🔭 astrophysics

Monte Carlo Simulations of Secondary Cosmic-Ray Variations in Atmospheric Electric Fields : Implications for Long Duration Electron and Gamma-ray Emissions from Thunderclouds

Using Monte Carlo simulations with the PHITS code, this study demonstrates that gamma rays are the primary source of seed electrons for long-duration thundercloud bursts and utilizes observational data from Yangbajing to constrain the electric field conditions necessary for generating high-energy emissions.

Original authors: Harufumi Tsuchiya

Published 2026-03-02

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Harufumi Tsuchiya

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Thunderclouds as Cosmic Particle Factories

Imagine a thundercloud not just as a storm, but as a massive, invisible particle accelerator. Inside these clouds, there are strong electric fields (like invisible magnets) that can grab tiny particles and shoot them toward the ground at nearly the speed of light.

Scientists have been trying to figure out two big mysteries:

Where do the "seed" particles come from? To start a chain reaction of high-speed particles, you need a starter pack of electrons. Where do they come from?
How strong does the electric field need to be to create the super-high-energy gamma rays (a type of light) that we see coming from these storms?

This paper uses a supercomputer simulation (a digital "flight simulator" for particles) to answer these questions.

1. The "Seed" Mystery: It's Not the Rain, It's the Background Noise

The Old Idea: Scientists thought the electric field inside the cloud mostly grabbed electrons that were already floating around in the air (from cosmic rays hitting the atmosphere) and sped them up.

The New Discovery: The simulation found that the electric field is actually doing a lot of work converting other particles into electrons.

The Analogy: Imagine a factory (the thundercloud) trying to make cars (electrons).
- Old Theory: The factory just picks up raw car chassis (existing electrons) from a pile and paints them.
- New Theory: The factory is actually taking bricks (gamma rays) and smashing them together to create the car chassis on the spot.

The Result: The study shows that gamma rays (high-energy light) are the most important "seeds." When these gamma rays hit the electric field, they smash into air molecules and instantly turn into new, fast-moving electrons. These new electrons then get accelerated, creating more gamma rays, which create more electrons, and so on. It's a snowball effect, but the snowball is made of light turning into matter.

2. The "Runaway" Effect: The Escalator vs. The Treadmill

To get particles moving fast enough to create these bursts, the electric field has to be strong enough to overcome the "friction" of the air.

The Analogy: Imagine a person walking on a moving walkway (the electric field) that is trying to push them forward, but the air is like thick mud trying to slow them down (ionization loss).
- Weak Field: If the walkway moves slowly, the mud wins. The person gets tired and slows down.
- Strong Field: If the walkway moves very fast, the person gains speed faster than the mud can slow them down. They start running away, gaining energy with every step. This is called a Relativistic Runaway Electron Avalanche (RREA).

The study found that for this "runaway" to happen and create the high-energy bursts we see, the electric field needs to be about 1.5 times stronger than the minimum required to just start the process.

3. The Shape of the Storm: A Long Hallway vs. A Wide Room

The researchers played with the shape of the electric field region in their simulation.

The Analogy: Think of the electric field as a hallway.
- Length (L): If the hallway is short, the particles don't have enough time to speed up before they hit the end. If the hallway is long (at least 500 meters), the particles can really build up speed.
- Width (W): If the hallway is too narrow, particles might bounce off the walls and escape sideways before they get fast enough. A wider hallway keeps them in the game longer.

The Result: To create the super-high-energy gamma rays (over 40 MeV) that were detected by observatories high in the mountains, the electric field needs to be a long, wide hallway (at least 500m long) with a very strong push.

4. The "Cloud Base" Factor: How Close is the Storm?

The study also looked at how high the bottom of the cloud is (Cloud Base Height).

The Analogy: Imagine throwing a ball from a cliff.
- Low Cliff (Cloud close to ground): If the cloud is very close to the ground (low altitude), the fast electrons have a short trip. They might survive the journey and hit the ground detectors directly.
- High Cliff (Cloud far from ground): If the cloud is high up, the electrons get tired (lose energy) in the thick air before they reach the ground. However, the gamma rays (which are like ghostly light) can pass through the air easily.

