Numerical Model of Ball Lightning
(István Bencsik, independent scientific researcher, October 2026)
Abstract
This study presents a new, autonomous numerical model of ball lightning based on the interaction between fly ash evaporated from the ground and a Yukawa-type dusty plasma. The model links observed characteristics—such as levitation and lifespan—to plasma-physical processes. The stability and fluid-like behavior of the spherical structure are maintained by the Debye-screened negative charge of the fly ash particles (Yukawa potential). The energy supply for the sphere’s 3000 K core, which compensates for thermal radiation losses, is provided by the slow surface oxidation of the carbon content within the fly ash, alongside non-linear chemical reaction equilibria involving hydroxyl radicals and carbon monoxide. Numerical simulations confirm the system’s self-regulating levitation; combined with low effective emission, this ensures a lifespan of 20–40 seconds.
This study presents a new, autonomous numerical model of ball lightning based on the interaction between fly ash evaporated from the ground and a Yukawa-type dusty plasma. The model links observed characteristics—such as levitation and lifespan—to plasma-physical processes. The stability and fluid-like behavior of the spherical structure are maintained by the Debye-screened negative charge of the fly ash particles (Yukawa potential). The energy supply for the sphere’s 3000 K core, which compensates for thermal radiation losses, is provided by the slow surface oxidation of the carbon content within the fly ash, alongside non-linear chemical reaction equilibria involving hydroxyl radicals and carbon monoxide. Numerical simulations confirm the system’s self-regulating levitation; combined with low effective emission, this ensures a lifespan of 20–40 seconds.
Keywords: Numerical ball lightning model, fly ash, streamer, hydroxyl radical, negative differential resistance, ball lightning, Yukawa dusty plasma
Introduction
The ball lightning model (Bencsik, I., 2026. The interaction between fly ash and Yukawa plasma: ball lightning, DOI: 10.13140/RG.2.2.26392.15369) is built upon three main pillars:
The model successfully bridges observed phenomena with plasma physics principles and rests on three main pillars:
• Catalyzed arc discharge: In the presence of a strong external electric field, nanoscale fly ash* and silicate particles induce "tip effects" (field enhancement at sharp points) and "bridging effects" (chain formation). These mechanisms initiate and sustain gas ionization—and thus an electric arc—at lower electric field strengths than would be required in air devoid of fly ash.
• A cohesive Yukawa potential that enforces a spherical shape: Following the cessation of the external electric field (the afterglow phase), the fly ash particles acquire a large negative charge by capturing fast-moving electrons. In the developing non-thermal plasma, Debye-shielded repulsion (Yukawa potential) and the surface tension arising from space-charge layers result in a fluid-like, elastic, spherical structure that remains stable even in the absence of an external field.
• The non-linear feedback of hydroxyl radicals, the dissociation of carbon dioxide into carbon monoxide, and the subsequent combustion of the latter stabilize the temperature of the sphere; meanwhile, the slow surface oxidation (incandescence) of carbon particles within the fly ash compensates for energy lost through heat and light radiation. The sudden appearance of the sphere—triggered by a pre-discharge or an external force field—can also be attributed to negative differential resistance; furthermore, the plasma sphere persists even after the external electric field has ceased. The explosive disintegration of the structure is caused by the collapse of ionization equilibrium, followed by a global recombination avalanche.
The ball lightning model (Bencsik, I., 2026. The interaction between fly ash and Yukawa plasma: ball lightning, DOI: 10.13140/RG.2.2.26392.15369) is built upon three main pillars:
The model successfully bridges observed phenomena with plasma physics principles and rests on three main pillars:
• Catalyzed arc discharge: In the presence of a strong external electric field, nanoscale fly ash* and silicate particles induce "tip effects" (field enhancement at sharp points) and "bridging effects" (chain formation). These mechanisms initiate and sustain gas ionization—and thus an electric arc—at lower electric field strengths than would be required in air devoid of fly ash.
• A cohesive Yukawa potential that enforces a spherical shape: Following the cessation of the external electric field (the afterglow phase), the fly ash particles acquire a large negative charge by capturing fast-moving electrons. In the developing non-thermal plasma, Debye-shielded repulsion (Yukawa potential) and the surface tension arising from space-charge layers result in a fluid-like, elastic, spherical structure that remains stable even in the absence of an external field.
