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质子照相是探测等离子体中场分布的一个有效方法。然而由于电磁场结构的复杂性，从质子束的成像反演电磁场分布是极其困难的，往往需要对场结构做一些对称性假设。借助机器学习的方法，我们开展了不依赖对称性假设的复杂质子成像反演磁场分布的研究。我们以数十个Weibel不稳定性产生的磁场作为基元构建出的复杂磁场为反演目标，通过GEANT4计算了50000份质子照相图像，搭建并训练了一个包含三层卷积层的轻量化卷积神经网络，在质子成像的散焦区实现对具有数个不对称焦散和显著通量聚集的复杂质子成像的三维（3D）磁场反演。在场反演过程中，涉及到对包含场结构、位置、旋转等信息在内的80个参数的预测。结果显示预测值平均绝对百分比误差仅为8.5%，反演获得的磁场所计算对应的质子成像图与原测试图像具有较好的一致性。该研究表明建立更为精准的空间网格点等方法反演更一般电磁场是可能的，为强激光等离子体作用中的电磁场反演提供了一个可行的方法。
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关键词:
- 质子照相 /
- 深度学习 /
- 磁场反演 /
- 激光等离子体相互作用
Proton radiography is an effective technique for diagnosing field distributions in plasmas. However, due to the complexity of electromagnetic field structures, reconstructing electromagnetic fields from proton radiographs is extremely challenging and often requires some simplified symmetry assumptions about the fields. Here, we present a machine learning approach to reconstruct three-dimensional (3D) magnetic field distributions from complex proton radiographs without relying on such assumptions.
To enable this, we construct the target 3D magnetic fields by linearly superposing multiple elementary magnetic structures generated from the Weibel instability. Each element is characterized by eight parameters—structural parameters (a, b, B0), spatial coordinates (x0, y0, z0), and rotation angles (θ, ϕ)—resulting in 80 degrees of freedom in total. Parameters were uniformly sampled within ±25% of their baseline values, and a dataset of 50,000 magnetic field–proton radiograph pairs was generated through forward simulation using GEANT4. All proton radiographs reside in the caustic regime, exhibiting multiple asymmetric caustics and significant flux concentrations.
A lightweight three-layer convolutional neural network (CNN) was designed for the reconstruction task. The network consists of an input layer, three convolutional modules (the first two following a ”convolution–batch normalization–max pooling” cascaded structure, and the third is simplified to a single convolutional layer), a flattening layer, a dropout layer, and an output layer. Bayesian optimization was applied to determine the optimal hyperparameters. The model was trained on 40000 samples, with 5000 samples for validation and 5000 for testing.
On the test set, the CNN achieves a mean absolute percentage error (MAPE) of 8.5% in predicting the 80 magnetic parameters, below the 12.9% random-guessing threshold. Prediction errors for most parameters follow near-zero-mean Gaussian distributions, with relative standard deviations under 6%. The reconstructed fields show high spatial agreement with the reference fields, and corresponding proton images match the originals with a cosine similarity of 0.89.
This study demonstrates that our CNN-based proton radiography reconstruction method can effectively reconstruct complex 3D magnetic fields without symmetry assumptions or manual parameter tuning, offering a novel tool for diagnosing electromagnetic fields in high-intensity laser-plasma interactions. Future work may incorporate multi-angle proton radiography and transfer learning from experimental data to enhance the method’s practicality and robustness.-
Keywords:
- Proton radiography /
- Deep learning /
- Magnetic field reconstruction /
- Laserplasma interactions
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