The Result:

If the storm is low, you might detect fast electrons hitting the ground.
If the storm is high, you mostly detect the gamma rays they produced.
This explains why some detectors see electrons and others only see light, depending on how close the storm is.

5. The "Nighttime" Connection

The paper mentions that these events happen more often at night.

Why? At night, the ground cools down, which often makes the bottom of the clouds sit lower (closer to the ground). As we learned in the "Cloud Base" section, a lower cloud means the fast electrons have a better chance of surviving the trip to the ground.

Summary of the "Takeaway"

Gamma rays are the heroes: They are the main source of the "seed" electrons that start the high-energy chain reaction in thunderclouds.
Size matters: To create the most energetic bursts, the electric field inside the cloud needs to be a long, wide region (at least 500 meters long).
Strength matters: The electric field needs to be very strong (about 220 kV/m or higher) to push particles to relativistic speeds.
Distance matters: If the cloud is low, we see electrons; if it's high, we mostly see the gamma rays they create.

This study helps scientists understand exactly what kind of "storm engine" is needed to produce these mysterious, high-energy flashes of light from the sky.

1. Problem Statement

Long-duration bursts of high-energy radiation (gamma-ray glows) from thunderclouds are observed at various altitudes, including ground level and high-altitude sites like Yangbajing (4.3 km). These phenomena are attributed to the acceleration of electrons by thundercloud electric fields (EFs) via Relativistic Runaway Electron Avalanches (RREA). However, a critical physical challenge remains:

The Seed Electron Problem: Observed atmospheric electric fields are typically too weak (often <1/10th of the breakdown threshold) to accelerate low-energy electrons to relativistic speeds because ionization losses exceed energy gains below ~0.1 MeV.
The Source Question: It is unclear which component of the secondary cosmic-ray background (electrons, positrons, muons, or gamma rays) most effectively supplies the necessary "seed" electrons (energies >0.1 MeV) to initiate and sustain these avalanches.
High-Energy Gamma Rays: High-altitude observations have detected gamma rays exceeding 40 MeV. The specific electric field configurations (strength and geometry) required to produce such high-energy photons, and whether secondary cosmic-ray electrons alone are sufficient to explain them, are not well understood.

2. Methodology

The study employs Monte Carlo (MC) simulations using the Particle and Heavy Ion Transport code System (PHITS) to model the interaction of steady-state secondary cosmic rays with localized thundercloud electric fields.

Input Spectra: Instead of using idealized monoenergetic beams, the study utilizes realistic secondary cosmic-ray spectra (gamma rays, electrons, positrons, $\mu^-$ , $\mu^+$ ) generated by the EXPACS model for an altitude of 4.3 km (Yangbajing).
Simulation Geometry:
- The EF region is modeled as a cuboid with horizontal width ( $W$ ) and vertical length ( $L$ ).
- The distance from the EF bottom to the ground is defined as the cloud base height ( $H$ ).
- Particles are injected from the top surface of the EF region with angular distributions ( $0^\circ$ to $60^\circ$ zenith angle).
Parameters Varied:
- EF Strength: 0 to 260 kV m $^{-1}$ (covering the RREA threshold of ~170 kV m $^{-1}$ at 4.3 km).
- Dimensions: $L$ (250–1000 m), $W$ (250–1000 m), and $H$ (50–1000 m).
Physics Processes: The simulation accounts for photoelectric effects, Compton scattering, pair production, bremsstrahlung, ionization losses, and Coulomb scattering.

3. Key Contributions

Systematic Evaluation of Seed Sources: Unlike previous studies that often focused on specific particle types or transient air showers, this work systematically evaluates the relative contributions of all major secondary cosmic-ray components (including gamma rays, positrons, and muons) to the generation of seed electrons.
Realistic Input Conditions: The use of EXPACS-derived spectra and realistic angular distributions provides a more accurate representation of the ambient particle environment compared to simulations using monoenergetic 1 MeV electron injections.
Constraint on EF Structures: The study correlates simulation outputs with observational data from Yangbajing to constrain the physical properties (strength and size) of the electric fields responsible for observed high-energy emissions.

