rus
Issue #5/2024
P. P. Maltsev
Pulsed Optical and X-ray Radiation of Fractals: Review of Hypotheses. Part I. Micro Runaway Breakdown
Pulsed Optical and X-ray Radiation of Fractals: Review of Hypotheses. Part I. Micro Runaway Breakdown
DOI: 10.22184/1993-7296.FRos.2024.18.5.358.374
Institute of Microwave Frequencies of the Russian Academy of Sciences, Moscow, Russia
The article presents the study results of the breakdown of fractals of the nano-sized aluminum droplets on the polymer filaments made of carbon benzene rings under a sudden voltage (discharge) of 1.6 kV cm−1 that is similar in magnitude to the electric field of 2.16 kV cm−1 required for the occurrence of micro-breakdown with the runaway electrons during the high-altitude lightning discharges. For the ordinary air breakdown, a voltage of 1–30 kV per centimeter is required. The photographs of radiation shapes in the optical spectral region for two types of breakdowns are provided. The possible reverse of the Doppler effect and Cherenko radiation on the fractal metamaterials is discussed.
Institute of Microwave Frequencies of the Russian Academy of Sciences, Moscow, Russia
The article presents the study results of the breakdown of fractals of the nano-sized aluminum droplets on the polymer filaments made of carbon benzene rings under a sudden voltage (discharge) of 1.6 kV cm−1 that is similar in magnitude to the electric field of 2.16 kV cm−1 required for the occurrence of micro-breakdown with the runaway electrons during the high-altitude lightning discharges. For the ordinary air breakdown, a voltage of 1–30 kV per centimeter is required. The photographs of radiation shapes in the optical spectral region for two types of breakdowns are provided. The possible reverse of the Doppler effect and Cherenko radiation on the fractal metamaterials is discussed.
Теги: надповерхностное высокопроводящее состояние плазма полимерные нити из волокна ароматического полиамида фракталы из наноразмерных капель алюминия
Pulsed Optical and X-ray Radiation of Fractals:
Review of Hypotheses. Part I. Micro Runaway Breakdown
P. P. Maltsev
Institute of Microwave Frequencies of the Russian Academy of Sciences, Moscow, Russia
The article presents the study results of the breakdown of fractals of the nano-sized aluminum droplets on the polymer filaments made of carbon benzene rings under a sudden voltage (discharge) of 1.6 kV cm−1 that is similar in magnitude to the electric field of 2.16 kV cm−1 required for the occurrence of micro-breakdown with the runaway electrons during the high-altitude lightning discharges. For the ordinary air breakdown, a voltage of 1–30 kV per centimeter is required. The photographs of radiation shapes in the optical spectral region for two types of breakdowns are provided. The possible reverse of the Doppler effect and Cherenko radiation on the fractal metamaterials is discussed.
Keywords: fractals from the nano-sized aluminum droplets, polymer filaments made of aromatic polyamide fiber, plasma, off-surface highly conductive condition
Article received: 11.06.2024
Article accepted: 11.07.2024
Runaway breakdown
The runaway breakdown was first theoretically predicted in the work of A. V. Gurevich, G. M. Milikha and R. A. Russell-Dupré (1992) [1]. This hypothesis is based on the peculiar interaction of the high-energy particles with the matter.
The runaway breakdown (RB) is related to the generation of secondary electrons occurred due to the ionization of neutral molecules by the high-energy runaway particles [2]. Although the bulk of secondary electrons have low energies, the electrons with a sufficiently high energy ε0 > εс can also be produced. Such electrons will also become runaway, i. e. they will be accelerated by the field and, in turn, will be able to generate particles with ε0 > εс during ionization. As a result, an exponentially growing avalanche of runaway electrons appears.
A large number of low-energy electrons are generated together with them that ultimately leads to the electrical breakdown of the matter. It is important that the runaway breakdown occurs in a relatively weak field Е > Ес that is by an order of magnitude lower than the threshold field of ordinary breakdown Еth. For example, in air at the atmospheric pressure, Еth is equal to 23 kV / cm, and Ес is equal to 2.16 kV / cm [2, 3].
However, to achieve the runaway breakdown, it is not enough to fulfill only one condition Е > Ес. It is necessary to have the seed high-energy electrons with an energy exceeding the critical runaway energy ε0 > εс > (0.1–1 MeV). It is even more important that the spatial size of the constant electric field in matter L should significantly exceed the specific length of the exponential growth of a runaway electron avalanche lа: L > lаa. Last value in the gaseous media turns out to be very significant that is mainly makes it difficult to actually implement the effect under consideration in the laboratory conditions. For example, in air at the atmospheric pressure lа is equal to 50 m.
However, in a thunderous atmosphere the situation is significantly different. In such a situation, the typical dimensions of clouds L are always much larger than lа. The high-energy seed electrons are also always available, since they are effectively generated by the cosmic rays (the flux density of secondary cosmic ray electrons with the energy E > 1 MeV of the order of 103 particles (m2s)–1). Therefore, the runaway breakdown in the thunderclouds turns out to be quite possible when the electric field reaches the value of Ес. As the measurements show, such fields are indeed observed. The runaway breakdown apparently plays a decisive role in the discovered phenomena, such as the giant high-altitude discharges between the thunderclouds and ionosphere (“Sprite”), accompanied by the powerful bursts of γ-radiation and X-ray radiation.
Certain attention should be paid to the special aspect of the physical essence of these processes. The atmosphere is a very dense medium, therefore, the free path length of both neutral molecules and thermal electrons and ions is only thousandths of a millimeter, and the lifetime of free electrons is tens of nanoseconds. Despite this fact, in a relatively weak electric field, the giant macroscopic (kilometer-long and even many-kilometer-long) processes occur, being determined by the purely kinetic effects.
