Neutron simulation

test version 0.1

This web-based system simulates neutron detectors, featuring real-time 3D visualization and integrated Monte Carlo physics simulations.

The system consists of the following main components:

1. Real-time Interactive 3D Visualization

• Dynamic Geometry Modeling: Allows for real-time adjustment of the detector’s geometric parameters, such as the radius and length of the moderator (HDPE) and the thickness of the shielding layer. With each parameter modification, the 3D model updates instantly, providing an intuitive visualization of the detector’s structural changes. The detector’s various components (He-3 tube, HDPE moderator, boron-containing shielding layer, neutron source) are assigned distinct colors and semi-transparent materials, making the internal structure clearly visible.
• Neutron Trajectory Visualization: As parameters are adjusted, the system simulates and renders the flight paths of neutrons inside the detector in real time. The color of the trajectory segments gradients from blue (high energy) to red (low energy), illustrating the process of neutrons being “moderated” (slowed down) and eventually captured.

2. Physics Simulation Based on the Monte Carlo Method

• Simulating the Relationship between Count Rate and Distance: By clicking the “Start Simulation” button, the system rapidly calculates the detection efficiency at various source-to-detector distances. This is achieved by simulating the behavior of thousands of virtual neutrons—some are absorbed by the shielding layer, while others successfully pass through the moderator and are detected by the He-3 tube.
• Energy Spectrum Analysis: The application simulates the energy changes of neutrons as they pass through the various material layers of the detector. (In Development)
• AmBe Source Spectrum: Displays the initial energy distribution of neutrons as they are emitted from the source, which is predominantly composed of high-energy neutrons.
• Arrival Spectrum: Shows the energy distribution of neutrons that reach the He-3 tube after passing through the moderator. (In Development)

3. Data Charts and Results Display

• Response Curve Chart
• Energy Spectrum Comparison Chart

Physics and Model Simplifications in the Simulation

1. Neutron Generation: Simulating the AmBe Source Spectrum

• Physical Fact: An Americium-Beryllium (AmBe) source produces neutrons via the ⁹Be(α, n)¹²C nuclear reaction. Its energy is not monoenergetic but is a continuous spectrum ranging from 0 to approximately 11 MeV, with a peak energy around 2-4 MeV.
• Model Simplification (in the sampleAmBeEnergyEV function): We do not simulate the nuclear reaction itself. Instead, we “sample” from an approximate probability distribution. A truncated exponential distribution (-2.0 * Math.log(1 - Math.random())) is used to rapidly generate random neutron energies between 0 and 10 MeV. Macroscopically, this aligns with the characteristic of an AmBe source, which consists predominantly of high-energy neutrons.

2. Neutron Transport and Interaction: A Layered Probabilistic Model

This is the core of the simulation. Each time a neutron enters a new region, we use a probabilistic model to determine its “fate.”

• Propagation in Air:
  • Physical Fact: Neutrons scatter in the air, and their flux follows the 1/r² inverse-square law.
  • Model Simplification: We merge these two effects into a single, simple exponential decay model: exp(-k*d). This is far faster than complex scattering calculations but similarly reflects the trend that “the farther the distance, the fewer neutrons arrive.”
• Passing Through the Boron-Containing Shielding Layer:
  • Physical Fact: The Boron-10 (¹⁰B) in the shielding layer has an extremely high absorption cross-section for low-energy (thermal) neutrons, which follows the 1/v law (i.e., absorption probability is proportional to 1/√E). High-energy neutrons, however, are almost unaffected.
  • Model Simplification (in the sigmaAbsBoron function): We directly implement the 1/√E law in the code to calculate the macroscopic absorption cross-section, Σa, for a given energy E. Then, using the Beer-Lambert Law, we calculate the probability that a neutron successfully passes through the shield of thickness tB without being absorbed: P_survive = exp(-Σa * tB). Finally, by comparing this probability to a random number between 0 and 1, we determine if this virtual neutron is “absorbed.”
• Moderation in the HDPE Moderator:
  • Physical Fact: This is the critical part of the detector. HDPE (High-Density Polyethylene) is rich in hydrogen atoms. High-energy neutrons undergo elastic collisions with hydrogen nuclei (protons), which have a similar mass. In each collision, a significant amount of energy is lost. This process is called “moderation.”
  • Model Simplification:
    • Number of Collisions: The number of collisions a neutron experiences is not fixed. We use a Poisson distribution (in the sampleCollisionCountHDPE function) to sample the number of collisions, where the mean number of collisions is proportional to the moderator’s thickness and density.
    • Energy Loss: Simulating true collision dynamics is computationally intensive. We employ a radical simplification: with each collision, the energy is multiplied by a random number between 0 and 1 (E *= Math.random()). While not physically precise, this method very efficiently simulates the overall trend of exponential energy decrease, rapidly “pulling” high-energy neutrons down to the low-energy region.
    • Scattering Out: After each collision, the neutron’s direction changes, and it is likely to “leak” out from the sides of the detector before reaching the He-3 tube. We model this effect with a forwardSurvivalProb function, where a higher number of collisions results in a lower probability of successfully reaching the central region.