4. Key Results

A. Dominance of Gamma Rays as Seed Sources

Primary Finding: Gamma rays are the dominant source of seed electrons for long-duration bursts, contributing approximately 60% of the total electron population at the bottom of the EF region, regardless of EF strength or geometry.
Mechanism: High-flux ambient gamma rays undergo electromagnetic interactions (Compton scattering, pair production) within the EF region to generate high-energy electrons.
Comparison: Incident electrons contribute ~30–35%, while positrons contribute ~5–8%. The contribution from incident electrons decreases as EF strength weakens.

B. Electron and Gamma-Ray Spectra Characteristics

Average Electron Energy ( $\epsilon_e$ ): The simulated average electron energy is 9–10 MeV, slightly higher than the conventional ~7 MeV value derived from monoenergetic 1 MeV injection studies. This increase is attributed to the inclusion of higher-energy incident electrons in the realistic spectrum.
Dependence on Geometry:
- Length ( $L$ ): Electron flux increases significantly with $L$ only when the EF strength exceeds the RREA threshold (~170 kV m $^{-1}$ ). Below this threshold, longer paths lead to greater attenuation due to ionization losses.
- Width ( $W$ ): Increasing $W$ enhances electron flux by reducing lateral escape (side-leakage) of Compton-scattered gamma rays, allowing them to interact again and produce secondary electrons.
High-Energy Gamma Rays: To produce gamma rays exceeding 40 MeV (as observed at Yangbajing), the simulations indicate a requirement for:
- EF Strength: $\ge$ 220 kV m $^{-1}$
- Vertical Length: $L \ge$ 500 m

C. Cloud Base Height ( $H$ ) and Particle Composition

Low Clouds ( $H \approx 50$ m): Electrons can reach the ground in significant numbers. The electron-to-gamma-ray ratio increases with EF strength, potentially making electrons the dominant detected component under strong fields.
High Clouds ( $H \approx 1000$ m): Electrons are largely attenuated by the atmosphere. Gamma rays (and muons) dominate the flux reaching the ground. Gamma rays constitute >50% of the flux, and their fraction increases with EF strength.

D. Comparison with Observations

The simulated particle enhancement factors were compared with data from the Yangbajing neutron monitor.
The study estimates that the observed long-duration bursts correspond to an enhancement factor of 0.05 to 1.4 relative to the background flux.
The simulation results confirm that EF conditions with strengths of $\ge$ 220 kV m $^{-1}$ and lengths of $\ge$ 500 m are physically consistent with the magnitude of observed high-energy gamma-ray events.

5. Significance

Resolution of the Seed Problem: The study definitively identifies steady-state secondary gamma rays as the primary mechanism for supplying seed electrons, resolving uncertainties about whether ambient electrons alone are sufficient.
Modeling Improvement: By demonstrating that realistic spectral inputs yield different average energies (~10 MeV vs. ~7 MeV) compared to monoenergetic assumptions, the paper advocates for more sophisticated input models in future atmospheric electric field simulations.
Observational Constraints: The work provides quantitative constraints on the electric field structures required to explain high-altitude gamma-ray glows, suggesting that such events require large, strong electric field regions ( $L \ge$ 500 m, $E \ge$ 220 kV m $^{-1}$ ).
Nocturnal Implications: The findings support the hypothesis that electron detection is more likely during nighttime when cloud base heights are lower, bringing the acceleration region closer to ground-based detectors.

In conclusion, this research utilizes advanced Monte Carlo simulations to clarify the particle physics mechanisms behind thundercloud radiation bursts, establishing gamma rays as the critical catalyst for electron acceleration and defining the specific electric field parameters necessary to generate the high-energy emissions observed in nature.