• The non-linear feedback of hydroxyl radicals, the dissociation of carbon dioxide into carbon monoxide, and the subsequent combustion of the latter stabilize the temperature of the sphere; meanwhile, the slow surface oxidation (incandescence) of carbon particles within the fly ash compensates for energy lost through heat and light radiation. The sudden appearance of the sphere—triggered by a pre-discharge or an external force field—can also be attributed to negative differential resistance; furthermore, the plasma sphere persists even after the external electric field has ceased. The explosive disintegration of the structure is caused by the collapse of ionization equilibrium, followed by a global recombination avalanche.
Principles and Challenges in Modeling Ball Lightning
Some models found in the literature assume an external energy source—that is, they are non-autonomous. In the case of suspended fly ash, the effect of gravity is negligible; thus, we can assume an autonomous sphere, where an external energy source is required only for its initial formation. Other models posit a layered, capacitor-like mechanism for electrostatic energy storage. We assume that the energy balance is maintained through chemical storage and replenishment, involving combustible, dissociated components derived from fly ash and air.
Some models found in the literature assume an external energy source—that is, they are non-autonomous. In the case of suspended fly ash, the effect of gravity is negligible; thus, we can assume an autonomous sphere, where an external energy source is required only for its initial formation. Other models posit a layered, capacitor-like mechanism for electrostatic energy storage. We assume that the energy balance is maintained through chemical storage and replenishment, involving combustible, dissociated components derived from fly ash and air.
As the plasma cools, it may be reheated—in the following order—by the combustion of hydrogen, carbon, free radicals, metals, and carbon monoxide, provided these are present. At high temperatures, certain substances may exist in their elemental state. The energy loss of the sphere is proportional to the fourth power of its temperature (in Kelvin) and its effective emissivity; the latter is estimated to be in the range of 10-4 - 10-3 . The combustion of the available fuel components must compensate for energy losses occurring via radiation, convection, conduction, and chemical processes.
A further condition—related to the rate of combustion and the phenomenon of levitation—is the requirement for self-regulating mechanisms. Explosive combustion must be ruled out. If the intensity of combustion were to decrease gradually, the sphere would typically descend slowly; however, observations show it remains in a state of steady levitation, which implies a consistent, controlled combustion process. Suitable mechanisms include the dissociation and subsequent recombination of carbon dioxide into carbon monoxide, and of water vapor into hydroxyl radicals—processes that occur concurrently with combustion. The sphere can appear unexpectedly, without any prior indication; for this reason—and to account for the ignition of cooling fly ash—it is necessary to posit the presence of a streamer (pre-discharge) or to assume negative differential resistance during the formation of the sphere, provided an external electric field is present.
Yukawa dusty plasma is one of the most common plasma phenomena in nature; it is associated with fly ash, smoke, the combustion of meteors, and UV radiation. A coupling constant in the estimated range of Γ = 50–100 is required due to surface energy; this phenomenon explains the spherical shape.
A further condition—related to the rate of combustion and the phenomenon of levitation—is the requirement for self-regulating mechanisms. Explosive combustion must be ruled out. If the intensity of combustion were to decrease gradually, the sphere would typically descend slowly; however, observations show it remains in a state of steady levitation, which implies a consistent, controlled combustion process. Suitable mechanisms include the dissociation and subsequent recombination of carbon dioxide into carbon monoxide, and of water vapor into hydroxyl radicals—processes that occur concurrently with combustion. The sphere can appear unexpectedly, without any prior indication; for this reason—and to account for the ignition of cooling fly ash—it is necessary to posit the presence of a streamer (pre-discharge) or to assume negative differential resistance during the formation of the sphere, provided an external electric field is present.
Yukawa dusty plasma is one of the most common plasma phenomena in nature; it is associated with fly ash, smoke, the combustion of meteors, and UV radiation. A coupling constant in the estimated range of Γ = 50–100 is required due to surface energy; this phenomenon explains the spherical shape.
Regarding the selection of input parameter ranges: among the various plausible models, the one that remains valid is that which yields meaningful results in numerical simulations—for instance, a sound effective surface energy coefficient. The possible intervals for the parameters align well with observed values. The model’s formulation is consistent with the spectral measurements conducted by Chinese researchers (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.035001), 2012 in which detected silicon, calcium, and iron in a natural ball lightning event, as well as with the temperatures estimated in that study (≈ 3000 K).
Input parameters
Environmental data:
Atmospheric pressure (P), ambient temperature (T).
