"IISRT"1999. Collection №159.

Fireball's physical nature.

Valentin G. Shironosov

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 shortwave 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 shortwave electromagnetic
oscillations during the thunderstorm.
In the present paper, basing on a number of assumptions
[39] that:
1) resonant shortwave 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) [48];
 we suggest a selfconsistent
resonance model for ball lightening.
Let us assume that a powerful
discharge occurs during the thunderstorm. Streak "lightning" (one, or
better two) induces crossed shorttime 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 shorttime 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~r_{0}=g ^{2}m, 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 selfstable 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 r_{0 } 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
r_{0}, d = n /(g H), w = g H, N_{0}/V_{0 }=
4mc^{2}/(e^{2}·d^{2}),
E = mv^{2}/2 = (mc^{2}/2)·(d/l
)^{2};
we arrive at:
E= (0.2 to 16) MJ, N_{0}/V_{0
} = (3 to 96)·10^{16} particles/cm^{3}, H
= (17 to 400) MOersted;
for m =(1 to 32)·m (proton).
So, inside the lightening ball,
in addition to shortwave electromagnetic oscillations assumed by P.L.Kapitsa,
strong magnetic fields ~ MOersted exist. In the first approximation
the ball lightening can be considered as a selfstable 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
selfstable plasma resonance structures controlled by electromagnetic
fields. It's amusing to note, that the temperature of such a selfconfining
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 t_{0 }is
large ~ Q (Qfactor). Using the formula for the total radiation power
of charged particles orbiting around the circle in a constant magnetic
field
Р=2·N_{0}·e^{4}·H^{2}·v^{2}/(3m^{2}·c^{5}·
(1v^{2}/c^{2}))
we arrive at the estimate P
~ 25 to 500 W, for d ~ 10 cm and, correspondingly, to t_{0}
~ E/P ~ 4·10^{3} sec.
The table below gives parameters obtained from
the selfconsistent resonance model of the fireball and observation
data [1, 2].
Lightening ball's parameters (for d ~ 10 cm).

E, in MJ 
N_{0}/V_{0}, in particle/cm^{3} 
H, in Oersted 
t_{0}, in sec 
T, in К 
P, in W 

(0.216) 
(396)*10^{16} 
(17400) 
4*10^{3} 
~ 0 
25500 
[1,2] 
(0.859.5) 
5.8*10^{16} 
170 
110^{3} 
4000 
10500 
[]/стр. 
[1]/71 
[1]/67 
[1]/80 
[1]/66,46 
[1]/76 
[2]/25 
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. 245248 (in Russian).
4. P.L.Kapitsa. ZhETF, 1951, v. 21, No. 5, pp. 588597.
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. 17 (in Russian)
6. V.G.Shironosov. Effect of two spin particle resonance
capture, Journal of Technical Physics,
1983, v. 53, No. 7, pp. 14141516 (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. 7478 (in Russian)
8. V.G.Shironosov. On the NonStable State Stability, Bifurcations,
and Chaos in NonLinear Systems, Reports of the USSR Academy of Science
(Doklady), 1990, v. 314, No. 2, pp. 316320 (in Russian)
9. P.N.Lebedev. Selected Works/ Edited by A.K.Timiryazev, Moscow, State
Publishing House for Technical Literature (Gostekhizdat), 1949, 244
pp.
