Emelin S.E.1, Pirozerski A.L. 1,
Skvortsov G.E. 1, Bychkov V.L. 2
1 Scientific-Research Institute of Physics at St.-Petersburg
State University, St.-Petersburg, 198904, Russia
2 Institute for High Temperature Russian Academy of Science, Izhorskaya 13/19, Moscow, 127412, Russia.
E-mail: Sergei.Emelin@pobox.spbu.ru, email@example.com
conditions of formation of the ball lightning with high energy density
considered as condensate of heavily
excited atoms have been studied. In our approach the ball lightning formation processes is considered as a form of energy-structure
self-organi-zation on the base of metastable substance and interchange. We propose different variants of the experimental method to
create autonomous formation on the base of the closed capillary discharge allowing to obtain the objects with the life time up to 2s
which burn through the foil, explode and can penetrate through the polymer wall without destroying it.
For a long time the ball lightning (BL) attracts attention of the investigators by extraordinary features of its behavior and by unusual characteristics of its tracks of effect on material objects. However attempts to clarify this phenomenon are complicated by occasional and transitory character of its appearance in the nature, by diversity and apparent inconsistency of the forms observed by the eyewitnesses. Also, the absence of reliable methods of its reproduction in the laboratory makes one to study similar but considerably less impressive effects.
We think that in the present situation the key moment is the realization of the fact that in BL investigations it is necessary to direct efforts to the laboratory experiments, because, on the one hand, they are capable to give effects, which, though being considerably weaker, are similar the naturally arising ones, and on the other hand, the laboratory experiments are carried out in controlled and reproducible conditions, which is the basis for researches advances. The reproducing of more stronger effects can be attained only as a result of a sure comprehension of the nature of effects obtained on the reached level of the researches followed by determination of directions for their perfecting.
To work out a method of creation of the artificial objects with sufficiently interesting properties it is necessary to draw attention to the physical conditions of the BL formation. We have extremely poor information about features of BL formation processes, so, concerning the existing hypotheses of BL nature, it remains only to discuss which of them are more or less probable. The experience of BL modeling gained at the previous investigations shows that if we have concentrated on improving of some parameter we obtain objects having only partial resemblance with BL. It seems, therefore, that the required physical conditions should represent a sensitive combination of rigid restrictions, characteristic features of these condition being high nonequilibrium and low stability.
Within the framework of the scientific approach, any attempt of reproduction of unexplored phenomenon requires sufficiently concrete supposition about its nature. Available on the present moment data admit to consider BL as a particular state of the matter whose the most essential feature consists in accumulation of energy, sufficiently exceeding the thermal one, with possibility of long and relatively stable conservation of this energy. Virtually, in this case we speak about metastable exited state of the matter keeping atoms or their part, without specification of the form of excitation energy and of the relative stability nature.
One of the principle form of energy contained in the matter is energy of electromagnetic fields of the nuclei and the electrons. According to the hypothesis of Bychkov V.L. , based on the electret physics, there exists a specific strongly charged state of dielectric substrate (in particular, polymer one) with estimated properties resembling BL. Another hypothesis, which is due to Manykin E.A. and co-authors , considers BL as metallic condensed state of the system of electron-excited atoms. In condensed disperse phase, dust plasma, and flame may exist high charged states of the particles, which in some cases take the form resembling BL. Note that in essence the chemical energy is also electrical. We suppose, that the electrical propinquity of all these forms of energy is the main cause of the existing resemblance between corresponding autonomous objects and the BL formations , the latter having especially strong electrical manifestations.
In this connection, among a great many of plasma physics objects the high non-equilibrium dense plasma with condensed phase is of special interest for experimental modeling of BL on small-size experimental installations. At this plasma there exist practically the all mentioned above forms of energy and the states of the matter, with active processes of their interaction and mutual transformations. This gives the confidence that, under the condition of right adjustment of the discharge mode, the output objects should contain the matter approaching on its characteristics to the BL matter.