Model of the RB high-altitude
discharge [2]
The need for the RB occurrence of a constant electric field that develops a significant asymmetry of the distribution function in the region ε0 > εс, also significantly distinguishes the runaway breakdown from other mechanisms of electrical matter breakdown.
It was assumed that both the electric field E and the flow of high-energy seed electrons are homogeneous in space. Moreover, the high-energy seed electrons can be rare. However, the last condition is not met. Therefore, let us consider how the runaway breakdown generated by one high-energy seed electron is developed. Let s be the motion direction of the high-energy electron, coinciding with the direction of the electric field E. The runaway breakdown then develops not only in the direction s, but also in the orthogonal plane r.
Thus, when the electric field E in the thundercloud reaches the value Ес, the RB process can develop. Moreover, since the secondary electrons of cosmic rays have an energy of up to 30 MeV and, due to the nuclear scattering, move in all directions, the breakdown can develop in any direction depending on the sign of the electric field, both down to the Earth and up to the ionosphere. The main role in this case is played by the possible occurrence of the required electric field that depends on the relations between the field E generation and relaxation processes.
It is normal to distinguish between two mechanisms for an electric field generation. The first one is the usual smooth field increase inside and at the boundaries of clouds due to the impact of atmospheric winds, gravity and capture of the charged particles by the water droplets, ice particles, and aerosols. The typical time of this process is about 1–10 min. The second mechanism is a sharp change in charge in the cloud due to a powerful electrical discharge to the Earth. The typical time of this process is milliseconds.
While comparing the typical times of these processes with the relaxation time, it is established that only in the second case is it possible for the field Е to significantly exceed Ес. Moreover, in the region of high altitudes (z ≥ 20–50 km), due to the rapid field relaxation, the RB conditions can only be met for a fairly short period of time Δt < 10 s.
An example of such a high-altitude discharge from the thundercloud into the ionosphere is shown in Fig. 1. The discharge duration is 10–200 ms. The height range is 25–100 km, the horizontal length is 10–50 km. The peak glow intensity occurs at the altitudes of 50–60 km. The total volume of the emitting region is usually more than 1 000 km3, and the radiation brightness is 10–100 kilo-Rayleigh (Rayleigh is a non-system unit of measurement used in the foreign literature, 1 Rayleigh = 106 photons (cm2s)−1). A millisecond radiation burst with the exceptionally high brightness stands out against the average background (about (1–5) 103 kilo-Rayleigh). The frequency of positive discharges is 0.3 s.
An important feature of the critical RB field is that it is decreased exponentially quickly at a height. Moreover, the air conductivity σ at the altitudes above 20–30 km is very high, so that the constant electric field at the altitudes of 20–50 km disappears in 10 s or even less due to polarization. Therefore, in a quasi-stationary state, the field is almost absent (E ≈ 0).
However, after a strong positive discharge to the Earth (the positive lightning transfers a charge of up to 100 C or more), the balance is disrupted and the field E may appear for a short period of time in a large spatial region significantly exceeding the critical one (Fig. 2). The electric field is directed towards the Earth, i. e. it accelerates the electrons towards the ionosphere. The flux of seed secondary electrons from the cosmic rays over a large discharge area (S ≥ 100 km2) is rather high, and even in a time of about 1 ms their total number can be 106–107.
The simplest model of such a system is shown in Fig.2. In a cloud with a diameter of 10 km there is a layer of 100 C positive charge C at an altitude of 18 km, and a relevant layer of negative charge is located at an altitude of 5 km. The electric field outside the cloud is screened by a polarization-induced negative charge located at an altitude of 25 km, and a positive charge at the lower ionosphere boundary at an altitude of 70 km. Due to the shielding, the field at an altitude of z > 25 km is almost absent: E = Et + EP ≈ 0.
As a result of a positive discharge Q inside the cloud, the field ET disappears, and a significant electric field EP remains in the region between the upper boundary of the cloud and the ionosphere. Its distribution along z on the system axis 10 μs after the discharge is shown in Fig. 3. It can be seen that in a large height region (from 20 km and down to the lower ionosphere), the field E exceeds the minimum runaway breakdown field. For the occurrence of a polarization field that compensates E in the altitude region z ≤ 50 km, about several seconds are required. During this period of time, it is possible to obtain occurrence of a giant high-altitude discharge caused by the runaway breakdown.
The number of typical ionization lengths that determine the exponential RB growth, is equal to L / la. When the RB is commenced at an altitude of 20 km, the value of this parameter is quite high: L / la ≥ 20–40. Due to the exponential growth of the avalanche and the large number of seed electrons, the total number of high-energy electrons developed the discharge at the height of about 50 km can reach very large values of 1016–1020. Moreover, due to the diffusion expansion of the beam, the width of the RB discharge region at a height of 40–60 km reaches 30 km.
Model of the RB optical radiation [2]
When the energetic electrons move through the air, the efficiency of optical radiation caused by them in various light ranges is known. Under the conditions of εe ≈ 0.1–10 MeV, it is almost independent of the energy of high-velocity electrons. This makes it possible to quite accurately determine the runaway discharge radiation at various heights [2].
Moreover, the blue radiation (Blue Jet) dominates at an altitude of up to 50 km, and red radiation (Red Sprite) dominates at the higher altitudes [2, 4]. This phenomenon is observed in the Sprite high-altitude discharges (Fig. 4 and Fig. 1). At the ionospheric altitudes, the discharge is blurred due to the diffuse scattering of the beam.
