Comment on the Article

In [1], an attempt was made to estimate—within a certain model—several parameters of ball lightning based on information that the passage of a ball lightning near a turned off incandescent lamp caused its glow, which ceases when the ball lightning receded. It was assumed that this effect had been caused by the heating of the filament by currents induced by an electromagnetic wave emitted by ball lightning [1]. Below, it is shown that the work [1] contains at least two fundamentally important errors that devalue a significant part of the results presented in it. Intensity I of electromagnetic radiation emitted by charge q moving with acceleration a was calculated in [1] by the formula

In [1], an attempt was made to estimate-within a certain model-several parameters of ball lightning based on information that the passage of a ball lightning near a turned off incandescent lamp caused its glow, which ceases when the ball lightning receded. It was assumed that this effect had been caused by the heating of the filament by currents induced by an electromagnetic wave emitted by ball lightning [1]. Below, it is shown that the work [1] contains at least two fundamentally important errors that devalue a significant part of the results presented in it.
Intensity I of electromagnetic radiation emitted by charge q moving with acceleration a was calculated in [1] by the formula (1) where ε 0 is the electric constant and c is the speed of light in a vacuum. This corresponds to the use of the term "intensity" in the sense of "energy radiated per unit time" [2,3], which can be seen first from the dimension. In [1], where formula (1) had number five and the abbreviation BL was used for ball lightning, the following statement was made: "to compare the radiation intensity calculated by Eq. (5) with that found at surface of a BL I ~ 0.1 W, the latter should be multiplied by the factor X that takes into account the attenuation of the field intensity in a wave with the distance. The numerical value of this coefficient is determined by the expression X ~ (L 2 /L 1 ) 2 , if we take that Eq. (5) determines the field intensity in a wave at distance L 1 and the distance from a BL to a bulb is L 2 . Assuming that L 1 ~ 1000 m, L 2 ~ 0.1 m, we obtain X 1 0 -8 ." The approach formulated in this statement contradicts the physical meaning of formula (1), and its = πε It should be emphasized that the value I ∼ 0.1 W in the above citation, where the sign "∼" probably means "of the order of" (or, in more detail, "has a value of the order of"), was obtained in [1] by the formula corresponding to the use of the term "intensity" in the sense of "energy of radiation passing per unit time through unit area" and giving a result of dimension in W/m 2 . The author of this Commentary failed to understand whether this mismatch of dimensions was a misprint, made several times, or a fundamental error affecting the authors' reasoning and the results presented. The reason is that, in the example presented in [1], the heating power of the filament is of the order of 1 W, but the possibility of matching this value with the aforementioned value of I is not discussed. It is natural to expect that the correct dimension of I will correspond to the lower bound of the radius of ball lightning, while the wrong one requires, even when estimating in order of magnitude, substantiation of a significant (by an order of magnitude) difference of heating power from I; however, issues of this kind were not addressed in [1].
In an attempt to justify the possibility of emitting by a ball lighting electromagnetic radiation causing the glow of an incandescent lamp at relatively small a, a second fundamental error was made in [1]. It was suggested that a charge whose accelerated motion causes the emission of electromagnetic radiation is induced in a ball lightning by an external electric field [1]. The following statement was made: "The charge induced in an electrically conducting sphere with radius R by external field E 0 is determined by the relation Q Ẽ 0 R 2 " [1]. In calculations in the SI system, used in [1], COMMENTS this statement is true only if the sign "∼" is understood in the sense of proportionality, which can be seen from the dimension. In the situation under discussion, the authors of [1] use this sign in the sense of approximate equality or indication of order of magnitude and give an example with E 0 ∼ 1000 V/m and R = 0.15 m (these quantities serve as examples of the ground surface electric field strength in thunderstorm weather and the radius of the ball lightning, respectively) and Q ∼ 20 C (thus, the fact that 1000 × 0.15 2 = 22.5 ≈ 20 is used). In book [4] (task 1 to Section 3 of Chapter I), the polarization of a conducting uncharged ball in an external uniform electric field is considered. By rewriting the expression obtained in this case for the electric charge surface density in the SI system and using the notation of [1], it is easy to show that, on one half of the ball (or a conducting sphere), a positive charge 3πε 0 E 0 R 2 is induced, which can be considered equal to Q, and, on the other half, a negative charge of the same absolute value is induced. For E 0 ≈ 1000 V/m and R = 0.15 m, we have 3πε 0 E 0 R 2 ≈ 1.9 × 10 -9 C, which is ten orders of magnitude smaller than the corresponding value from [1].
Thus, the authors of [1] did not provide correct estimates that could illustrate the fundamental possibility of heating the filament to a visually detectable glow by currents induced by an electromagnetic wave emitted by a ball lightning.
In conclusion, it should be noted that the establishment of one or more physical mechanisms of the contactless influence of ball lightning on various objects and people (see, e.g., review [5] and the bibliography in [1,5]) is necessary to determine the danger of ball lightning to people and aircraft, as well as to optimize the treatment of people affected by the effects of ball lightning. The ability of the model of ball lightning to explain reliable reports of such effects can be considered as one of the criteria for the expediency of its experimental verification. Unfortunately, both remarks by M.L. Shmatov are fair, and the authors are very grateful for them.
The first remark, however, does not change much in the numerical estimates, which were carried out in order of magnitude, and the remark itself (despite the gross error of the authors), when taken into account, leads to a numerical coefficient of 3.
The second remark is really significant (systems of physical units are confused): as a result, the role of the charge induced by an external electric field in the generation of electromagnetic radiation of BL is insignificant in comparison with the role of the intrinsic uncompensated charge.
Nevertheless, the authors, recognizing their own unfortunate blunder, believe that the material presented in the work is of scientific interest and the scrupulous attitude of the attentive reader has improved the quality of the study of the issue considered in the work.