Geometry and material:
Sphere diameter (D),
Required mass of fly ash (m),
Carbon content of the fly ash (sz),
Density of the fly ash (s),
Average particle diameter (d).
Thermodynamics:
Core temperature (Ti), surface temperature (To).
Plasma physics characteristics:
Electron temperature (Te),
Emission coefficient (εeff),
Effective surface energy coefficient (γeff).
Environmental data:
Atmospheric pressure (P), ambient temperature (T).
Geometry and material:
Sphere diameter (D),
Required mass of fly ash (m),
Carbon content of the fly ash (sz),
Density of the fly ash (s),
Average particle diameter (d).
Thermodynamics:
Core temperature (Ti), surface temperature (To).
Plasma physics characteristics:
Electron temperature (Te),
Emission coefficient (εeff),
Effective surface energy coefficient (γeff).
Output parameters
Geometric and structural output parameters
Surface area: The external contact surface of the sphere, expressed in square meters. Volume: The internal capacity of the sphere, measured in cubic meters.
Number of particles (N): The total quantity of fly ash particles contained within the plasma.
Coupling constant (Γ): A value characterizing the internal fluid state of the dusty plasma and its electrostatic potential.
Thermodynamic and heating parameters:
Total heat loss (radiation): Energy loss due to surface radiation, measured in watts.
Heating / Energy supply: Heat generation resulting from the slow oxidation of carbon particles and the recombination of radicals.
Dissociation rate: The temperature-dependent percentage of gas molecule (e.g., CO₂) decomposition.
Plasma physics parameters:
Debye length: The electrical shielding distance of electrons, measured in micrometers.
Effective surface energy coefficient (γ): A coefficient analogous to surface tension that maintains the spherical shape.
Levitation and lifespan parameters:
Total mass of the sphere: The combined weight of the fly ash and the hot air contained within.
Buoyancy of the hot gas: The mass equivalent of the buoyant force exerted by the ambient air.
Net equilibrium (net buoyancy): The resultant force that directly enables levitation.
Lifespan: The duration for which the ball lightning persists, measured in seconds, until the fuel is exhausted. Stability state: A negative-feedback equilibrium of heating and cooling processes.
Geometric and structural output parameters
Surface area: The external contact surface of the sphere, expressed in square meters. Volume: The internal capacity of the sphere, measured in cubic meters.
Number of particles (N): The total quantity of fly ash particles contained within the plasma.
Coupling constant (Γ): A value characterizing the internal fluid state of the dusty plasma and its electrostatic potential.
Thermodynamic and heating parameters:
Total heat loss (radiation): Energy loss due to surface radiation, measured in watts.
Heating / Energy supply: Heat generation resulting from the slow oxidation of carbon particles and the recombination of radicals.
Dissociation rate: The temperature-dependent percentage of gas molecule (e.g., CO₂) decomposition.
Plasma physics parameters:
Debye length: The electrical shielding distance of electrons, measured in micrometers.
Effective surface energy coefficient (γ): A coefficient analogous to surface tension that maintains the spherical shape.
Levitation and lifespan parameters:
Total mass of the sphere: The combined weight of the fly ash and the hot air contained within.
Buoyancy of the hot gas: The mass equivalent of the buoyant force exerted by the ambient air.
Net equilibrium (net buoyancy): The resultant force that directly enables levitation.
Lifespan: The duration for which the ball lightning persists, measured in seconds, until the fuel is exhausted. Stability state: A negative-feedback equilibrium of heating and cooling processes.
Characteristics of the model
Ball lightning is a chemical plasma sphere—featuring a hot, atomic, and ionic core, and an outer, cloud-like, swirling envelope—whose structure and dynamics are consistent with the 2012 Chinese spectral recording, various observational data, and the video footage available at https://www.24h.com.vn/media-24h/bi-an-hien-tuong-set-hon-cuc-hiem-trong-tu-nhien-c762a1479345.html (note that the substance exhibits a viscosity greater than that of water):
1. Evaporation of material from the ground
When a linear lightning bolt strikes the ground, it vaporizes silicon, iron, and calcium present in the soil; their oxides form the particulate matter (fly ash). The Chinese spectral recordings have clearly demonstrated that, throughout the entire lifespan of the ball lightning, atomic emission lines from silicon (Si), iron (Fe), and calcium (Ca) impurities remain dominant—a finding that necessitates the revision of theories based solely on pure charge distributions.