Let us note one important feature [2]. The electric field E significantly exceeds the minimum field Ec near the thundercloud (at the altitudes z ≈ 15–25 km) and far from it (at the altitudes z ≈ 35–50 km). At first, a decrease in the field E, determined by an increase in the distance from the charge, prevails, and then an exponential drop in the atmospheric density dominates, while greatly reducing the value of Ec.
Thus, there are somewhat two region (near and far) where the runaway breakdown can be effectively developed. In the intermediate region (z ≈ 30–35 km) it develops only at especially large values of the released charge Q. The given feature is always qualitatively available; it slightly depends on the selected model.
The radiation caused by a beam of high-energy electrons can create the millisecond pulses with gigantic intensity, such as several mega-Rayleigh (Fig. 5). The much longer portion of the radiation (several tens of milliseconds) is generated by the slower electrons and has an intensity of tens of kilo-Rayleigh. The calculation results are in accordance with the observational data [2].
It should be noted that the model proposed in [2] for explaining the optical radiation of the Sprite discharge and based only on the RB, is not the only one. Other mechanisms are also possible: breakdown in the radiation field generated by a super-powerful intercloud discharge, breakdown in a quasi-static field, or their combination with the RB. The influence of meteors on the Sprite generation is also noted.
However, an important additional argument in favor of the direct connection of high-altitude discharges with the RB is the observed intense pulses of X-ray and gamma radiation [2].
The type of optical radiation from the high-altitude discharge can be explained on the analogy with the Huygens waves: a spherical front of the light wave emanates from each point along the motion path of a high-energy particle (cosmic rays) while propagating through the medium at the speed of light, and each subsequent spherical wave is emitted from the next point along the motion path of the particle.
The optical radiation from the Sprite high-altitude discharges (Red Sprite) has the shape of a cone (Fig. 1). However, there is a peculiarity, since the cone of radiation is predominantly directed towards the source of high-energy seed particles (cosmic rays), i. e. it is a reciprocal vector to the direction of particle propagation, rather than along the flow of particles towards the Earth.
Anomalous X-ray bursts of the RB [2]
According to the theory, the X-ray bursts [5] are associated with the multiple micro runaway breakdowns (MRB), occurring in the vast areas of about several square kilometers [2]. Namely, since the thunderclouds have a plane-layered structure, the average electric field in them is close in direction to the vertical z and each secondary electron of cosmic rays generates an avalanche of runaway electrons in the thundercloud. In this case, the number of high-velocity electrons is increased greatly. This process, called MRB, is responsible for the observed X-ray burst.
The calculation results of intensity and spectrum of X-ray radiation during the MRB are stable [2]. It always has a significant maximum value in the region of 50–60 keV and quickly decreases both to the region of low energies (due to the photoionization) and to the region of high energies of 100–150 keV (due to the Compton losses). As for the spatial distribution of the X-ray radiation intensity, it reaches a maximum value in the vicinity of the electric field maximum – the shift of the X-ray radiation maximum is about 100–200 m in the direction of electron motion.
It is very important that far from the maximum, the X-ray radiation intensity is decreased greatly. Already at a distance of about 1–1.5 km from the maximum of the electric field, it is almost indistinguishable from the background.
Two conclusions significant for observation follow from the calculation results of anomalous X-ray bursts caused by the MRB:
the spectrum has a standard form with a typical maximum in the region of 50–60 keV;
an intense radiation can be observed only within 1–1.5 km at a height from the electric field maximum.
Since, according to the numerous measurement data, the values |E|≈Ec are achieved in the thunderclouds only at the heights z ≥ 4 km. It means that the X-ray radiation from the MRB can actually be observed only at z ≥ 2.5–3 km.
Both conclusions are confirmed by the observational data [2]. It should also be noted that, according to the calculations, a noticeable increase in the number of high-velocity electrons and the X-ray radiation generated by them occurs already in the pre-breakdown conditions as the field E approaches Ec (more precisely, at E > 0.95 Ec).
The critical field voltage Ec is decreased exponentially with the height: z = 6.3 km – field Ec = 100 kV / m; z = 11 km – field Ec =50 kV / m.
The atmospheric conductivity σ is determined by the air ionization by cosmic rays. In the presence of clouds and precipitation near the Earth’s surface (at an altitude of up to 2 km), a significant contribution is made by the radiation of radioactive elements. In the case of clear weather, the ion concentration is about 103 cm−3 that corresponds to the relaxation time of the electric field τg = (4πσ)–1 ≈ 400 s. The conductivity is increased rapidly at the height due to a decrease in the number of collisions υm as a result of decreased molecule concentration Nm. On the contrary, conductivity in the clouds may decrease due to the adhesion of charges to the water droplets and aerosols.
When the MRB occurs, the number of high-energy electrons and, accordingly, the number of ionization events in a layer with a thickness of about 100–500 m in the vicinity of the thunderstorm field maximum is increased greatly. Accordingly, the X-ray radiation intensity rises sharply. While using the experimental data on an increase in the X-ray radiation intensity by 102–103 times, it is possible to estimate the number of exponentials in real conditions in the accelerating layer z ≈ (5–6) la and, thus, determine the number of high-velocity electrons generated by one initial particle.
However, according to the RB theory [2], the distribution function of high-velocity electrons effectively increases with the decreasing electron energy not only at ε > εс, but also in the region of low energies ε < εс. All these electrons make a significant contribution to the atmospheric ionization, both high-energy (ε > εc ≈ 100 keV) and fairly low-energy (up to the maximum ionization cross section ε ≈ 0.1–1 keV). Due to this fact, the generation intensity of free electrons Qc in a layer with a thickness of about la at the boundary of the RB region is increased significantly.
