrium) is not instantaneous and depends on the longitudinal relaxation time T

_{1}of the sample:

_{p}represents the macroscopic magnetization vector intensity of a sample when it flows out of the polarizing field, and t

_{p}represents the time it takes for the sample to flow through the polarizing magnetic field. M

_{0}is the maximum longitudinal magnetization vector achieved with a polarizing magnetic field B

_{p}. During the t

_{pd}time, it takes to flow out of the polarizing magnetic field into the magnetic field to be measured. If the sample is not affected by interference, its macroscopic magnetization vector decays according to the T

_{1}law:

- 2.
- Excitation

_{1}perpendicular to the magnetic field B

_{m}being measured. Protons at a low energy level absorb RF energy and undergo energy level transitions. When an RF magnetic field B

_{1}is applied to the plane perpendicular to the measured magnetic field B

_{m}at the same Larmor frequency, the longitudinal magnetization vector M

_{p}flips around the B1 axis perpendicular to the plane. During the measurement process, a π/2 RF pulse to flip M

_{p}by 90 degrees is applied.

- 3.
- Detection

_{xy}undergoes a loss of phase due to the spin–spin interaction of the atomic nuclei, resulting in the composite vector gradually decaying to zero, according to the formula:

_{2}is the transverse relaxation time, which represents the time it takes for a magnetization vector generated in the transverse plane to decay to zero. T

_{2}* is shorter than T

_{2}because, in the measurement processes, there are factors such as field gradients and others that render the field inhomogeneous, causing the transverse magnetization to decay faster.

^{1}H nuclei, (γ/2π) = 42.57747892 MHz/T. The magnetic field value has a linear relationship with the frequency, and the proportionality coefficient is the gyromagnetic ratio γ, which is a constant.

#### 2.2. Factors Affecting NMR

_{m}= 3 mm, diameter = 5 mm, water pipe length from polarizing magnet to detection coil (L

_{pd}) = 2 m, polarizing magnetic field strength = 1.3 T, measurement field magnetic field strength = 30 mT.

_{f}(unit: mL/min), the length of the measurement coil covering the pipeline as L

_{m}(unit: m), and the length of the pipeline between the polarizing field and the detection field as L

_{pd}(unit: m).

_{r}) is about 5 μs, the equation for D is Formula (7).

_{2}* (which is closely related to the inhomogeneous of the magnetic field). As the decay rate accelerates, the spectral lines in the frequency spectrum analysis become smoother, and the peak-to-width ratio of the FFT frequency spectrum analysis curve becomes smaller, which is counterproductive to our goal of sharpening the spectral lines and indicates that the measurement of the NMR magnetometer requires homogeneity restriction of the magnetic field. By reducing the size of the probe, the measurement ability of the flow-type magnetic resonance magnetometer can be improved for inhomogeneous fields. The smaller the size of the probe coil, the smaller the area of the magnetic field it excites, and the smaller the corresponding variation in magnetic field intensity within the area, which can significantly improve the T

_{2}* duration of the FID signal. In addition, reducing the size of the probe also has the advantage of improving spatial resolution.

## 3. System Design

## 4. Experiment

_{2}*, resulting in faster signal decay. This proves that the homogeneity of the magnetic field is crucial to the NMR signal, which can inform the design of meter probes, as smaller probes can provide better measurement capability for uneven magnetic fields while also improving the spatial resolution of the measured magnetic field.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The effect of pre-polarization on the FID signal and the corresponding amplitude spectrum.

**Figure 5.**Halbach magnet structure and real picture (picture (

**a**) shows the distribution of 16 magnets on one layer; picture (

**b**) shows the structure of 6 layers; picture (

**c**) shows the entity of the magnets).

**Figure 6.**Simulation diagram of the magnetic field at different positions of the magnet (assuming that the height of the middle of the magnet axis is 0; (

**a**) shows the 1/4 cross-sectional simulation of the interface with a height of 0; (

**b**) shows the magnetic field at a height of 50 mm; (

**c**) shows the magnetic field at a height of 100 mm; (

**d**) shows the magnetic field at a height of 150 mm).

**Figure 14.**Measurement results for different probe coils (Picture (

**a**) shows that the probe coil has a diameter of 5 mm and a length of 7 mm. Picture (

**b**) shows that the probe coil has a diameter of 5mm and a length of 3 mm).

**Figure 15.**Measurement results of an 8 mT magnetic field generated by the solenoid coil. (in the left image, The blue line represents the imaginary part data, and the yellow line represents the real part data).

Literature Work | Experimental Magnetic Field Strength | Measurement Accuracy | Sample | Measurement Time | Spatial Resolution |
---|---|---|---|---|---|

Pendlebury (1979) | 250 mT | unknown | water | unknown | unknown |

Woo (1997) | 46.985 mT | 320 nT | water | >4 min | >1.2 cm^{3} |

Davydov (2015) | 10.9 mT | 0.04 mT | a distillate water isolated with methanol | 4 min | >1 cm^{3} |

Michal Ulvr (2018) | 2.3 mT | 57.5 nT | water | 30 min | <0.5 cm^{3} |

This paper | 8 mT | 22 nT | pure water | <10 s | <0.5 cm^{3} |

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**MDPI and ACS Style**

Guo, T.; He, W.; Wan, C.; Zhang, Y.; Xu, Z.
NMR Magnetometer Based on Dynamic Nuclear-Polarization for Low-Strength Magnetic Field Measurement. *Sensors* **2023**, *23*, 4663.
https://doi.org/10.3390/s23104663

**AMA Style**

Guo T, He W, Wan C, Zhang Y, Xu Z.
NMR Magnetometer Based on Dynamic Nuclear-Polarization for Low-Strength Magnetic Field Measurement. *Sensors*. 2023; 23(10):4663.
https://doi.org/10.3390/s23104663

**Chicago/Turabian Style**

Guo, Taoning, Wei He, Cai Wan, Yuxiang Zhang, and Zheng Xu.
2023. "NMR Magnetometer Based on Dynamic Nuclear-Polarization for Low-Strength Magnetic Field Measurement" *Sensors* 23, no. 10: 4663.
https://doi.org/10.3390/s23104663