# Ball Lightning as Plasma Vortexes: A Reinforcement of the Conjecture
## 1 Introduction  
The observation of ball lightning has been documented for centuries. Despite all efforts, the development of a full theory remains a challenging subject, and this is particularly true because of the lack of reproducible data. Nevertheless, a series of more or less plausible hypotheses have been proposed in the last few decades, although a widely accepted explanation of this phenomenon has yet to come. Here is an incomplete list of (relatively recent) publications on the subject: [1; 2; 3; 4; 5; 6; 7; 8; 9]. An up-to-date review paper [10] provides a survey of the latest developments.  
These spherical luminous objects of variable size are often associated with thunderstorms, though they look quite stable and last for a relatively long time. They may show up in multiple events in the course of a single electric storm [11]. Nowadays, the widespread use of cameras has increased the chance to catch an event, also from different viewpoints [12], offering support for a more in-depth analysis. Luminous plasmoids have been reproduced in the laboratory [13; 14], sharing similarities with natural phenomena. An experiment attempting to generate glowing balls directly from natural thunderstorms was conducted in [15], through a complex apparatus involving the launch of rockets to trigger the events. Occurrences resembling ball lightning were actually observed in some circumstances.  
The main features of ball lightning are reported in numerous publications. The balls show up with different appearances and move along rectilinear trajectories, sometimes varying their direction unpredictably. They display an averaged diameter of the order of decimeters and may last up to minutes. They carry a relevant amount of energy and their decay can happen in various fashions.  
Several hypotheses have been proposed to explain the physical mechanism of such peculiar structures. Earlier suggestions that ball lightning is comprised of trapped waves of electromagnetic nature were provided in [16]. In particular, many theories try to establish connections with the properties of plasma. In this framework, for instance, ball lightning is regarded as a magnetostatic spherical plasmoid in equilibrium [17]. Stationary conditions for a thin ring have been investigated, for example in [18] for a conducting gas in a magnetic field. In [19], it is assumed that the cohesion inside the balls comes from photon exchange forces. The study of hydrostatic equilibrium for a plasma sphere in microwave fields is a subject developed in [20]. Estimates for the hydrodynamic equilibrium of a ball are provided in [21].  
It is argued that the energy stored in plasma balls is far below the one seemingly involved in practice (see [22] and, e.g., the review papers [23; 24]). The claims are based on an application of the virial theorem. Actually, explicit estimates of the forces responsible for the thermodynamic equilibrium show inconsistencies with reality. This theoretical restriction can, however, be circumvented, as proposed by several authors. We refer for instance to [25] and the references therein.  
Although in this paper we still pursue the idea of a plasma in equilibrium, our approach is rather different from the usual ones. In fact, we are able to show the theoretical existence of electromagnetic rotating waves in toroid regions, which are stable according to magneto-hydrodynamics. This means that their pressure potential assumes zero normal gradient at the surface of the body. The vortexes can be also of Hill's type, so that they look like spheres, though their topology is that of a ring. In atmosphere, these ensembles of stored energy mix with molecules, so becoming a real plasma. As we shall see, the stability properties of the new object do not descend from physical particles interactions, but from the gluing action of the electromagnetic part, which can hypothetically carry an arbitrary amount of energy.