It should be noted that all newly born electrons that initially have an energy of several electron volts, lose it in a very short period of time (~10–8 s) due to the inelastic interactions with air molecules. In addition, due to the triple collisions, the electrons quickly stick to the O2 and H2O molecules while forming the negative ions. The typical lifetime of a free electron at the heights of thunderclouds is only about 70–100 ns. Thus, the electrons disappear rather quickly. However, in the forced atmospheric layer the density of positive Ni+ and negative Ni– ions increases. It is the ions that determine the increased conductivity in the MRB region (although the electrons, despite their very short lifetime, can contribute to the increase in conductivity).
Under the MRB conditions in a thundercloud, over a period of several tens of seconds, the ion concentration is increased by one and a half to two orders of magnitude. A layer of anomalously high conductivity occurs that, naturally, should greatly affect the electrodynamic processes in the thundercloud.
The phenomenon of an anomalous increased conductivity at E > Ec was predicted in [1] in the form of a hypothesis. It is called the “fast charge transfer” in this work.
According to the calculations [2], the number of high-velocity electrons is changed by many times when the E / Ec ratio changes by only 10%. Then in the real conditions of the thundercloud, the ion concentration can change just as strongly, and, consequently, the anomalously high conductivity in the layer that arises at E ≈ Ec. Thus, the above estimates determine only the “average anomalous conductivity”. The real conductivity can have strong fluctuations, including any spatial fluctuations inside the layer, differing from the “average” ones by several times.
It should be noted that the above estimate of the increased conductivity should be considered only as the preliminary stage. For example, it did not consider the absorption of free ions by the water droplets, ice particles, aerosols in the thundercloud, or reverse processes. The role of collisions of high-velocity electrons with the same particles and the entire chain of changes in the comprehensive physical and chemical processes occurring in the clouds have not been studied. However, it is possible that all these processes are slower than the MRB.
Micro runaway breakdowns
and fractals [2]
The data show that within 100–500 ms prior to occurrence of the first lightning strike, an activity occurs in a wide area of clouds with the width of a kilometer or several kilometers.
This process can be represented as the slowly drifting multiple small discharge currents. Each radiation burst is localized within the resolution region of the interferometer (50 m), however, the centers of the radiation regions are constantly shifted. The activity of the bursts is increased until there is a strong burst of radiation. During this period of time, the radiation intensity initially continues to increase rapidly, and then, in a time of less than 1 ms, falls sharply.
Moreover, there is a sharp decrease in the electric field, apparently related to the first lightning strike. Such processes with a typical development time of about 0.1–1 s precede the main discharge that usually contains several lightning strikes both inside the clouds and on the Earth.
The lightning discharge associated with the development of a highly conductive channel and collection of the thundercloud electrical charge from an area of 1–100 km2 during the period of 1–10 s is a very comprehensive process that has been studied in numerous publications. Let us note only a few points related to the role of runaway breakdown.
This is, firstly, the above-mentioned abnormal increase in conductivity caused by the MRB. An increase in conductivity should naturally contribute to the rapid transfer process of electric charge distributed in the cloud. Although this increase in conductivity is rather high, “on average” it is apparently not enough to collect an electric charge. Secondly, it can be increased significantly due to the highly inhomogeneous random structure of the conducting area, noted above. The latter can contribute to the generation of efficient conductive channels.
It is possible that it is precisely this “fractal” nature of conductivity in the cloud layer prior to the first lightning discharge caused by the MRB that is partially reflected by the radio interferometric observations [2]. The possible occurrence of a fractal conductivity structure in the cloud, caused by small ordinary discharges should be noted.
Gamma radiation bursts of the RB [2]
The important role of RB in the high-altitude discharges can be confirmed by the intense bursts of gamma radiation observed on the Compton satellite [2]. It has been established that the gamma bursts [6] come from the Earth from the regions with the most intense thunderstorm formation [2]. The duration of gamma bursts is several milliseconds, the energy spectrum corresponds to the spectrum that appears during the RB.
It can be noted that, in comparison with the observations of X-ray radiation in a thundercloud, the gamma radiation spectrum is shifted towards the higher energies (its maximum is about 300–500 keV) [2].
This fact indicates a large electron acceleration length and significant losses of γ-radiation in the atmosphere that directly corresponds to the theory. The radiation intensity is very high (about 100 photons (cm2s)−1). The results of model RB calculations are in the sufficient compliance with the observational data of γ-bursts [2].
It should be emphasized that currently the unambiguous connection of high-altitude discharges with the powerful gamma radiation pulses is only a hypothesis, although a very plausible one. Any findings about the direct and simultaneous observations of optical and gamma radiation of the high-altitude discharges are not yet available.
Cherenkov radiation
In 1934 P. A. Cherenkov performed researches on the fluid luminescence under the influence of gamma radiation in the S. I. Vavilov’s laboratory and discovered weak blue radiation of an unknown nature [6]. Already the first experiments of P. A. Cherenkov, undertaken on the initiative of S. I. Vavilov, revealed a number of inexplicable features of such a radiation: the luminescence was observed in all transparent liquids, and the brightness depended little on their chemical composition and chemical nature, the radiation was polarized with the predominant direction of an electric vector along the particle propagation direction, while, in contrast to luminescence, there was no phenomenon of thermal or impurity quenching. Based on these findings, S. I. Vavilov made the fundamental statement that the discovered phenomenon was not luminescence, and the light was emitted by high-velocity electrons moving in the liquid.
