磁共振测井在石油探测中扮演着关键角色．磁体系统是磁共振测井传感器的一个重要组成部分．然而，目前的磁体系统设计通常依赖于经验结构，缺乏对最优结构的理论研究．本研究提出了一种基于变密度法拓扑优化的单侧磁共振测井传感器磁心结构设计方法，将测井探头二维截面模型的磁心设计域剖分为N个密度在0 ~ 1之间的小单元，应用梯度下降的移动渐近线法，基于目标函数对密度的梯度信息更新单元密度，迭代逐步逼近最优解．本文基于优化结果，制作了缩小比例的磁共振传感器样机，进行实验验证．传感器的外半径为2.5 cm，能够在远端感兴趣区域（ROI）内生成强度为641.0 ~ 1 108.6 G（1 G=10^-4 T），梯度为303.0 ~ 683.6 G/cm的静态磁场．实测磁场分布数据与仿真优化设计的结果一致．在此基础上，对设计的磁共振测井传感器进行了水模测量实验，实验测得传感器的信噪比为23.5．

Magnetic resonance logging plays a pivotal role in petroleum exploration. The magnet system serves as a crucial component of the magnetic resonance logging sensor. However, current designs of magnet systems often rely on empirical structures and lack theoretical research on optimal configurations. This paper proposes a design method for the magnetic core structure of a single-side magnetic resonance logging sensor based on topology optimization using the variable density method. The design domain of the magnetic core in the two-dimensional cross-section model of the logging probe is divided into N small units with densities ranging from 0 to 1. The moving asymptote method of gradient descent is employed to update the density based on gradient information from the objective function, leading to an iterative approach for achieving an optimal solution. Based on these optimization results, a scaled-down prototype of the magnetic resonance sensor is fabricated for experimental verification. With an external radius of 2.5 cm, this sensor can generate a static magnetic field with intensities ranging from 641.0 G (1 G=10^-4 T) to 1108.6 G and gradients from 303.0 G/cm to 683.6 G/cm within the remote region of interest (ROI). The measured data regarding magnetic field distribution aligns with simulation-based optimization results. Subsequently, water mode measurement experiments are conducted using this designed magnetic resonance logging sensor, yielding a signal-to-noise ratio of 23.5.