3. Neutron Detection: The Final Probabilistic Check

• Physical Fact: When a low-energy (thermal) neutron enters the He-3 tube, it has a certain probability of being captured by the ³He(n, p)³H reaction. This reaction releases energy and produces a measurable electrical signal.
• Model Simplification (the capture probability in simulatePoint): We do not simulate the specific path of the neutron inside the He-3 tube. Instead, we abstract this into a final “capture probability.” This probability is based on an empirical formula that is positively correlated with all factors that intuitively increase detection efficiency, such as the He-3 gas pressure (P), the tube’s radius (rt) and length (L), and whether the neutron has been sufficiently moderated.

基于Web技术的中子探测器模拟系统,集成了实时3D可视化、蒙特卡洛物理过程模拟。

主要包括以下几个部分：

• 1. 实时交互的3D可视化
  • 动态几何建模：可以实时调整探测器的各项几何参数，如慢化体（HDPE）半径、长度、屏蔽层厚度等。每一次参数修改，3D模型都会即时更新，直观感受探测器结构的变化。为探测器的各个组件（He-3管、HDPE慢化体、含硼屏蔽层、中子源）赋予了不同的颜色和半透明材质，内部结构一目了然。
  • 中子轨迹可视化：调整参数时，系统会实时模拟并绘制出中子在探测器内部的飞行轨迹。轨迹线段的颜色从蓝色（高能）渐变为红色（低能），展示了中子被“慢化”并最终被俘获的过程。
• 2. 基于蒙特卡洛方法的物理模拟
  • 模拟计数率与距离的关系：通过点击“开始模拟”按钮，系统会快速计算不同源-探距离下的探测效率。这是通过模拟成千上万个虚拟中子的行为来实现的——它们有的被屏蔽层吸收，有的则成功穿过慢化体并被He-3管探测到。
  • 能谱分析：应用模拟了中子在穿过探测器各层材料时的能量变化。（开发中)
  • AmBe源谱：展示了中子源发射时的原始能量分布，以高能中子为主。
  • 到达谱：展示了经过慢化体后，到达He-3管的中子能量分布。（开发中)
• 3. 数据图表与结果展示
  • 响应曲线图
  • 能谱对比图

1. 中子的产生：模拟AmBe源谱

• 物理事实: 镅-铍(AmBe)源通过 ⁹Be(α, n)¹²C 核反应产生中子。其能量不是单一的，而是一个从0到约11 MeV的连续谱，峰值能量在2-4 MeV左右。
• 模型简化 (sampleAmBeEnergyEV函数): 我们不模拟核反应本身，而是从一个近似的概率分布中进行“抽样”。这里使用了一个截断的指数分布 (-2.0 * Math.log(1 - Math.random()))来快速生成能量在0到10 MeV之间的随机中子能量，这在宏观上符合AmBe源以高能中子为主的特征。

2. 中子的输运与相互作用：分层概率模型

这是模拟的核心。中子每进入一个新区域，我们都用一个概率模型来决定它的“命运”。

在空气中传播:

• 物理事实: 中子在空气中会发生散射，且通量遵循 1/r² 反比定律。
• 模型简化: 我们将这两个效应合并为一个简单的指数衰减模型 exp(-k*d)。这比复杂的散射计算快得多，但同样能反映出“距离越远，到达的中子越少”的趋势。

穿过含硼屏蔽层:

• 物理事实: 屏蔽层中的硼-10 (¹⁰B)对低能（热）中子有极高的吸收截面，遵循 1/v 定律（即吸收概率与 1/√E 成正比）。高能中子则几乎不受影响。
• 模型简化 (sigmaAbsBoron函数): 我们直接在代码中实现了 1/√E 定律，计算出给定能量 E 下的宏观吸收截面 Σa。然后，利用比尔-朗伯定律，计算中子成功穿过厚度为 tB 的屏蔽层而不被吸收的概率 P_survive = exp(-Σa * tB)。最后，通过与一个0到1的随机数比较，来决定这个虚拟中子是否被“吸收”。

在HDPE慢化体中慢化:

• 物理事实: 这是探测器的关键部分。HDPE（高密度聚乙烯）富含氢原子。高能中子与质量相近的氢核（质子）发生弹性碰撞，每次碰撞都会损失大量能量，这个过程被称为“慢化”。
• 模型简化:
  • 碰撞次数: 中子在慢化体中经历的碰撞次数不是固定的。我们使用泊松分布 (sampleCollisionCountHDPE函数)来抽样决定碰撞次数，其平均碰撞次数与慢化体的厚度和密度成正比。
  • 能量损失: 模拟真实的碰撞动力学非常复杂。我们采用了极端的简化：每次碰撞，能量乘以一个0到1的随机数 (E *= Math.random())。这虽然不精确，但能非常高效地模拟出能量指数级下降的总体趋势，将高能中子快速“拉”到低能区。
  • 散射出射: 每次碰撞后，中子方向会改变，很可能还没到达He-3管就从探测器侧面“漏”出去了。我们用一个forwardSurvivalProb函数来模拟这个效应，碰撞次数越多，能成功到达中心区域的概率就越低。

3. 中子的探测：最终的概率判定

• 物理事实: 当一个低能（热）中子进入He-3管，它有一定概率被 ³He(n, p)³H 反应俘获，释放出能量，产生可测量的电信号。
• 模型简化 (simulatePoint中的capture概率): 我们不模拟中子在He-3管内的具体路径，而是将其抽象为一个最终的**“俘获概率”**。这个概率是基于一个经验公式，它与所有直观上能提高探测效率的因素正相关，例如：He-3气体压力P、计数管的半径rt和长度L，以及中子是否被充分慢化。

点击这里直接访问应用。