The relativity theory states that no material body, including the high-velocity elementary particles with high energies, can move at a speed exceeding the speed of light in a vacuum. However, in the optically transparent media, the velocity of fast charged particles can be greater than the phase speed of light in this medium. Indeed, the phase speed of light in a medium cm is equal to the speed of light in a vacuum c divided by the medium refractive index n:
cm = c / n.
Moreover, for example, water has a refractive index of 1.33, and the refractive indices of various brands of optical glass range from 1.43 to 2.1. Accordingly, the phase speed of light in such media is 50–75% of the speed of light in the vacuum. Therefore, it turns out that the relativistic particles which speed is close to the speed of light in vacuum, move in such media with a speed exceeding the phase speed of light. The high-velocity electrons are knocked out of the atomic envelopes in the medium by gamma radiation.
If a particle moves faster than the speed of light in the medium, then it overtakes the light waves. The set of tangent lines to the spherical wave fronts drawn from a point passing through the particle generates a circular cone, namely the wave front of Cherenkov radiation.
The detectors that record Cherenkov radiation are widely used in the high-energy physics to record the relativistic particles and determine their velocities and directions of motion. If the mass of particles generating Cherenkov radiation is known, then their kinetic energy is immediately determined.
This phenomenon can be explained by analogy with the Huygens waves; a spherical front of the light wave emanates from each point along the motion path of a high-velocity particle, propagating through the medium at the speed of light, and each subsequent spherical wave is emitted from the next point along the path of the particle. The theoretical explanation of this phenomenon was given by I. E. Tamm and I. M. Frank in 1937.
In 1958, P. A. Cherenkov, I. E. Tamm and I. M. Frank were awarded the Nobel Prize in physics with the wording: “For the discovery and interpretation of the Cherenkov effect”. Manne Siegbahn from the Royal Swedish Academy of Sciences noted in his acceptance speech that “the discovery of phenomenon currently known as the Cherenkov effect provides an interesting example of how a relatively simple physical observation, if done correctly, can lead to the important discoveries and break new paths for further research”.
The Cherenkov-Vavilov radiation or Cherenkov radiation is a glow caused in a transparent medium by a charged particle moving at a speed exceeding the phase speed of light propagation in this medium.
The occurrence of Cherenkov radiation is similar to the occurrence of a shock wave in the form of a Mach cone from a body moving at the supersonic speed in a gas or liquid, for example, a cone-shaped shock wave in the air from a supersonic aircraft or bullet.
Conclusions: part 1
Under the conditions of micro runaway breakdown (MRB) in a thundercloud, the ion concentration is increased by one and a half to two orders of magnitude over several tens of seconds. A layer of anomalously high conductivity occurs that, naturally, should greatly affect the electrodynamic processes in the thundercloud. The phenomenon of an anomalously increased conductivity at E > Ec has been predicted and called the “fast charge transfer”. Let us note only a few points related to the role of runaway breakdown.
Firstly, it is the above-mentioned abnormal increase in conductivity caused by the MRB. An increase in conductivity should naturally contribute to the rapid transfer process of electric charge distributed in the cloud. Although this increase in conductivity is rather high, “on average” it is apparently not enough to collect an electric charge. Secondly, it can be increased significantly due to the highly inhomogeneous random structure of the conducting area (“fractals”) noted above. The latter can contribute to the generation of efficient conducting channels on the “fractals”.
It is possible that precisely this “fractal” nature of conductivity in the cloud layer prior to the first lightning discharge caused by the MRB is partially reflected by the radio interferometric observations. It is possible that the fractal conductivity structure in the cloud may occur due to the small ordinary discharges.
Since the thunderclouds have a plane-layered structure, the average electric field in them is close in direction to the vertical z and each secondary electron of cosmic rays generates an avalanche of runaway electrons in the thundercloud. In this case, the number of high-velocity electrons is increased greatly. This process, called MRB, is responsible for the observed X-ray burst.
Two conclusions significant for observation follow from the calculation results of anomalous X-ray bursts caused by the MRB:
the spectrum has a standard form with a typical maximum in the region of 50–60 keV;
an intense radiation can be observed only within 1–1.5 km at a height from the electric field maximum.
The optical radiation from the Sprite high-altitude discharges (Red Sprite) has the shape of a cone (Fig. 1). However, there is a peculiarity, since the cone of radiation is predominantly directed towards the source of high-energy seed particles (cosmic rays), i. e. it is a reciprocal vector to the direction of particle propagation, rather than along the flow of particles towards the Earth.
It should be noted that the Sprite high-altitude discharges observed in the upper atmosphere differ not only in the optical glow color at various altitudes (Red Sprite and Blue Jet), but also in the glow cone direction in relation to the flow of seed cosmic particles that depends on the properties of fractals in which the MRB occurs.
It should be emphasized that currently the unambiguous connection of high-altitude discharges with the powerful gamma radiation pulses is only a hypothesis, although a very plausible one. Any findings about the direct and simultaneous observations of optical and gamma radiation of the high-altitude discharges are not yet available. The RB existence is confirmed by the cyclotron researches, but with due regard to some limitations during the experiment.
The question arises about possible development of the nature-like “fractals” for the formation and study of high-altitude discharges in the laboratory conditions on Earth.
In the continuation of the review (Part II), the properties of metamaterials will be considered, and an analysis of publications that indicate the possibility of low–field emission of various semiconductor and polymer materials at the size of nanogreens or points 20–30 nm is carried out. We will show that for the manufacture of a source of high-energy seed fast electrons and the realization of breakdown on escaping electrons, it is sufficient to use a thread 30-50 m long with fractals of aluminum nanostructures (nanodrops) with a size of 10–30 nm.