2. Ball lightning does not possess a uniform temperature; rather, it maintains a temperature gradient, with a temperature of ~3000 K in the inner core—reaching even higher temperatures toward the center. At these temperatures, silicon does not exist in the form of nanoparticles, but rather as dissociated, partially gaseous atomic silicon. The outer surface layer (~2000 K, plus a few hundred Kelvin): the outermost layer of the sphere—the part in contact with the surrounding environment—is the coldest, with a temperature of around 2000 Kelvin.
3. Cloud-like, irregular form: unlike the smooth, liquid-like surface of Yukawa dust plasmas, this formation does not have a perfectly smooth surface. Metal vapors and radicals flowing outward from the hot inner core encounter the cooler ambient air, causing them to continuously condense and swirl. Both visually and structurally, the surface of the sphere resembles a dense, billowing, glowing cloud—a site of combustion where gases and radicals recombine and condensing aerosol phases intermix.
4. Due to the heating effect of chemical oxidation—which proceeds slowly at the surface because of limited oxygen influx—the sphere cools down gradually and in a self-regulated manner over the course of seconds or even tens of seconds. The self-sustainment of the ball lightning is driven by the combustion of carbon dust. Materials that have dissociated at high temperatures—flowing from the 3000–4000 K inner core toward the surface (including particulate ions, atoms, reactive gas components like O/H, and hydroxyl radicals, which also serve as energy storage)—recombine upon reaching the 2000 K zone, stabilizing the temperature through a negative feedback mechanism. A series of exothermic surface-chemical reactions, along with the recombination of ions and radicals, generates the heat that protects the inner atomic core from rapid cooling; this process also produces the characteristic opalescent glow of ball lightning (see video) and enables it to hover. The dissociation equilibrium for hydroxyl radicals reaches 55% at approximately 3000 degrees Celsius.
1. Evaporation of material from the ground
When a linear lightning bolt strikes the ground, it vaporizes silicon, iron, and calcium present in the soil; their oxides form the particulate matter (fly ash). The Chinese spectral recordings have clearly demonstrated that, throughout the entire lifespan of the ball lightning, atomic emission lines from silicon (Si), iron (Fe), and calcium (Ca) impurities remain dominant—a finding that necessitates the revision of theories based solely on pure charge distributions.
2. Ball lightning does not possess a uniform temperature; rather, it maintains a temperature gradient, with a temperature of ~3000 K in the inner core—reaching even higher temperatures toward the center. At these temperatures, silicon does not exist in the form of nanoparticles, but rather as dissociated, partially gaseous atomic silicon. The outer surface layer (~2000 K, plus a few hundred Kelvin): the outermost layer of the sphere—the part in contact with the surrounding environment—is the coldest, with a temperature of around 2000 Kelvin.
3. Cloud-like, irregular form: unlike the smooth, liquid-like surface of Yukawa dust plasmas, this formation does not have a perfectly smooth surface. Metal vapors and radicals flowing outward from the hot inner core encounter the cooler ambient air, causing them to continuously condense and swirl. Both visually and structurally, the surface of the sphere resembles a dense, billowing, glowing cloud—a site of combustion where gases and radicals recombine and condensing aerosol phases intermix.
4. Due to the heating effect of chemical oxidation—which proceeds slowly at the surface because of limited oxygen influx—the sphere cools down gradually and in a self-regulated manner over the course of seconds or even tens of seconds. The self-sustainment of the ball lightning is driven by the combustion of carbon dust. Materials that have dissociated at high temperatures—flowing from the 3000–4000 K inner core toward the surface (including particulate ions, atoms, reactive gas components like O/H, and hydroxyl radicals, which also serve as energy storage)—recombine upon reaching the 2000 K zone, stabilizing the temperature through a negative feedback mechanism. A series of exothermic surface-chemical reactions, along with the recombination of ions and radicals, generates the heat that protects the inner atomic core from rapid cooling; this process also produces the characteristic opalescent glow of ball lightning (see video) and enables it to hover. The dissociation equilibrium for hydroxyl radicals reaches 55% at approximately 3000 degrees Celsius.
According to the Stefan–Boltzmann law of radiation, the energy loss of ball lightning is proportional to the fourth power of its temperature (in Kelvin) and its emissivity (a positive value less than one—in this case, on the order of 10-4 . At high temperatures, the cooling process is governed by the recombination temperature ranges of the constituent components. These components include ions derived from fly ash—most notably carbon—as well as elements from the surrounding air, primarily water vapor. Down to approximately 2000 K, the cooling process is determined by the combination of C, H, and O elements and the dissociation of the resulting compounds.
