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Dependence of the estimated electric potential in thunderstorms observed at GRAPES-3 on the hadronic interaction generators used in simulations

This study analyzes how the choice of hadronic interaction generators in CORSIKA simulations affects the estimated electric potential of thunderstorms observed by the GRAPES-3 muon telescope, revealing that low-energy generators induce significantly larger variations in the results compared to high-energy ones.

Original authors: B. Hariharan, S. K. Gupta, Y. Hayashi, P. Jagadeesan, A. Jain, S. Kawakami, H. Kojima, P. K. Mohanty, Y. Muraki, P. K. Nayak, A. Oshima, M. Rameez, K. Ramesh, L. V. Reddy, S. Shibata, M. Zuberi

Published 2026-06-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: B. Hariharan, S. K. Gupta, Y. Hayashi, P. Jagadeesan, A. Jain, S. Kawakami, H. Kojima, P. K. Mohanty, Y. Muraki, P. K. Nayak, A. Oshima, M. Rameez, K. Ramesh, L. V. Reddy, S. Shibata, M. Zuberi

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: Catching Lightning with a Net

Imagine a thunderstorm as a giant, invisible battery floating in the sky. For nearly a century, scientists have guessed that these "batteries" could hold a massive amount of electricity—about 1.3 billion volts (1.3 Gigavolts). This was a prediction made by a scientist named C.T.R. Wilson long ago, but proving it was like trying to weigh a cloud without touching it.

The GRAPES-3 experiment in India did exactly that. They didn't use a ladder or a balloon; they used a giant "net" on the ground called a Muon Telescope. This net catches tiny, fast-moving particles called muons that rain down from space.

Here's the trick: Muons are like tiny, charged marbles. When they fly through a thundercloud, the cloud's massive electric field acts like a giant magnet or a wind tunnel. It speeds some muons up and slows others down. By counting how many muons arrive and from which direction, the scientists can calculate how strong the "wind" (the electric field) inside the cloud is.

The Problem: The "Recipe" for Simulations

To figure out the exact voltage of the cloud, the scientists had to run a computer simulation. Think of this simulation as a video game where they try to recreate the path of every single muon as it flies through the atmosphere.

However, the atmosphere is messy. When cosmic rays hit the air, they crash into atoms and create a shower of new particles (pions, kaons, and more muons). To simulate these crashes, the computer needs a "rulebook" or a generator that tells it how particles behave when they smash into each other.

The paper discovered a big issue: There isn't just one rulebook. There are several different software programs (called generators) that scientists use to write these rules. Some are good for slow crashes (low energy), and some are for fast crashes (high energy).

The Experiment: Testing the Rulebooks

The researchers asked a simple question: "Does it matter which rulebook we use?"

They took the data from a massive thunderstorm that happened on December 1, 2014, and ran the simulation nine different times. They mixed and matched three different "low-energy" rulebooks with three different "high-energy" rulebooks (3 x 3 = 9 combinations).

The Results:

The "Safe" Guess: When they used a specific combination called SIBYLL-FLUKA, the simulation said the cloud had a potential of 1.3 GV. This was the lowest number they got.
The "High" Guess: When they used other combinations (like QGSJETII-GHEISHA), the simulation said the cloud was much stronger, estimating 1.6 GV.
The Difference: Depending on which rulebook you picked, your estimate of the storm's power changed by up to 26%.

The Key Discovery: Who Matters More?

The scientists found that the low-energy rulebooks were the ones causing the biggest confusion.

Analogy: Imagine you are baking a cake. The high-energy rulebooks are like the oven temperature (important, but you have a good idea of what it should be). The low-energy rulebooks are like the specific brand of flour or the type of sugar you use.
Why? Most of the muons the telescope sees are created by particle crashes that happen at "low speeds" (energies below 80 GeV). Because the "flour" (low-energy physics) is used so much more often in the recipe, small differences in how the rulebooks describe these low-speed crashes make a huge difference in the final result.

The high-energy rulebooks only changed the result by about 8%, while the low-energy ones changed it by about 14%.

What This Means for the 1.3 GV Claim

In their previous work, the scientists reported the 1.3 GV number. This paper confirms that they made the most conservative (safest) choice.

If they had picked a different rulebook, they might have reported a higher number (like 1.6 GV).
By sticking with the SIBYLL-FLUKA combination, they are essentially saying: "Even with the most cautious rulebook, the cloud is still at least 1.3 billion volts."

They also checked this against seven other major thunderstorms from 2011 to 2020. In every case, the SIBYLL-FLUKA combination gave the lowest (most conservative) estimate of the voltage.

Summary in a Nutshell

The Goal: Measure the electric power of a thundercloud using muons (space particles).
The Method: Use computer simulations to guess the voltage based on how muons behave.
The Twist: The computer needs different "rulebooks" to simulate particle crashes. Different rulebooks give different answers.
The Finding: The rulebooks for "slow" crashes (low energy) change the answer the most.
The Conclusion: The original claim of 1.3 GV is solid because it was calculated using the rulebook that gives the lowest possible estimate. If the cloud is actually stronger (up to 1.6 GV), that just means the original number was a safe, minimum guarantee, not an exaggeration.