Financing of the study
The study was supported by the grant provided by the Russian Science Foundation No. 24-29-00129,
https://rscf.ru/project/24–29–00129/.
AUTHOR
Maltsev Petr P., Doctor of Technical Sciences, Professor, Chief Researcher,
V. G. Mokerov Institute of Ultra High Frequency Semiconductor
Electronics of the Russian Academy of Sciences (IUHFSE RAS),
Moscow, Russia.
Review of Hypotheses. Part I. Micro Runaway Breakdown
P. P. Maltsev
Institute of Microwave Frequencies of the Russian Academy of Sciences, Moscow, Russia
The article presents the study results of the breakdown of fractals of the nano-sized aluminum droplets on the polymer filaments made of carbon benzene rings under a sudden voltage (discharge) of 1.6 kV cm−1 that is similar in magnitude to the electric field of 2.16 kV cm−1 required for the occurrence of micro-breakdown with the runaway electrons during the high-altitude lightning discharges. For the ordinary air breakdown, a voltage of 1–30 kV per centimeter is required. The photographs of radiation shapes in the optical spectral region for two types of breakdowns are provided. The possible reverse of the Doppler effect and Cherenko radiation on the fractal metamaterials is discussed.
Keywords: fractals from the nano-sized aluminum droplets, polymer filaments made of aromatic polyamide fiber, plasma, off-surface highly conductive condition
Article received: 11.06.2024
Article accepted: 11.07.2024
Runaway breakdown
The runaway breakdown was first theoretically predicted in the work of A. V. Gurevich, G. M. Milikha and R. A. Russell-Dupré (1992) [1]. This hypothesis is based on the peculiar interaction of the high-energy particles with the matter.
The runaway breakdown (RB) is related to the generation of secondary electrons occurred due to the ionization of neutral molecules by the high-energy runaway particles [2]. Although the bulk of secondary electrons have low energies, the electrons with a sufficiently high energy ε0 > εс can also be produced. Such electrons will also become runaway, i. e. they will be accelerated by the field and, in turn, will be able to generate particles with ε0 > εс during ionization. As a result, an exponentially growing avalanche of runaway electrons appears.
A large number of low-energy electrons are generated together with them that ultimately leads to the electrical breakdown of the matter. It is important that the runaway breakdown occurs in a relatively weak field Е > Ес that is by an order of magnitude lower than the threshold field of ordinary breakdown Еth. For example, in air at the atmospheric pressure, Еth is equal to 23 kV / cm, and Ес is equal to 2.16 kV / cm [2, 3].
However, to achieve the runaway breakdown, it is not enough to fulfill only one condition Е > Ес. It is necessary to have the seed high-energy electrons with an energy exceeding the critical runaway energy ε0 > εс > (0.1–1 MeV). It is even more important that the spatial size of the constant electric field in matter L should significantly exceed the specific length of the exponential growth of a runaway electron avalanche lа: L > lаa. Last value in the gaseous media turns out to be very significant that is mainly makes it difficult to actually implement the effect under consideration in the laboratory conditions. For example, in air at the atmospheric pressure lа is equal to 50 m.
However, in a thunderous atmosphere the situation is significantly different. In such a situation, the typical dimensions of clouds L are always much larger than lа. The high-energy seed electrons are also always available, since they are effectively generated by the cosmic rays (the flux density of secondary cosmic ray electrons with the energy E > 1 MeV of the order of 103 particles (m2s)–1). Therefore, the runaway breakdown in the thunderclouds turns out to be quite possible when the electric field reaches the value of Ес. As the measurements show, such fields are indeed observed. The runaway breakdown apparently plays a decisive role in the discovered phenomena, such as the giant high-altitude discharges between the thunderclouds and ionosphere (“Sprite”), accompanied by the powerful bursts of γ-radiation and X-ray radiation.
Certain attention should be paid to the special aspect of the physical essence of these processes. The atmosphere is a very dense medium, therefore, the free path length of both neutral molecules and thermal electrons and ions is only thousandths of a millimeter, and the lifetime of free electrons is tens of nanoseconds. Despite this fact, in a relatively weak electric field, the giant macroscopic (kilometer-long and even many-kilometer-long) processes occur, being determined by the purely kinetic effects.
Model of the RB high-altitude
discharge [2]
The need for the RB occurrence of a constant electric field that develops a significant asymmetry of the distribution function in the region ε0 > εс, also significantly distinguishes the runaway breakdown from other mechanisms of electrical matter breakdown.
It was assumed that both the electric field E and the flow of high-energy seed electrons are homogeneous in space. Moreover, the high-energy seed electrons can be rare. However, the last condition is not met. Therefore, let us consider how the runaway breakdown generated by one high-energy seed electron is developed. Let s be the motion direction of the high-energy electron, coinciding with the direction of the electric field E. The runaway breakdown then develops not only in the direction s, but also in the orthogonal plane r.
Thus, when the electric field E in the thundercloud reaches the value Ес, the RB process can develop. Moreover, since the secondary electrons of cosmic rays have an energy of up to 30 MeV and, due to the nuclear scattering, move in all directions, the breakdown can develop in any direction depending on the sign of the electric field, both down to the Earth and up to the ionosphere. The main role in this case is played by the possible occurrence of the required electric field that depends on the relations between the field E generation and relaxation processes.
It is normal to distinguish between two mechanisms for an electric field generation. The first one is the usual smooth field increase inside and at the boundaries of clouds due to the impact of atmospheric winds, gravity and capture of the charged particles by the water droplets, ice particles, and aerosols. The typical time of this process is about 1–10 min. The second mechanism is a sharp change in charge in the cloud due to a powerful electrical discharge to the Earth. The typical time of this process is milliseconds.
