Research on the Environmental Characteristics and Patterns of High-Altitude Strong Pulses

(Northwest Institute of Nuclear Technology, Xi'an)

Abstract

This paper investigates the environmental characteristics and physical patterns of strong electromagnetic pulses generated at high altitudes. By analyzing the coupling mechanisms between high-altitude radiation environments and the Earth's atmosphere, we characterize the spatial and temporal distribution of the resulting electromagnetic fields. The study focuses on the influence of altitude, atmospheric density, and geomagnetic field interactions on pulse propagation. High-precision simulations of long-distance transport of intense pulsed $\gamma$-rays at high altitudes were achieved using the Monte Carlo method combined with variance reduction techniques. The spatial distributions of peak dose rate (Si) and total dose (Si) were calculated for various source altitudes.

By analyzing the distribution characteristics of the radiation field, the concept of mass thickness was introduced to describe the effects of atmospheric absorption and scattering on $\gamma$-ray transmission. Based on these findings, a generalized empirical formula was developed to calculate the spatial distribution of peak dose rate (Si) and total dose (Si) across different source altitudes. The results obtained from this formula maintain a deviation of less than $10\%$ compared to numerical simulations. This approach provides a high-altitude intense pulsed $\gamma$-ray environment calculation method that balances computational accuracy and efficiency for the radiation protection design of spacecraft.

Keywords: High-altitude intense pulse; Peak dose rate (Si); Dose (Si); Monte Carlo simulation

1. Introduction

High-altitude strong electromagnetic pulses represent a critical area of research in atmospheric physics and electromagnetic compatibility. When high-energy radiation interacts with the rarefied upper atmosphere, it triggers a complex sequence of physical processes, primarily the production of Compton electrons. These electrons, accelerated by the geomagnetic field, generate intense, wideband electromagnetic radiation that can cover vast geographical areas.

With the increasing frequency of human space activities, the threat posed by the space radiation environment to orbiting spacecraft has become increasingly severe \cite{1-5}. High-altitude intense pulsed $\gamma$-rays, as a high-energy transient radiation source, pose a significant challenge to the reliability and lifespan of spacecraft electronic systems. These $\gamma$-rays are characterized by high instantaneous flux and a broad energy spectrum; they can directly damage semiconductor devices through ionization effects, leading to performance degradation or even functional failure \cite{6-8}.

Current research focuses primarily on ground-based experimental simulations and numerical methods \cite{9-12}. However, ground-based experiments struggle to fully replicate the complex physical conditions of the actual space environment. Traditional numerical simulation methods, particularly those based on Monte Carlo algorithms, exhibit excellent precision but suffer from prohibitive computational costs for large-scale scenes. Furthermore, theoretical formulas derived for vacuum conditions often mislead the design of spacecraft radiation protection by overestimating direct peak dose rates while underestimating scattered components. Consequently, there is an urgent need to establish a simulation method that balances accuracy and efficiency.

2. Physical Mechanisms and Simulation Methodology

2.1 Compton Scattering and Electron Production

As high-energy photons penetrate the atmosphere, they undergo Compton scattering, ejecting electrons from atmospheric atoms. The trajectory of these relativistic electrons is governed by the Lorentz force as they move through the Earth's magnetic field. The mathematical representation of the current density $\vec{J}$ is given by:
$$\vec{J}(\vec{r}, t) = -e \int v \cdot f(\vec{r}, \vec{p}, t) d^3p$$
where $e$ is the elementary charge, $v$ is the velocity, and $f$ is the distribution function of the electrons.

2.2 Geometric Model for Long-Distance Transport

The upper atmosphere is modeled as a cylinder of height $H$, stratified horizontally to account for non-homogeneous density. The atmosphere from 0 to 500 km is divided into $N_1$ layers of thickness $d_1$, and from 500 to 1000 km into $N_2$ layers of thickness $d_2$. Each layer is filled with air of uniform density derived from the MSIS00 atmospheric model. The radiation source is approximated as an isotropic point source.

2.3 Variance Reduction Methods (DXTRAN)

To address the challenges of insufficient effective particle counts in large-scale simulations, this paper adopts the DXTRAN sphere variance reduction method. When a photon undergoes a collision, an isotropic point source is artificially generated on a specific DXTRAN surface directed toward the region of interest. [TABLE:1] illustrates that while the peak dose rate trends remain consistent with direct simulations, the DXTRAN method significantly reduces computational duration.

[FIGURE:1]

3. Results and Analysis

3.1 Spatial Distribution of Peak Dose Rate (Silicon)

The spatial distribution of the peak dose rate under vacuum conditions is typically calculated as:
$$\dot{D}_p = \frac{K}{r^2}$$
where $r$ represents the distance in meters. However, simulation results show that when the source altitude is low, the peak dose rate is consistently lower than vacuum predictions due to atmospheric absorption. The direct component of the peak dose rate often exceeds 90%, indicating it is primarily influenced by absorption rather than scattering. As shown in [FIGURE:2], when the source altitude exceeds a specific threshold, atmospheric effects become negligible for observation points above a certain height.

3.2 Dose Characteristics and Atmospheric Effects

The total dose $D_{\text{Si}}$ is the integrated energy deposition over the pulse duration. Unlike the peak dose rate, the direct-to-total dose ratio exhibits a complex relationship with distance, first decreasing and then stabilizing. This is because the total dose is contributed by both high-energy and low-energy photons, the latter being significantly influenced by atmospheric scattering.

[FIGURE:3]

3.3 Derivation of the Universal Computational Formula

Based on the simulation data, the concept of mass thickness $M$ is used to describe the atmospheric effects. The propagation path traverses $N$ discrete layers, and the mass thickness is defined as:
$$M = \sum_{i=1}^{N} \rho_i \cdot \Delta l_i$$
where $\rho_i$ is the density of the $i$-th layer. The peak dose rate and total dose can be modified using an absorption factor $f_a$ and a scattering factor $f_s$:
$$\dot{D} = \dot{D}{vac} \cdot f_a(M)$$
$$D = D \cdot f_a(M) \cdot f_s(M)$$
The absorption factor $f_a$ exhibits an exponential decay trend as mass thickness increases. For the peak dose rate, the maximum relative deviation between this modified formula and Monte Carlo results is less than 10%.

[TABLE:1]

4. Conclusion

This study successfully combined the Monte Carlo method with the DXTRAN variance reduction technique to characterize high-altitude intense pulsed $\gamma$-ray environments. The findings indicate that while the peak dose rate is primarily governed by atmospheric absorption, the total dose is influenced by a competition between absorption and scattering.

The developed generalized formulas provide a high-precision, high-efficiency alternative to full numerical simulations. Within the specified range, the deviation remains within 10% for most scenarios. This methodology provides reliable data support for the radiation-hardened design and safe operation of spacecraft electronic systems in complex high-altitude environments.

References

\cite{1-19} (As listed in the source text)