Multifield lighting Simulator

Multifield Lightning Monitor is a computational physics simulator that integrates geophysics, acoustics, and electromagnetism.

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1. Theoretical Framework and Supporting Equations

The simulator solves in real time the propagation of disturbances due to a lightning strike in three different media (vacuum/air, Earth's crust, and atmosphere), based on the following laws:

A. Electromagnetism (Hertz Dipole Approximation)

For calculating the electric field, lightning is modeled as a vertical elementary dipole. Since it is an impulsive transient event, Maxwell's equations are simplified in the near field and radiation zone:

• Static and Inductive Components: The potential decays with the inverse square of the distance.

• Electric Field Equation: This is the dipole moment (proportional to the power in MNewtons).

• Dielectric Breakdown Threshold: Air loses its insulating capacity at 3 MV/m³ (under standard conditions), but for human safety purposes in the simulator, the value of 25 MV/m³ has been set as the Lethal Survival (Lethal) limit, the point at which air ionization causes a direct shock to the receiver.

B. Elastic Wave Seismology (Solution to Lamb's Problem in 2 Dimensions)

Earthquakes are governed by the propagation of mechanical waves in a linear, isotropic elastic medium. The simulator separates the solutions into:

1. Body Waves (P and S):

o P-waves (Primary): Compressional (longitudinal). They are the fastest (approx. 4.0 km/s).

o S-waves (Secondary): Shear (transverse). They do not travel in liquids (approx. 2.3 km/s).

2. Rayleigh Waves (approx. 2.1 km/s):

• Nature: These are surface waves that combine longitudinal and transverse motions in a retrograde elliptical path.

• Destructiveness: They are the most destructive because their energy is confined near the surface and their attenuation is less compared to body waves. In the simulator, these waves generate the greatest amplitude on the seismograph (brown trace).

C. Atmospheric Acoustics (Shock Wave)

Thunder is the adiabatic expansion of air heated by the plasma of lightning.

• Speed: Approximately 340 m/s, dependent on air density.

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2. Control Parameters and Critical Simulation

• Power (MNewtons): Represents the linear momentum transfer of the lightning strike to the ground. Scales the seismic amplitude and field intensity.

• Geographic Scale (4000 meters): The canvas maps each pixel to 5 real meters, allowing observation of large-scale phenomena such as the "silence" before the thunder over long distances.

• Dynamic Destruction Physics: The camp operates under a Dynamic Pressure condition. If the Rayleigh wave energy combined with air pressure exceeds a critical deformation threshold: The object enters a ballistic projectile state with Euler integration for the trajectory.

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3. Seismogram Interpretation

The lower monitor is a record of acceleration vs. time.

• Brown Trace (Ground): Identifies the sequential arrival of phases (P, S, and Rayleigh).

• White Trace (Air): Records the acoustic noise of the thunder. Its amplitude decreases more rapidly with distance due to atmospheric absorption.

• Electromagnetic Field Legend: The electromagnetic wave has been artificially slowed to one millionth the speed of light to be perceptible, allowing us to understand its role as the "trigger" of the event.