While comparing the typical times of these processes with the relaxation time, it is established that only in the second case is it possible for the field Е to significantly exceed Ес. Moreover, in the region of high altitudes (z ≥ 20–50 km), due to the rapid field relaxation, the RB conditions can only be met for a fairly short period of time Δt < 10 s.
An example of such a high-altitude discharge from the thundercloud into the ionosphere is shown in Fig. 1. The discharge duration is 10–200 ms. The height range is 25–100 km, the horizontal length is 10–50 km. The peak glow intensity occurs at the altitudes of 50–60 km. The total volume of the emitting region is usually more than 1 000 km3, and the radiation brightness is 10–100 kilo-Rayleigh (Rayleigh is a non-system unit of measurement used in the foreign literature, 1 Rayleigh = 106 photons (cm2s)−1). A millisecond radiation burst with the exceptionally high brightness stands out against the average background (about (1–5) 103 kilo-Rayleigh). The frequency of positive discharges is 0.3 s.
An important feature of the critical RB field is that it is decreased exponentially quickly at a height. Moreover, the air conductivity σ at the altitudes above 20–30 km is very high, so that the constant electric field at the altitudes of 20–50 km disappears in 10 s or even less due to polarization. Therefore, in a quasi-stationary state, the field is almost absent (E ≈ 0).
However, after a strong positive discharge to the Earth (the positive lightning transfers a charge of up to 100 C or more), the balance is disrupted and the field E may appear for a short period of time in a large spatial region significantly exceeding the critical one (Fig. 2). The electric field is directed towards the Earth, i. e. it accelerates the electrons towards the ionosphere. The flux of seed secondary electrons from the cosmic rays over a large discharge area (S ≥ 100 km2) is rather high, and even in a time of about 1 ms their total number can be 106–107.
The simplest model of such a system is shown in Fig.2. In a cloud with a diameter of 10 km there is a layer of 100 C positive charge C at an altitude of 18 km, and a relevant layer of negative charge is located at an altitude of 5 km. The electric field outside the cloud is screened by a polarization-induced negative charge located at an altitude of 25 km, and a positive charge at the lower ionosphere boundary at an altitude of 70 km. Due to the shielding, the field at an altitude of z > 25 km is almost absent: E = Et + EP ≈ 0.
As a result of a positive discharge Q inside the cloud, the field ET disappears, and a significant electric field EP remains in the region between the upper boundary of the cloud and the ionosphere. Its distribution along z on the system axis 10 μs after the discharge is shown in Fig. 3. It can be seen that in a large height region (from 20 km and down to the lower ionosphere), the field E exceeds the minimum runaway breakdown field. For the occurrence of a polarization field that compensates E in the altitude region z ≤ 50 km, about several seconds are required. During this period of time, it is possible to obtain occurrence of a giant high-altitude discharge caused by the runaway breakdown.
The number of typical ionization lengths that determine the exponential RB growth, is equal to L / la. When the RB is commenced at an altitude of 20 km, the value of this parameter is quite high: L / la ≥ 20–40. Due to the exponential growth of the avalanche and the large number of seed electrons, the total number of high-energy electrons developed the discharge at the height of about 50 km can reach very large values of 1016–1020. Moreover, due to the diffusion expansion of the beam, the width of the RB discharge region at a height of 40–60 km reaches 30 km.
Model of the RB optical radiation [2]
When the energetic electrons move through the air, the efficiency of optical radiation caused by them in various light ranges is known. Under the conditions of εe ≈ 0.1–10 MeV, it is almost independent of the energy of high-velocity electrons. This makes it possible to quite accurately determine the runaway discharge radiation at various heights [2].
Moreover, the blue radiation (Blue Jet) dominates at an altitude of up to 50 km, and red radiation (Red Sprite) dominates at the higher altitudes [2, 4]. This phenomenon is observed in the Sprite high-altitude discharges (Fig. 4 and Fig. 1). At the ionospheric altitudes, the discharge is blurred due to the diffuse scattering of the beam.
Let us note one important feature [2]. The electric field E significantly exceeds the minimum field Ec near the thundercloud (at the altitudes z ≈ 15–25 km) and far from it (at the altitudes z ≈ 35–50 km). At first, a decrease in the field E, determined by an increase in the distance from the charge, prevails, and then an exponential drop in the atmospheric density dominates, while greatly reducing the value of Ec.
Thus, there are somewhat two region (near and far) where the runaway breakdown can be effectively developed. In the intermediate region (z ≈ 30–35 km) it develops only at especially large values of the released charge Q. The given feature is always qualitatively available; it slightly depends on the selected model.
The radiation caused by a beam of high-energy electrons can create the millisecond pulses with gigantic intensity, such as several mega-Rayleigh (Fig. 5). The much longer portion of the radiation (several tens of milliseconds) is generated by the slower electrons and has an intensity of tens of kilo-Rayleigh. The calculation results are in accordance with the observational data [2].
It should be noted that the model proposed in [2] for explaining the optical radiation of the Sprite discharge and based only on the RB, is not the only one. Other mechanisms are also possible: breakdown in the radiation field generated by a super-powerful intercloud discharge, breakdown in a quasi-static field, or their combination with the RB. The influence of meteors on the Sprite generation is also noted.
However, an important additional argument in favor of the direct connection of high-altitude discharges with the RB is the observed intense pulses of X-ray and gamma radiation [2].