This study didn't invent new technology or predict future weather; it simply double-checked the math behind their previous discovery to ensure that their "gigavolt" claim holds up, no matter which scientific rulebook you use.

Technical Summary: Dependence of Estimated Thundercloud Potential on Hadronic Interaction Generators in GRAPES-3 Simulations

Problem Statement
The GRAPES-3 muon telescope (G3MT) previously inferred a massive 1.3 GV potential difference across a thundercloud using muon intensity variations, confirming C.T.R. Wilson's century-old prediction. However, this estimation relies heavily on Monte Carlo simulations (specifically CORSIKA) to model the acceleration of muons in atmospheric electric fields. A critical uncertainty in this process is the choice of hadronic interaction generators used to simulate the development of extensive air showers (EAS). CORSIKA utilizes different generators for low-energy (<80 GeV) and high-energy (>80 GeV) interactions. Since the specific combination of generators that most accurately describes hadronic interactions in the relevant energy range is not definitively known, it remains unclear how much the choice of generator influences the estimated thundercloud potential. This paper addresses the sensitivity of the potential estimation to these simulation parameters.

Methodology
The study utilizes data from the G3MT, which records over 4 billion muons daily across 169 sky directions. The analysis focuses on eight major thunderstorm events recorded between April 2011 and December 2020, including the seminal event of December 1, 2014.

Simulation Framework: The authors employed CORSIKA (v74001) to simulate EAS development. They modified the code to include the EFIELD option for hadronic particles (pions, kaons, and muons) within a defined thundercloud layer (8–10 km altitude).
Generator Combinations: The study systematically explored all nine possible combinations of three high-energy generators (SIBYLL, EPOS-LHC, QGSJETII) and three low-energy generators (FLUKA, GHEISHA, UrQMD).
Analysis Strategy:
- For the December 1, 2014 event, the team compared the simulated muon intensity variation ( $\Delta I_\mu$ ) against the observed deficit to derive the required thundercloud potential for each generator combination.
- The SIBYLL-FLUKA combination was used as the reference baseline, as it was employed in the initial 1.3 GV estimation.
- The analysis was extended to seven additional major events to assess the generalizability of the findings.
- A secondary validation was performed using the latest CORSIKA release (v78000) with updated SIBYLL 2.3e and FLUKA 2024.1 models to check for version-dependent variability.

Key Results

Generator Dependence: The estimated thundercloud potential varies significantly depending on the generator combination. For the December 1, 2014 event, the estimated potentials ranged from 1.3 GV to 1.6 GV across the nine combinations.
Low-Energy Dominance: The variation in estimated potential is driven primarily by the choice of low-energy generators. The study found that low-energy generators produce a variation of approximately 14% in the estimated potential, whereas high-energy generators contribute only about 8%. This is attributed to the fact that the majority of cosmic rays (and thus the muons detected by G3MT) originate from interactions below 80 GeV, where low-energy generators are active.
Specific Generator Performance:
- The SIBYLL-FLUKA combination consistently yielded the lowest estimated potentials across all eight events.
- The QGSJETII-GHEISHA combination produced the highest deviation, yielding potentials up to 26% higher than the SIBYLL-FLUKA baseline for the 2014 event.
- Generally, GHEISHA and QGSJETII combinations resulted in higher potential estimates, while FLUKA and SIBYLL combinations resulted in lower estimates.
Version Stability: Comparisons between CORSIKA v74001 and the newer v78000 (with updated generators) showed a mean deviation of only –(0.3±4.8)% in estimated potentials. This difference is statistically insignificant and falls within the measurement uncertainties, confirming the robustness of the SIBYLL-FLUKA baseline.

Key Contributions

Quantification of Systematic Uncertainty: The paper provides the first quantitative assessment of how hadronic interaction models affect the estimation of gigavolt-scale thundercloud potentials using ground-based muon telescopes.
Conservative Baseline Validation: It validates the choice of the SIBYLL-FLUKA combination as the most conservative estimator, justifying the previously reported 1.3 GV value as a lower-bound estimate.
Expanded Dataset Analysis: The study extends the analysis from a single event to a decade-long dataset of eight major thunderstorms, demonstrating that the generator dependence is a consistent feature across different storm events.
Identification of Critical Energy Range: The work highlights that the low-energy interaction regime (<80 GeV) is the dominant factor in simulation uncertainties for GeV muon studies, guiding future model improvements.

Significance and Claims
The paper claims that the estimation of thundercloud potentials is not an absolute value but is contingent upon the physics models used in simulations. By demonstrating that the SIBYLL-FLUKA combination yields the lowest potential estimates, the authors argue that their previously reported value of 1.3 GV is a conservative lower limit. This strengthens the claim that thunderclouds can indeed generate gigavolt potentials, as even the most conservative simulation models support this magnitude.

The authors emphasize that while the choice of generator introduces systematic variations (up to ~14% from low-energy models), the core finding—that thunderclouds possess gigavolt-scale potentials—remains robust across all tested combinations. The study concludes that future investigations into atmospheric electricity using muon telescopes must account for these generator-induced uncertainties, and that the SIBYLL-FLUKA combination remains the standard for conservative estimation.