Around 2000 °C (2273 K), approximately 1–2% of CO₂ molecules undergo decomposition; at 3000 K, 40% of the carbon dioxide molecules are dissociated. Once the dissociation level exceeds 50%, the internal heat generation ceases. Water begins to dissociate at 2200°C, and at 3000°C, it is approximately 50% dissociated. The thermal equilibrium of ball lightning is governed by the combustion of carbon and hydrogen, the dissociation of carbon dioxide and water, and the continuous processes of radical formation and recombination. An increase in the rate of recombination exerts a heating effect, while a decrease results in a cooling effect—a mechanism that contributes to its levitation. According to spectral measurements conducted in China, its temperature approaches 4000 Kelvin.
The 2000 K range represents a transitional state known as the "chemical freezing zone."
Around 2000 K, the temperature is no longer high enough to cleave stable molecules such as oxygen, water, or carbon dioxide (thermal dissociation ceases); however, the previously formed reactive atoms and free radicals continue to collide and react with one another at high velocities. Dominant reactions at 2000 K (within a C-O-H system) include the following: the –OH radical acts as an aggressive oxidizing agent, stripping away from water molecules. The hydroperoxyl radical (–HO₂) is generated through the rapid reaction between hydrogen radicals and oxygen molecules. Atomic oxygen exists as a free radical possessing an unpaired electron. Carbon monoxide, formyl radical: CO and -CHO (*CHO); and because the energy of the gas molecules remains high at 2000 K, the radicals do not simply neutralize—instead, they sustain chain reactions.
Equilibrium between water and carbon monoxide: a rapid, reversible interconversion takes place between the carbon monoxide and hydroxyl radicals remaining from the high-temperature phase. The dissociation equilibrium determines the final amounts of carbon dioxide and toxic CO present at the end of the process.Chain reactions involving hydrogen and oxygen: free hydrogen atoms are capable of breaking apart oxygen molecules, resulting in the formation of –OH radicals and oxygen—essentially generating two new radicals from one, thereby maintaining a high level of gas activity. When the gas temperature drops below 2000 K, the reaction rates suddenly become asymmetric; the forward direction of reversible reactions ceases because there is insufficient thermal energy to break chemical bonds. Below 2000 K, only metal oxides form from the fly ash—for instance, silicon undergoes combustion. Following this collapse, what remains is a small amount of fly ash, some CO, water vapor, CO2, and NOx
Around 2000 °C (2273 K), approximately 1–2% of CO₂ molecules undergo decomposition; at 3000 K, 40% of the carbon dioxide molecules are dissociated. Once the dissociation level exceeds 50%, the internal heat generation ceases. Water begins to dissociate at 2200°C, and at 3000°C, it is approximately 50% dissociated. The thermal equilibrium of ball lightning is governed by the combustion of carbon and hydrogen, the dissociation of carbon dioxide and water, and the continuous processes of radical formation and recombination. An increase in the rate of recombination exerts a heating effect, while a decrease results in a cooling effect—a mechanism that contributes to its levitation. According to spectral measurements conducted in China, its temperature approaches 4000 Kelvin.
The 2000 K range represents a transitional state known as the "chemical freezing zone."
Around 2000 K, the temperature is no longer high enough to cleave stable molecules such as oxygen, water, or carbon dioxide (thermal dissociation ceases); however, the previously formed reactive atoms and free radicals continue to collide and react with one another at high velocities. Dominant reactions at 2000 K (within a C-O-H system) include the following: the –OH radical acts as an aggressive oxidizing agent, stripping away from water molecules. The hydroperoxyl radical (–HO₂) is generated through the rapid reaction between hydrogen radicals and oxygen molecules. Atomic oxygen exists as a free radical possessing an unpaired electron. Carbon monoxide, formyl radical: CO and -CHO (*CHO); and because the energy of the gas molecules remains high at 2000 K, the radicals do not simply neutralize—instead, they sustain chain reactions.
