The stability of the ball lightning dust plasma
is due to the Yukawa potential
(4. Marc 2026)
In Yukawa plasmas, the mobile charge carriers (electrons and ions) rearrange and neutralize the field of an external electric test charge placed in the plasma. The effect fundamentally determines the behavior of plasmas.
The charge in a Yukawa plasma does not create the usual potential in a vacuum, but an exponentially decaying field. The Yukawa potential has the form: Q exp(-r/λD) /4πεr, where λD is the Debye length, r is the distance, and the parameter λD determines the degree of shielding: beyond this distance, the effect of the charge becomes negligible. In a vacuum, the potential is a Coulomb potential inversely proportional to the distance, which in a plasma changes with an exponential decrease. The modified form is called the Yukawa potential or also called the shielded Coulomb potential.
The charge in a Yukawa plasma does not create the usual potential in a vacuum, but an exponentially decaying field. The Yukawa potential has the form: Q exp(-r/λD) /4πεr, where λD is the Debye length, r is the distance, and the parameter λD determines the degree of shielding: beyond this distance, the effect of the charge becomes negligible. In a vacuum, the potential is a Coulomb potential inversely proportional to the distance, which in a plasma changes with an exponential decrease. The modified form is called the Yukawa potential or also called the shielded Coulomb potential.
The temperature dependence of the modified Yukawa potential: if the plasma temperature is higher, the kinetic energy of the particles is higher, which makes it more difficult to form a shielding cloud, so the Debye length increases. The Debye length is directly proportional to the square root of the temperature. As the temperature increases, the shielding becomes less effective, the range of the Coulomb potential increases, and the Yukawa potential begins to transform back into the long-range Coulomb potential. The dependence of the modified Yukawa potential is also strong on its density, because if the plasma is denser, more charges are available for shielding. Higher temperature plasma has fewer particles and a lower specific gravity: n1 T1 = n2 T2
Surface tension in Yukawa plasmas: In systems that can be described by the Yukawa potential (strongly coupled dust plasmas), the surface tension appears as the result of the attractive or repulsive forces between the particles at the phase boundaries, as the surface tension (γ), and holds the system together, γ = ΔPR/2, where ΔP is the pressure difference on both sides of the surface, and R is the radius of the sphere, we will assume R ≈ 30 cm and T = 4000K degrees. ΔP between the two sides of the surface is close to zero, otherwise the sphere expands, because the system is at atmospheric pressure. In reality, the envelope must have a minimum value, because convection flows (hot gas flows would deform the sphere, which would can be observed, and the membrane must prevent the high-speed plasma particles from diffusing into the outside air.
The degree of surface tension is closely related to the shielding Debye length parameter; if the shielding becomes short-range (the Debye length is short), the surface tension decreases. A plasma membrane is formed because the faster electrons also form a positively charged layer, the layer is a few Debye lengths thick and forms an electrical barrier that keeps the particle currents in balance. A Debye membrane is a thin, positively charged plasma layer that forms at the interface and is created as a result of the faster-moving electrons negatively charging the surface. It acts as a potential barrier that balances the electron and ion fluxes, and its thickness typically spans a few Debye lengths. (https://en.wikipedia.org/wiki/Debye_sheath.) In a gas plasma Micrometer-sized dust particles can accumulate a huge charge and interact with each other through the Yukawa potential, often forming "plasma particles". It affects the plasma surface, the surface tension, and forms a cohesive force in the case of ball lightning. The Yukawa potential (shielded Coulomb potential) basically determines the forces holding the system together and the surface properties, but the effect differs from the case of classical media. The Yukawa potential is often repulsive in itself (for example, between similarly charged dust particles in plasma), when a system "combines" and has a surface tension, an attractive component is also necessary: the attraction between ions and electrons holds the system together. The surface tension arises from the asymmetry of the cohesive forces occurring at the phase boundary. If the Debye length is small (strong shielding), the particles only interact with their immediate neighbors when the surface tension is lower, because the range limited.
The degree of surface tension is closely related to the shielding Debye length parameter; if the shielding becomes short-range (the Debye length is short), the surface tension decreases. A plasma membrane is formed because the faster electrons also form a positively charged layer, the layer is a few Debye lengths thick and forms an electrical barrier that keeps the particle currents in balance. A Debye membrane is a thin, positively charged plasma layer that forms at the interface and is created as a result of the faster-moving electrons negatively charging the surface. It acts as a potential barrier that balances the electron and ion fluxes, and its thickness typically spans a few Debye lengths. (https://en.wikipedia.org/wiki/Debye_sheath.) In a gas plasma Micrometer-sized dust particles can accumulate a huge charge and interact with each other through the Yukawa potential, often forming "plasma particles". It affects the plasma surface, the surface tension, and forms a cohesive force in the case of ball lightning. The Yukawa potential (shielded Coulomb potential) basically determines the forces holding the system together and the surface properties, but the effect differs from the case of classical media. The Yukawa potential is often repulsive in itself (for example, between similarly charged dust particles in plasma), when a system "combines" and has a surface tension, an attractive component is also necessary: the attraction between ions and electrons holds the system together. The surface tension arises from the asymmetry of the cohesive forces occurring at the phase boundary. If the Debye length is small (strong shielding), the particles only interact with their immediate neighbors when the surface tension is lower, because the range limited.