In the present paper we present our approach to this problem and some
results of the BL experimental modeling. More information is available
on our site at http://balllightning.narod.ru
2 Approach to creation of long-life plasma formations.
We think of the ball lightning (BL) with strong electrical manifestations as condensate of heavily excited states of multi-electron atoms [1,2]. We consider the BL formation as the processes of specific energy increasing and concentrating of a part of the atoms of the active plasma medium in the form of energy-structure self-organization on the base of metastable excited substance and the interchange.
The interchange is a complex of mass-energy transfer phenomena with a preferred direction . Self-focusing and convergence of transport-wave fluxes, which have small loss in the metastable substance as in a active medium, may result in appearing of energy distribution inhomogeneities which should be then significantly strengthened by non-linear effects in heterogeneous dense plasma. Segregation of exited states with highest specific energy, which arise in regions of higher nonequilibrium, may results in forming of a new phase which come apart as an autonomous object a ball lightning.
All above mentioned phenomena taken separately are well known, and the
task of the realization of energy-structure self-organization consists
in self-consistent combining of them in single and likely multi-stage process
which could go far enough, first of all, in respect of the specific energy
of output phase atoms.
2 Erosive plasma features, most important for the experimental ball lightning modeling
2.1 Erosive capillary discharge plasma
Investigations of the erosive plasma of electrical capillary discharge have confirmed the capability of supercooled erosive plasma with condensed phase to create a substance resembling the one we are looking for . Many interesting properties of this plasma have been discovered, but achieved parameters were found to be insufficient for direct laboratory reproducing of the ball lightning.
With all variety of discharge modes and dischargers designs and materials, the capillary discharge allows to obtain the plasma with sufficiently large range of characteristics. Avramenko R.F. have found a discharge regime creating long and thin plasma jet with the following properties: the low temperature together with the formation enthalpy being about the total single ionization energy, effective liberation of a considerable part of the input energy on metallic targets, long life time after the disconnection from the energy source and capability to generate autonomous plasma formations when interacting with some targets, etc . Further investigations  show that the jet has pronounced structural features, its vibrational temperature is in the order of magnitude greater than the gasokinetic one and that the interaction of the jet substance with the UHF radiation is of the threshold character .
2.2 Critical mode of the discharge
In papers [3,8-10] we found a series of peculiarities of the capillary discharge near the critical voltage value, below of which the stationary discharge is impossible. For example, at this mode the form of the plasma jet changes: fig.1a, 1b, 1c show frames of videotape record of steady-state jet from asymmetric capillary discharger  with aluminium inner electrode at above critical voltage, and fig.1d shows the jet on the last frame before breaking of the current.
Figures 2a and 2b show the integral image of non-stationary discharge in the symmetric discharger, representing through hole in a polymer plate, respectively in the ordinary and in the critical modes. It may be seen that in the latter case the jet appears only in the negative electrode direction.
One more feature of the critical mode in the case of the asymmetric discharger is generation of low-frequency oscillations of the current and the voltage on the discharge which appear only when the negative potential is applied to the inner electrode, similarly to the corona discharge on the electrode of small curvature radius. In  the dependence of the energy input into the evaporable material of the capillary on the discharge voltage is given, which shows that with decreasing of the voltage the working substance is more actively involved in the discharge.
These effects together with another ones, not mentioned here, show that the critical mode is characterized not only by increasing of the mobility of positive carriers with respect to negative ones, but even (on some stage) by the possibility of motion of the carriers against to the external field, which is possible only after preaccumulation of the energy and formation of corresponding activity of the medium (similar phenomena are considered by Stepanov S.I. ). Increasing of the current part transferred by positive carriers, similarly to the cathode layer of the glow discharge, may be explained in this case by increasing of the positive particles charge, connected, in particular, with the increasing of their sizes and with decreasing on the ionization energy due to the presence of the metastable phase.
These features of the critical mode are very important for the constructing of plasma current interrupters and were used by us to create the radially-slotted discharge .