Equilibrium between water and carbon monoxide: a rapid, reversible interconversion takes place between the carbon monoxide and hydroxyl radicals remaining from the high-temperature phase. The dissociation equilibrium determines the final amounts of carbon dioxide and toxic CO present at the end of the process.Chain reactions involving hydrogen and oxygen: free hydrogen atoms are capable of breaking apart oxygen molecules, resulting in the formation of –OH radicals and oxygen—essentially generating two new radicals from one, thereby maintaining a high level of gas activity. When the gas temperature drops below 2000 K, the reaction rates suddenly become asymmetric; the forward direction of reversible reactions ceases because there is insufficient thermal energy to break chemical bonds. Below 2000 K, only metal oxides form from the fly ash—for instance, silicon undergoes combustion. Following this collapse, what remains is a small amount of fly ash, some CO, water vapor, CO2, and NOx
According to the model, the sphere can be ignited by a precursor lightning stroke or a corona discharge (as observed in an incident involving an aircraft windshield). A corona discharge (or "silent" discharge) occurs in gases at standard atmospheric pressure within a strong electric field, provided that the voltage gradient at a specific point on an electrically charged surface exceeds the threshold required for gas ionization under the given conditions—yet remains below the breakdown voltage (which would result in a "noisy" discharge, such as a spark or an electric arc). Under atmospheric conditions, a corona discharge requires a voltage gradient of approximately a few hundred kV/m; this value also depends significantly on the shape of the object causing the ionization of the air. During a corona discharge, the gas in the immediate vicinity becomes ionized and electrically conductive, resulting in the formation of so-called "cold plasma."
Numerical Example
Geometric and structural parameters
Diameter: 30 cm,
Surface area ≈ 0.283 m²
Volume ≈ 0.0141 m³
Required mass of fly ash: 15.0 grams.
Material of the Yukawa plasma particles: fly ash, containing approximately 0.3 grams of pure carbon.
Number of particles (N): ≈ 8.8 × 10¹⁰ (with an average particle diameter of 5 μm); each particle carries a charge of Q ∼ 1000 e.
Coupling constant (Γ): ≈ 75; the dusty plasma within the interior exists in a strongly coupled liquid state.
Diameter: 30 cm,
Surface area ≈ 0.283 m²
Volume ≈ 0.0141 m³
Required mass of fly ash: 15.0 grams.
Material of the Yukawa plasma particles: fly ash, containing approximately 0.3 grams of pure carbon.
Number of particles (N): ≈ 8.8 × 10¹⁰ (with an average particle diameter of 5 μm); each particle carries a charge of Q ∼ 1000 e.
Coupling constant (Γ): ≈ 75; the dusty plasma within the interior exists in a strongly coupled liquid state.
Thermodynamic and heating parameters
Core temperature: ≈ 3000 K
Surface temperature: ≈ 2000 K, producing an orange-white incandescence. The surface consists of an optically thin, recombination plasma.
Total heat loss (radiation) ≈ 260 W (surface radiation, εeff ≈ 10⁻⁵ – 10⁻⁴).
Heating: the heat is supplied by the slow oxidation of the 0.3 g of carbon present on the surface of the particles. Plasma physics parameters
Debye length ≈ 35–45 μm; electron temperature is around 10⁴ K.
Effective surface energy coefficient of the dusty Yukawa phase—which functions as "surface tension" within the model:
γ ≈ 10⁻⁵ – 10⁻⁶ N/m.
Core temperature: ≈ 3000 K
Surface temperature: ≈ 2000 K, producing an orange-white incandescence. The surface consists of an optically thin, recombination plasma.
Total heat loss (radiation) ≈ 260 W (surface radiation, εeff ≈ 10⁻⁵ – 10⁻⁴).
Heating: the heat is supplied by the slow oxidation of the 0.3 g of carbon present on the surface of the particles. Plasma physics parameters
Debye length ≈ 35–45 μm; electron temperature is around 10⁴ K.
Effective surface energy coefficient of the dusty Yukawa phase—which functions as "surface tension" within the model:
γ ≈ 10⁻⁵ – 10⁻⁶ N/m.
Levitation and lifespan parameters
Total mass of the sphere: ≈ 17 grams (mass of the fly ash + weight of the hot air).
Buoyant force of the hot gas: ≈ a force equivalent to 17 grams of mass (buoyancy).
Net equilibrium: ≈ 0.2 grams of net buoyant force, which enables levitation; the sphere floats stably within a turbulent, high-pressure thunderstorm air layer, depending on the atmospheric pressure.
Lifespan: 20–40 seconds.
Total mass of the sphere: ≈ 17 grams (mass of the fly ash + weight of the hot air).
Buoyant force of the hot gas: ≈ a force equivalent to 17 grams of mass (buoyancy).