What is the temperature of the ball lightning plasma? As a first approximation, many thousands of degrees K. Usually, in the case of non-thermal (cold) plasmas, the temperature is one to two thousand degrees K, which is the temperature of the ions and neutral particles, while the electrons are much hotter, 10,000–100,000 degrees K. Even in the non-thermal (cold) plasma state, the electrons are extremely hot, but the temperature of the heavy particles (ions and gas molecules) can only range from room temperature (300 K) up to 2,500 K. In thermal (hot) plasma, all particles are at the same, very high temperature, the temperature range usually starts at 4,000 K and can last up to 20,000 K (or more), and such plasma is used for melting and cutting metals (e.g. welding arc, plasma cutter). Due to the relationship n1 T1 = n2 T2, we assume a low-temperature plasma (ultimately 2000 Kelvin, for the sake of the lifetime), because at higher temperatures the particle number and density decrease, in which case either the sphere would rise and not float, or a relatively high dust content would have to be assumed to avoid rising. Due to the floatation, the density of the sphere is equal to the density of air. As an example, we will arbitrarily assume a silicon content of 125g*, which compensates for the decrease in density due to the high temperature. Si dust particles acquire a strong negative charge in the plasma, and the charged particles interact electrically with each other, which in some cases gives the plasma its own surface tension. At 3000 and 4000 Kelvin, the calculation is:
Temperature State of Silicon Radius () for levitation Note
3000 K Liquid (powder) 32.3 cm Almost the original 30 cm size.
4000 K Gas (steam) 72.5 cm It expands enormously due to gasification.
3000 K Liquid (powder) 32.3 cm Almost the original 30 cm size.
4000 K Gas (steam) 72.5 cm It expands enormously due to gasification.
At 3000 K, silicon is no longer a gas and does not exert extra partial pressure. The size of the sphere became 32.3 cm (instead of 30 cm) because the density of hot air at 3000 K is slightly higher than at 4000 K, so a little more buoyancy (larger volume) is needed to balance the same 125 grams of weight. So at 3000 K the sphere would almost exactly maintain its original size of 30-32 cm and would float stably, since the silicon is in the form of "powder" (liquid droplets). Unfortunately, there is a problem: the surface of the sphere radiates, and since the heat capacity of the gas is small compared to the radiation loss, the plasma would "extinguish" in 75-100 milliseconds. Until then, the sphere would glow white (like a huge flash of light).
Ball lightning (https://www.24h.com.vn/media-24h/bi-an-hien-tuong-set-hon-cuc-hiem-trong-tu-nhien-c762a1479345.html)
Let the temperature of the model calculation be to 2000 Kelvin: at 2000 K, silicon is no longer a gas, nor does it even boil, but is present in the form of liquid melt (droplets). This is the "coldest" state, where we can still speak of plasma (weakly ionized gas), and at this point the size of the sphere is the smallest: in order for the 125 g mixture of silicon and hot air to float, the silicon must float in the sphere in the form of glowing, liquid micro-droplets (like a dense, luminous fog).
Temperature Radius (for hovering) Radiation loss Lifetime (approx.)
2000 K 29 cm 96 kW 3.6 s
3000 K 32.3 cm 6 MW 0.075 s
4000 K 72.5 cm 63 MW 0.01 s
10000 K 132 cm 750 MW 0.001 s
2000 K 29 cm 96 kW 3.6 s
3000 K 32.3 cm 6 MW 0.075 s
4000 K 72.5 cm 63 MW 0.01 s
10000 K 132 cm 750 MW 0.001 s
The 2000 K sphere is the most stable: almost exactly the same size as the original 30 cm, and "only" a serious industrial power source (96 kW) would be needed to maintain it continuously. At a lower temperature, at 1600 K, the model: the temperature of 1600 K is a special physical limit point, because silicon is no longer liquid, but in a solid (powder) state, since the melting point of silicon is 1687 K. Therefore, 1600 degrees is already "cold" for the plasma state, at 1600 K the natural ionization of the air is practically zero. In order to call this a plasma:
- the silicon powder would have to be electrically charged.
- an external ionizing source (e.g. microwave radiation or high-voltage field) would be needed.
- at this temperature the sphere would resemble a glowing dust cloud rather than a real plasma.
Comparison
Temperature (K) Radius (for hovering) Radiation loss Silicon state
1600 K 27.6 cm 35.6 kW Solid (powder)
2000 K 29.0 cm 96 kW Liquid (drop)
3000 K 32.3 cm 6 MW Liquid (drop)
4000 K 72.5 cm 63 MW Gas (steam)
10000 K 132.0 cm 750 MW Plasma
Temperature (K) Radius (for hovering) Radiation loss Silicon state
1600 K 27.6 cm 35.6 kW Solid (powder)
2000 K 29.0 cm 96 kW Liquid (drop)
3000 K 32.3 cm 6 MW Liquid (drop)
4000 K 72.5 cm 63 MW Gas (steam)
10000 K 132.0 cm 750 MW Plasma
Taking into account the Yukawa potential, it is possible to model the sphere with a plasma of about 2000 K. Taking into account the Yukawa potential (or shielded Coulomb potential) is crucial for dust plasmas, since the free electrons and ions in the plasma shield the charge of the dust particles. If the electrons are hotter, the potential of the particles becomes more negative, and the sphere will float in the air if its radius is at least 27.6 cm. The Yukawa potential shields silicon particles, then for the Debye length ≈ 0.31μm, which is negligible compared to the 29 cm radius of the sphere, the interior of the plasma is perfectly shielded. Due to the exponential term of the Yukawa potential, the electrostatic interaction only acts in the immediate vicinity of the dust particles. Due to the short range of the Yukawa potential, 125 g of silicon dust may be able to form a "pseudo" framework or ordered structure within the plasma, which may explain the stability of the spherical shape and the slow (3.6 s) energy release. Due to the Yukawa interaction, the plasma pressure will be lower than that of an ideal gas at the same temperature, which affects the levitation equilibrium: The external pressure/force required to maintain the 29 cm radius is slightly modified because the internal electrostatic repulsion (which would expand the sphere) is weakened by the shielding. The 3.6 s lifetime is determined by the radiation loss (96 kW) and particle recombination. The Yukawa potential slows down the collision cross section of charged particles at low energies and influences the kinetics of silicon oxidation on the dust surface, which gives the energy reserve of the plasma. At high dust density (125g is a significant mass in such a large sphere), the Yukawa potential allows for the formation of a kind of structure within the plasma (i.e., the plasma is strongly coupled), which increases the stability of the system, explaining the relatively long (3.6 s) lifetime, which a pure gas plasma would not achieve.
Conclusion: due to the observed lifetimes of many seconds, ball lightning has a relatively high dust content, a low plasma temperature (≈ 2000K), and, of course, is at atmospheric pressure, floating. Their existence is made possible by the Yukawa potential.
Conclusion: due to the observed lifetimes of many seconds, ball lightning has a relatively high dust content, a low plasma temperature (≈ 2000K), and, of course, is at atmospheric pressure, floating. Their existence is made possible by the Yukawa potential.
*The connection between ball lightning and silicon is one of the most important explanations for the phenomenon in modern physics, and has been confirmed by instrumental observations in recent years.
According to John Abrahamson and James Dinniss, researchers at the University of Canterbury in New Zealand, ball lightning is created when a conventional lightning bolt strikes the ground. The steps in the process (AI answer):
Evaporation: The enormous energy of the lightning strike vaporizes the silica (sand) in the soil.
Reduction: In the presence of carbon in the soil, the silica is converted into pure silicon vapor.
Nanospheres: As the vapor cools, it forms a cloud of tiny silicon nanoparticles.
Oxidation: When exposed to oxygen in the air, the silicon slowly begins to oxidize, releasing heat and light – creating the floating, glowing ball.
The silicon theory was first directly supported by measurements in 2012. Jienyong Cen and his colleagues (Northwest Normal University, China) accidentally recorded a ball lightning with a spectrometer while observing a storm, and spectral analysis revealed the presence of silicon, iron, and calcium in the ball – the exact same elements that were also found in the local soil. The observation confirmed that the light of the ball lightning is powered by the combustion/oxidation of elements from the soil, and is not a purely electrical phenomenon.
According to John Abrahamson and James Dinniss, researchers at the University of Canterbury in New Zealand, ball lightning is created when a conventional lightning bolt strikes the ground. The steps in the process (AI answer):
Evaporation: The enormous energy of the lightning strike vaporizes the silica (sand) in the soil.
Reduction: In the presence of carbon in the soil, the silica is converted into pure silicon vapor.
Nanospheres: As the vapor cools, it forms a cloud of tiny silicon nanoparticles.
Oxidation: When exposed to oxygen in the air, the silicon slowly begins to oxidize, releasing heat and light – creating the floating, glowing ball.
The silicon theory was first directly supported by measurements in 2012. Jienyong Cen and his colleagues (Northwest Normal University, China) accidentally recorded a ball lightning with a spectrometer while observing a storm, and spectral analysis revealed the presence of silicon, iron, and calcium in the ball – the exact same elements that were also found in the local soil. The observation confirmed that the light of the ball lightning is powered by the combustion/oxidation of elements from the soil, and is not a purely electrical phenomenon.