So, under effective carriers binding the transition to the critical mode and the conductivity decreasing are due to the decreasing of the carriers mobility and their leaving to the external area. To maintain the conductivity new carriers should be created in the discharge together with increasing of the charge of existing carriers. This process results in the appearing and growth of metastable substance particles and, therefore, is very important for the experimental ball lightning modeling.
2.3 Dynamic state of excited metastable substance
In  it was found that the metastable substance of the erosive discharge jet can be at a dinamic state. This state is characterized by the interchange process which represent, in this case, a complex of energy-mass transfer phenomena in the form of wave-transport fluxes with preferential direction along the jet.
For existance of the metastable phase a relatively stable spatial charges separation is necessary. In general, systems of fields preventing the charges from recombination need not necessarily be of the stationary wave character. It may be a travelling wave provided that the separated charges are frozen into the corresponding regions of the transport wave field.
In particular, for metastable substance on the base of ionized heavy particles in electronegative mediums (gases, aerosols, liquids) the following situation is possible. If mobilities of large charge heavy particles (e.g. multiply charged ions) and of small particles (electrons) are different, then, the velocity lag of the latters together with the charge trapping lead to the charges separation which is necessary for the metastability. Stability of this (avalanche) charge separation is directly determined by the mobilities difference and by the effect of an external force stimulating the metastable substance motion. The mobilities difference may be connected with onset of oscillations in system of particles of only one sign.
2.4 Excitation of the substance by ablation roughing of the particles
Under the interchange conditions powerful energy fluxes act on the heavy
particles surface resulting in their ionization. At the dynamic state of
the metastable substance the torn off electrons move away from the particles,
so the quasineutrality condition is not satisfied on the particle surface,
which involve them in the radiation energy exchange. In the critical mode,
when the mobility of the particles is directly related with their charges,
the most heavily ionized particles, moving faster than the others, outrun
the energy bunch that determine the conic form of the flux. Energy transfer
along the bunch motion direction under condition of the conic form of the
flux serves as energy pumping and increases ionization degree of particles
at the end of the jet. Then, the jet end detaches and forms a new bunch
with higher specific energy of the particles, etc. This process may occur
in the form of consequent detachment and disintegration of the bunchs.
3 Experimental modeling of the ball lightning
3.1 Experimental setup
The experimental setup consists of a pulse storage capacitor C0 = 0.8mF x 5kV, inductance L = 40mH 7.6mH, integrated with pulse ignition transformer, and current limiting resistor R = 0400W. We used a camcoder Sony DCR-TRV11E, sensitive in the near infra-red range, for videotape recording.
Dischargers were made up of polyethylene tube of dimension-types (din x dout) 1.35mm x 8.65mm and 20mm x 25mm with symmetrically installed electrodes; for dischargers of the greater diameter the electrodes have on their face cylindrical inserts of polymethylmethacrylate 10mm long with diameter 16.4mm.
3.2 Discharge modes and autonomous objects characteristics
To obtain autonomous objects we always choose sufficiently low discharge voltage, so that soon after the beginning the discharge go into the critical mode main signs of which are large voltage drop on the discharger, increasing of the discharge duration and breaking of the current before objects coming out.
Non-compliance with these conditions results in ejection of substance without signs of completeness of the all process stages. For the tube of the small diameter at R=400W, U0=2.5kV we observed by sight an ejection of several tens of low brightness small objects with decreased drop velocity. The video recording (fig.3) shows the ejection of a thin jet which diverges then to the several liters of brightly luminous substance. As the luminous volume expand, it disintegrates on parts of irregular or ball shapes which turn then into dropping sparks. Total mass of the ejected substance is ~20mg. The residues constitute loose pieces of the heavily dispersed polymer containing smallest balls of the electrode material iron.
When decreasing the initial voltage to 1.8kV and placing into the 6mm interelectrode channel a piece of copper wire with diameter ~0.1mm, shaped as a 5mm long five-turn spiral of diameter 1.2mm, the discharge switching-off voltage was ~1.2kV. After formation of a small hole a luminous ball 5-10cm in diameter appears, which multitude of small objects 1-3mm in diameter fly out from (see fig.4).