Net equilibrium: ≈ 0.2 grams of net buoyant force, which enables levitation; the sphere floats stably within a turbulent, high-pressure thunderstorm air layer, depending on the atmospheric pressure.
Lifespan: 20–40 seconds.
Stability: an increase in the number of recombination events exerts a heating effect, while a decrease exerts a cooling effect.
Based on the heat of combustion of carbon (≈ 393 kJ/mol), the complete combustion of 0.3 grams of carbon contained within the sphere would—theoretically, assuming black-body behavior—take approximately 0.038 seconds in pure oxygen; however, given the effective emission coefficient (εeff ≈ 10⁻⁵–10⁻⁴) of ball lightning, this smoldering process is extended to the observed duration of 10–40 seconds. Radiative capacity is linked to a material's absorption capacity. In most instances of ball lightning, observations indicate that the surface layer is optically thin—essentially a nearly transparent gas or plasma structure. Since the majority of light passes through it unimpeded (due to low absorption), its emissivity—relative to that of a black body—is negligibly small. The observed luminosity is primarily driven by "cold" luminescence, the recombination of excited atoms or ions, or slow surface chemical reactions involving nanoscale particles (such as burning carbon or metal particles). Carbon particles oxidize slowly in the outer/transition zone of the sphere, and the energy derived from this oxidation helps sustain the excitation and temperature of the internal plasma. The rate of this slow combustion is determined by the influx of O₂ and/or the reaction kinetics at the carbon surface. Hydroxyl radicals are continuously generated and undergo recombination.
Dissipation: Once the 0.3 grams of fuel is consumed (converted into carbon dioxide and water vapor), the ball lightning suddenly collapses and cools down, while any remaining fine dust disperses invisibly into the air.
(Based on the parameters—15 g / 5 μm / 1000e / 35 μm—the verification process indeed yielded a strongly coupled Yukawa fluid with a coupling parameter of approximately Γ = 75. (I used AI Gemini in the same way I previously used Google, and AI Gemini cumputed the model.)
Dissipation: Once the 0.3 grams of fuel is consumed (converted into carbon dioxide and water vapor), the ball lightning suddenly collapses and cools down, while any remaining fine dust disperses invisibly into the air.
(Based on the parameters—15 g / 5 μm / 1000e / 35 μm—the verification process indeed yielded a strongly coupled Yukawa fluid with a coupling parameter of approximately Γ = 75. (I used AI Gemini in the same way I previously used Google, and AI Gemini cumputed the model.)
Parameter "Tuning" (Simulation Model)
Chemistry and Oxygen Supply: The carbon content within the sparse 1.4-gram cloud of fly ash scales down to 0.03 grams; the heat of combustion from this carbon provides 982 Joules of energy. Oxygen demand is brought into precise balance through diffusion across a smaller surface area, as the heating requirement (55 W) is also significantly lower.
Chemistry and Oxygen Supply: The carbon content within the sparse 1.4-gram cloud of fly ash scales down to 0.03 grams; the heat of combustion from this carbon provides 982 Joules of energy. Oxygen demand is brought into precise balance through diffusion across a smaller surface area, as the heating requirement (55 W) is also significantly lower.
Parameters for a new, resized sphere (at 0.001 emission):
Parameter Original model (30 cm) Modified model (14 cm)
Diameter 30 cm 14 cm
Effective emission 0.0001 0.001
Required fly ash mass 15.0 g 1.4 g
Carbon content 0.30 g 0.03 g
Radiative loss ~256 W ~55.5 W
Estimated lifespan ~38.3 seconds ~17.7 seconds
Diameter 30 cm 14 cm
Effective emission 0.0001 0.001
Required fly ash mass 15.0 g 1.4 g
Carbon content 0.30 g 0.03 g
Radiative loss ~256 W ~55.5 W
Estimated lifespan ~38.3 seconds ~17.7 seconds
Conclusions
The study presents a new, autonomous, numerically evaluable model of ball lightning that bridges the fields of dusty plasma physics and chemical thermodynamics. It demonstrates that ball lightning originating from carbonaceous fly ash—once initially formed by a linear lightning strike or a corona discharge—does not require a continuous external energy source to persist. The stability and characteristic spherical shape of the phenomenon are explained by the properties of a strongly coupled Yukawa dusty plasma (γ ≈ 75), in which the Debye-shielded negative charges of the dust particles give rise to a liquid-like surface tension. Its thermodynamic stability and 20–40 second lifespan are governed by a chemical feedback loop. The slow surface oxidation of the carbon particles provides the necessary heat generation, while the endothermic dissociation—followed by the exothermic recombination—of hydroxyl radicals (–OH) and carbon dioxide acts as a thermal buffer, preventing both rapid cooling and explosive overheating.
