Fireball's physical nature.

The fourth russian academic conference "Scientific and applied", Izhevsk:
book publisher Udmurt State University, 1999, parts 7.
Theses of reports, part 7, p.58 (Izhevsk).

      The physical nature of ball lightening remains a puzzle. Many different hypotheses have been forwarded for its explanation [1, 2]. However, only few of them have sustained the test of time and evolved in certain directions of experimental research and results. The resonance model seems to be the most promising, suggested by P.L.Kapitsa more than 40 years ago [3]. It was the first to explain the occurrence and stability of the fireball by the short-wave resonance electromagnetic oscillation effect, during a thunderstorm, on the ion's movement.

      P. L. Kapitsa's resonance model, while explaining many of fireball's properties, did not elucidate the mechanisms for the emergence and existence of strong short-wave electromagnetic oscillations during the thunderstorm.

In the present paper, basing on a number of assumptions [3-9] that:

      1) resonant short-wave electromagnetic radiation exists in the interior of ball lightening (with wave length l comparable to the geometric dimensions d [3]);

      2) the most stable motions in nature are resonant ones [6], which feature one and the same character not dependent on the nature of interacting bodies [9] (с. 89);

      3) statically unstable states may become stable ones in dynamic conditions (traps for charged particles; Kapitsa inverse pendulum in the parametric resonance zones and beyond; systems of one, two or more magnetized gyroscopes in resonance) [4-8];

      - we suggest a self-consistent resonance model for ball lightening.

      Let us assume that a powerful discharge occurs during the thunderstorm. Streak "lightning" (one, or better two) induces crossed short-time magnetic and electromagnetic fields (Hertz emitter [9]) . The resulting motion of the produced ions will occur in complex combined electromagnetic fields ("constant" and variable ones). Induced "constant" fields will produce short-time current loops of opposite polarity m ⁺ and m ^- . In the first approximation, we can consider the system of two current loops m ⁺ and m ^- as magnetized and oppositely charged gyroscopes. Under certain conditions stable dynamic magnetic resonance states can develop in such a system at distances r~r₀=g ²m, where g is the gyromagnetic ration and m is the mass [7]. In this way, the lightning discharge can result, under certain circumstances, in the emergence of a self-stable plasma lump.

      The very mechanism of the stable motion state emergence in the resonance is rather simple [6, 7, 8]. Due to precession of magnetized charged gyroscopes m ⁺ and m ^- in each other's field at a certain distance r₀ the dipole repulsion can develop in the resonance, and the system will become stable [7, 8].

      Let us estimate the parameters of such a system. "Effective absorption of the external intensive radio waves of the ionized plasma cloud electromagnetic oscillations can occur only in resonance, when the proper period of plasma electromagnetic oscillations coincides with the absorbed radiation period. Assuming that the absorbed frequency corresponds to the sphere proper oscillations, the absorbed wave length shall be approximately equal to four ball lightening diameters (more exactly, l =3.65 d)" [3].

      Most often lightening balls are observed at 10 to 20 cm in diameter, to which the wave lengths from 35 to 70 cm correspond. For d ~ 10 cm, taking into account well known relations:

      g = e/(2mc), l = 3.65·d, d = 2 r₀, d = n /(g H), w = g H, N₀/V₀ = 4mc²/(e²·d²),

      E = mv²/2 = (mc²/2)·(d/l )²;

we arrive at:

      E= (0.2 to 16) MJ, N₀/V₀ = (3 to 96)·10¹⁶ particles/cm³, H = (17 to 400) MOersted;

      for m =(1 to 32)·m (proton).

      So, inside the lightening ball, in addition to short-wave electromagnetic oscillations assumed by P.L.Kapitsa, strong magnetic fields ~ MOersted exist. In the first approximation the ball lightening can be considered as a self-stable plasma "confining" itself in proper resonance variable and constant magnetic fields. The resonance mode of the lightening ball, under more detailed investigation, may explain many its peculiar features not only qualitatively, but also in quantitative terms allowing, in particular, to reproduce in the experiment self-stable plasma resonance structures controlled by electromagnetic fields. It's amusing to note, that the temperature of such a self-confining plasma is, in terms of chaotic motion, almost vanishing, since we deal with a strictly ordered synchronous motion of charged particles. Correspondingly, the lightening ball's (resonance system) life time t₀ is large ~ Q (Q-factor). Using the formula for the total radiation power of charged particles orbiting around the circle in a constant magnetic field

      Р=2·N₀·e⁴·H²·v²/(3m²·c⁵· (1-v²/c²))

      we arrive at the estimate P ~ 25 to 500 W, for d ~ 10 cm and, correspondingly, to t₀ ~ E/P ~ 4·10³ sec.

      The table below gives parameters obtained from the self-consistent resonance model of the fireball and observation data [1, 2].

Lightening ball's parameters (for d ~ 10 cm).

      where Н is the field strength at a distance of ~1 m from the ball lightening (unfortunately, the distance to the bell in case [1] is not known exactly).

      References

1. G. Barry. Ball and Beaded Lightning (Russian translation), Moscow, "Mir" Publishers, 1983, 288 pp.

2. B.M.Smirnov. The Nature of Ball Lightening. Moscow, "Nauka" Publishers, 1988, 208 pp. (in Russian)

3. P.L.Kapitsa. On the Nature of Ball Lighting, Reports of the USSR Academy of Science (Doklady), 1955, v.1, No. 2, pp. 245-248 (in Russian).

4. P.L.Kapitsa. ZhETF, 1951, v. 21, No. 5, pp. 588-597.

5. V.G.Shironosov. On the Kapitsa pendulum in the parametric resonance zone and beyond,

Journal of Technical Physics, 1990, v. 60, No. 12, pp. 1-7 (in Russian)

6. V.G.Shironosov. Effect of two spin particle resonance capture, Journal of Technical Physics,

1983, v. 53, No. 7, pp. 1414-1516 (in Russian)

7. V.G.Shironosov. Problem of Two Magnetic Dipoles with the Account of their Spin Equation of Motion, Izvestiya VUZov, Physics, 1985, No. 7, pp. 74-78 (in Russian)

8. V.G.Shironosov. On the Non-Stable State Stability, Bifurcations, and Chaos in Non-Linear Systems, Reports of the USSR Academy of Science (Doklady), 1990, v. 314, No. 2, pp. 316-320 (in Russian)

9. P.N.Lebedev. Selected Works/ Edited by A.K.Timiryazev, Moscow, State Publishing House for Technical Literature (Gostekhizdat), 1949, 244 pp.