On the first meter of the trajectory they slow down to ~2m/s, float in the air, can burn through foil and guide in several centimeters from the wall. If breaks of current occur in the discharge (that happen very rarely), then instead of the great ball an autonomous object 3-6mm in diameter come out, which fly several meters, can burn through foil and carbonize wooden surfaces. Their residues represent fragile dielectric plates which may be attracted by a magnet.
Discharge in the tube of the larger diameter with a band over the electrodes, at minimal voltage ensuring the break of the tube, results in appearance of luminous toroidal objects (fig.5) or large ball-like objects of irregular shapes (fig.6) with the luminescence time up to 120 ms, which leave behind a puff of dove-colored smoke.
To increase amount of the metal in the aerogel the discharge process was divided into two consecutive discharges. At the first one the capacitor C0=0.75mF at U0=4kV were discharged without current-limiting elements on discharger with copper foil 0.02mm thick placed on the tube inner surface which short-circuit the electrodes. At second discharge applying the voltage results in smooth increasing of the current followed by burn-through development (fig.7).
The autonomous objects were released not only through the lateral wall of the tube, but also by ejection of a metal plug. For example consider the discharge in the smaller diameter tube 47mm long. Cathode in the form of copper wire 1.4mm in diameter was embedded into the tube channel on 20 mm. At distance of 3mm from the inner end of the cathode we place a piece of the same wire of length 4mm. On the polyethylene tube end the piece of a metal tube of 8.5mm in inner diameter anode was mounted. The whole of the polyethylene tube were squeezed by a dielectric band, and a piece of copper wire 25mm long and 0.08mm in diameter was placed in the channel between the plug and the anode. At the discharge with initial voltage U0= 1.5kV through the inductance L=0.72mH, right after the residue of the plug, ejected from the channel with a large velocity, an autonomous objects flied out which exploded with formation of a plasmoid with diameter ~0.3m at the distance of ~0.5m from the discharger (fig.8).
4 Penetrating of autonomous objects through the wall without destroying it.
Usually, the ejection of plasma formations were accompanied by a loud flap and by destroying of the tube, made up of the polyethylene which under standard conditions is in the vitreous state. In some cases the objects ejection was soundless, with burn-off of the outlet and, sometimes, with formation of several outlets. By varying discharge parameters we succeeded to find a regime when the objects penetrated through the wall without visible traces of its destruction.
Over the electrodes of the discharger made up from the tube of the larger diameter a band was placed which makes the inner chamber to be totally hermetical. With the current limiting resistor R=44W, we looked up the maximal voltage value U0 at which the discharger chamber remained hermetical after the discharge. To increase this value the discharge was initiated by a corona discharge rather then by a breakdown.
Videotape recording show that after termination of all the stage of the burn-through process the tube become swollen due to excessive internal pressure and take a barrel-like shape. Inside the tube a weak luminescence remains, which then terminates abruptly. At the moment of the luminescence termination several luminous autonomous objects ~1mm in diameter appears outside of the tube, accompanied by a low short crackle (fig.9).
During the several frames the objects were flying or floating and then
dropped. The objects which dropped on the table surface made a few jumps
and disappeared. The tube remained hermetical. We failed to find on the
tube surface any traces of passing of the objets. Mechanism of the objects
formation  and the penetration through the polymer in the vitreous state
represents a self-focusing interchange ejection from the active plasma
medium into the dielectric and is connected with moving of metallic particles
[13,14] through the electronegative viscous liquid and their excitation
under influence of the radiation.
Thus, the method developed by us allows to create the energy-containing long-living autonomous objets. The best of obtained by us objects, which can be considered as analogs of the ball lightning, have the following characteristics: the diameter less then 1cm, the life time ~1s, the energy density ~100J/cm3; these objets float at the atmosphere, burn through the foil, can guide along the wall.
Appearance and existence of the objects may be described by the following scheme: