In the plasma of ball lightning
the Yukawa potential modifies the electric potential (Debye shielding)
(February 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 the plasma does not create the usual potential in a vacuum, but an exponentially decaying field, the process is also called Debye shielding. The Yukawa potential has the form:
Q exp(-r/λD) /4πεr, where λD is the Debye length, the parameter λD determines the degree of shielding: beyond this distance the effect of the charge becomes negligible. In vacuum, the potential is a Coulomb potential inversely proportional to the distance, which in plasma is modified by an exponential decay. The modified form is called the Yukawa potential (or 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 potential increases, and the Yukawa potential begins to transform back into the long-range Coulomb potential. The presence of Yukawa-type interactions fundamentally modifies the thermodynamic properties of the system. The dependence of the modified Yukawa potential is even stronger on its density, because if the plasma is denser, more charges are available for shielding.
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 potential increases, and the Yukawa potential begins to transform back into the long-range Coulomb potential. The presence of Yukawa-type interactions fundamentally modifies the thermodynamic properties of the system. The dependence of the modified Yukawa potential is even stronger on its density, because if the plasma is denser, more charges are available for shielding.
Surface tension in Yukawa plasmas
In systems that can be described by the Yukawa potential (such as strongly coupled dust plasmas or colloids), surface tension appears as the result of attractive or repulsive forces between particles at the phase boundaries and holds the system together. The magnitude of the surface tension is closely related to the shielding Debye length parameter; if the shielding becomes short-ranged (the Debye length is short), the surface tension decreases.
A plasma membrane forms because the faster electrons 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. The Debye membrane is a thin, positively charged plasma layer that forms at the interface and is created as a result of the faster electrons negatively charging the surface. It acts as a potential barrier that balances electron and ion fluxes, and its thickness typically spans a few Debye lengths. A full explanation can be found on the Wikipedia page on the Debye length: https://en.wikipedia.org/wiki/Debye_sheath
In systems that can be described by the Yukawa potential (such as strongly coupled dust plasmas or colloids), surface tension appears as the result of attractive or repulsive forces between particles at the phase boundaries and holds the system together. The magnitude of the surface tension is closely related to the shielding Debye length parameter; if the shielding becomes short-ranged (the Debye length is short), the surface tension decreases.
A plasma membrane forms because the faster electrons 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. The Debye membrane is a thin, positively charged plasma layer that forms at the interface and is created as a result of the faster electrons negatively charging the surface. It acts as a potential barrier that balances electron and ion fluxes, and its thickness typically spans a few Debye lengths. A full explanation can be found on the Wikipedia page on the Debye length: https://en.wikipedia.org/wiki/Debye_sheath
In the case of dust plasmas
Micrometer-sized dust particles in a gas plasma 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 cohesive forces and surface properties of the system, but the effect differs from that of classical liquids. The Yukawa potential itself is often repulsive (for example, between similarly charged dust particles in a plasma), when a system "assembles" and has a surface tension, an attractive component is also necessary: the attraction between ions and electrons holds the system together. Surface tension arises from the asymmetry of the cohesive forces 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 is limited. At long-range effects, the shielding is weak, and the particles "see" each other from further away, which increases the internal energy and the work required to form the surface, so the surface tension increases. In Yukawa systems, the surface is not a sharp line, but a transition layer: at the interface, the particle density does not suddenly jump to zero, but decays within a distance comparable to the Debye length. In strongly coupled systems (e.g. dust plasmas), particles can arrange themselves in layers along the surface, which can lead to anisotropy (direction dependence) of the surface tension. In the case of a plasma gas, shielding prevents the gas from flying apart due to its own electrostatic repulsion (quasi-neutrality). The Yukawa potential controls the range of cohesive forces due to shielding. The smaller the Debye length (stronger shielding), the "softer" and less stable the surface. The shielding becomes less effective, the potential range increases, and the Yukawa potential begins to transform back into the long-range Coulomb potential.
Micrometer-sized dust particles in a gas plasma 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 cohesive forces and surface properties of the system, but the effect differs from that of classical liquids. The Yukawa potential itself is often repulsive (for example, between similarly charged dust particles in a plasma), when a system "assembles" and has a surface tension, an attractive component is also necessary: the attraction between ions and electrons holds the system together. Surface tension arises from the asymmetry of the cohesive forces 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 is limited. At long-range effects, the shielding is weak, and the particles "see" each other from further away, which increases the internal energy and the work required to form the surface, so the surface tension increases. In Yukawa systems, the surface is not a sharp line, but a transition layer: at the interface, the particle density does not suddenly jump to zero, but decays within a distance comparable to the Debye length. In strongly coupled systems (e.g. dust plasmas), particles can arrange themselves in layers along the surface, which can lead to anisotropy (direction dependence) of the surface tension. In the case of a plasma gas, shielding prevents the gas from flying apart due to its own electrostatic repulsion (quasi-neutrality). The Yukawa potential controls the range of cohesive forces due to shielding. The smaller the Debye length (stronger shielding), the "softer" and less stable the surface. The shielding becomes less effective, the potential range increases, and the Yukawa potential begins to transform back into the long-range Coulomb potential.
Decrease in surface tension
Like classical liquids, the surface tension decreases in Yukawa systems as the temperature increases. Higher temperature increases the thermal pressure of the particles trying to fly apart, which counteracts the cohesive forces. Above a certain critical temperature, the cohesive forces are no longer able to hold the system together, and the surface tension decreases to zero. The state of the system is determined by the ratio of temperature to potential energy, a coupling parameter. At high temperatures, thermal energy dominates, the system becomes chaotic, and behaves like an ideal gas or a weakly coupled plasma.
Like classical liquids, the surface tension decreases in Yukawa systems as the temperature increases. Higher temperature increases the thermal pressure of the particles trying to fly apart, which counteracts the cohesive forces. Above a certain critical temperature, the cohesive forces are no longer able to hold the system together, and the surface tension decreases to zero. The state of the system is determined by the ratio of temperature to potential energy, a coupling parameter. At high temperatures, thermal energy dominates, the system becomes chaotic, and behaves like an ideal gas or a weakly coupled plasma.