Numerical simulations confirm that the low effective emissivity—characteristic of optically thin recombination zones—reduces radiative losses to a level that balances the heat generated by chemical processes. This equilibrium sustains a hot core (≈ 3000 K) and provides the buoyancy required for stable levitation. The model is consistent with historical observations as well as spectral measurements conducted in China in 2012.
The study presents a new, autonomous, numerically evaluable model of ball lightning that bridges the fields of dusty plasma physics and chemical thermodynamics. It demonstrates that ball lightning originating from carbonaceous fly ash—once initially formed by a linear lightning strike or a corona discharge—does not require a continuous external energy source to persist. The stability and characteristic spherical shape of the phenomenon are explained by the properties of a strongly coupled Yukawa dusty plasma (γ ≈ 75), in which the Debye-shielded negative charges of the dust particles give rise to a liquid-like surface tension. Its thermodynamic stability and 20–40 second lifespan are governed by a chemical feedback loop. The slow surface oxidation of the carbon particles provides the necessary heat generation, while the endothermic dissociation—followed by the exothermic recombination—of hydroxyl radicals (–OH) and carbon dioxide acts as a thermal buffer, preventing both rapid cooling and explosive overheating.
Numerical simulations confirm that the low effective emissivity—characteristic of optically thin recombination zones—reduces radiative losses to a level that balances the heat generated by chemical processes. This equilibrium sustains a hot core (≈ 3000 K) and provides the buoyancy required for stable levitation. The model is consistent with historical observations as well as spectral measurements conducted in China in 2012.
Bibliography
Bencsik, I. ( 2026): The interaction between fly ash and Yukawa plasma: ball lightning, DOI: 10.13140/RG.2.2.26392.15369
Cen, J., Yuan, P., & Xue, S. (2014). Observation of the Optical and Spectral Characteristics of Ball Lightning. Physical Review Letters, 112(3), 035001. doi.org, (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.035001)
Video: https://www.24h.com.vn/media-24h/bi-an-hien-tuong-set-hon-cuc-hiem-trong-tu-nhien-c762a1479345.html
Bencsik, I. ( 2026): The interaction between fly ash and Yukawa plasma: ball lightning, DOI: 10.13140/RG.2.2.26392.15369
Cen, J., Yuan, P., & Xue, S. (2014). Observation of the Optical and Spectral Characteristics of Ball Lightning. Physical Review Letters, 112(3), 035001. doi.org, (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.035001)
Video: https://www.24h.com.vn/media-24h/bi-an-hien-tuong-set-hon-cuc-hiem-trong-tu-nhien-c762a1479345.html
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Fly ash consists of burnt and scorched material. It is a light, loosely structured, ash-like residue that becomes airborne. It is frequently produced during combustion—such as in fires, boilers, or forest fires—and travels through the air in the form of tiny soot-like flakes. It is easily picked up and carried away by air currents. It is a mixture of incompletely combusted solid particles and mineral substances. It appears as a grey or black residue, consisting of small, plate-like, angular, or flaky particles. When flue gas cools rapidly, the material in the fly ash largely adopts an amorphous, glass-like structure. The chemical components and elements of fly ash include carbon, while the vast majority of its mass (up to 80–90%) consists of oxides:
Silicon dioxide (SiO₂): the primary component, a substance similar to quartz sand.
Aluminium oxide (Al₂O₃): a major component derived from clay minerals.
Iron oxides (Fe₂O₃, Fe₃O₄): these give the fly ash its greyish or brownish colour.
Calcium oxide (CaO): quicklime, which is particularly significant when burning brown coal or wood.
Magnesium oxide (MgO) and potassium oxide (K₂O) are present only in smaller quantities.
Silicon dioxide (SiO₂): the primary component, a substance similar to quartz sand.
Aluminium oxide (Al₂O₃): a major component derived from clay minerals.
Iron oxides (Fe₂O₃, Fe₃O₄): these give the fly ash its greyish or brownish colour.
Calcium oxide (CaO): quicklime, which is particularly significant when burning brown coal or wood.
Magnesium oxide (MgO) and potassium oxide (K₂O) are present only in smaller quantities.