The type of optical radiation from the high-altitude discharge can be explained on the analogy with the Huygens waves: a spherical front of the light wave emanates from each point along the motion path of a high-energy particle (cosmic rays) while propagating through the medium at the speed of light, and each subsequent spherical wave is emitted from the next point along the motion path of the particle.
The optical radiation from the Sprite high-altitude discharges (Red Sprite) has the shape of a cone (Fig. 1). However, there is a peculiarity, since the cone of radiation is predominantly directed towards the source of high-energy seed particles (cosmic rays), i. e. it is a reciprocal vector to the direction of particle propagation, rather than along the flow of particles towards the Earth.
Anomalous X-ray bursts of the RB [2]
According to the theory, the X-ray bursts [5] are associated with the multiple micro runaway breakdowns (MRB), occurring in the vast areas of about several square kilometers [2]. Namely, since the thunderclouds have a plane-layered structure, the average electric field in them is close in direction to the vertical z and each secondary electron of cosmic rays generates an avalanche of runaway electrons in the thundercloud. In this case, the number of high-velocity electrons is increased greatly. This process, called MRB, is responsible for the observed X-ray burst.
The calculation results of intensity and spectrum of X-ray radiation during the MRB are stable [2]. It always has a significant maximum value in the region of 50–60 keV and quickly decreases both to the region of low energies (due to the photoionization) and to the region of high energies of 100–150 keV (due to the Compton losses). As for the spatial distribution of the X-ray radiation intensity, it reaches a maximum value in the vicinity of the electric field maximum – the shift of the X-ray radiation maximum is about 100–200 m in the direction of electron motion.
It is very important that far from the maximum, the X-ray radiation intensity is decreased greatly. Already at a distance of about 1–1.5 km from the maximum of the electric field, it is almost indistinguishable from the background.
Two conclusions significant for observation follow from the calculation results of anomalous X-ray bursts caused by the MRB:
the spectrum has a standard form with a typical maximum in the region of 50–60 keV;
an intense radiation can be observed only within 1–1.5 km at a height from the electric field maximum.
Since, according to the numerous measurement data, the values |E|≈Ec are achieved in the thunderclouds only at the heights z ≥ 4 km. It means that the X-ray radiation from the MRB can actually be observed only at z ≥ 2.5–3 km.
Both conclusions are confirmed by the observational data [2]. It should also be noted that, according to the calculations, a noticeable increase in the number of high-velocity electrons and the X-ray radiation generated by them occurs already in the pre-breakdown conditions as the field E approaches Ec (more precisely, at E > 0.95 Ec).
The critical field voltage Ec is decreased exponentially with the height: z = 6.3 km – field Ec = 100 kV / m; z = 11 km – field Ec =50 kV / m.
The atmospheric conductivity σ is determined by the air ionization by cosmic rays. In the presence of clouds and precipitation near the Earth’s surface (at an altitude of up to 2 km), a significant contribution is made by the radiation of radioactive elements. In the case of clear weather, the ion concentration is about 103 cm−3 that corresponds to the relaxation time of the electric field τg = (4πσ)–1 ≈ 400 s. The conductivity is increased rapidly at the height due to a decrease in the number of collisions υm as a result of decreased molecule concentration Nm. On the contrary, conductivity in the clouds may decrease due to the adhesion of charges to the water droplets and aerosols.
When the MRB occurs, the number of high-energy electrons and, accordingly, the number of ionization events in a layer with a thickness of about 100–500 m in the vicinity of the thunderstorm field maximum is increased greatly. Accordingly, the X-ray radiation intensity rises sharply. While using the experimental data on an increase in the X-ray radiation intensity by 102–103 times, it is possible to estimate the number of exponentials in real conditions in the accelerating layer z ≈ (5–6) la and, thus, determine the number of high-velocity electrons generated by one initial particle.
However, according to the RB theory [2], the distribution function of high-velocity electrons effectively increases with the decreasing electron energy not only at ε > εс, but also in the region of low energies ε < εс. All these electrons make a significant contribution to the atmospheric ionization, both high-energy (ε > εc ≈ 100 keV) and fairly low-energy (up to the maximum ionization cross section ε ≈ 0.1–1 keV). Due to this fact, the generation intensity of free electrons Qc in a layer with a thickness of about la at the boundary of the RB region is increased significantly.
It should be noted that all newly born electrons that initially have an energy of several electron volts, lose it in a very short period of time (~10–8 s) due to the inelastic interactions with air molecules. In addition, due to the triple collisions, the electrons quickly stick to the O2 and H2O molecules while forming the negative ions. The typical lifetime of a free electron at the heights of thunderclouds is only about 70–100 ns. Thus, the electrons disappear rather quickly. However, in the forced atmospheric layer the density of positive Ni+ and negative Ni– ions increases. It is the ions that determine the increased conductivity in the MRB region (although the electrons, despite their very short lifetime, can contribute to the increase in conductivity).
Under the MRB conditions in a thundercloud, over a period of several tens of seconds, the ion concentration is increased by one and a half to two orders of magnitude. A layer of anomalously high conductivity occurs that, naturally, should greatly affect the electrodynamic processes in the thundercloud.
The phenomenon of an anomalous increased conductivity at E > Ec was predicted in [1] in the form of a hypothesis. It is called the “fast charge transfer” in this work.
According to the calculations [2], the number of high-velocity electrons is changed by many times when the E / Ec ratio changes by only 10%. Then in the real conditions of the thundercloud, the ion concentration can change just as strongly, and, consequently, the anomalously high conductivity in the layer that arises at E ≈ Ec. Thus, the above estimates determine only the “average anomalous conductivity”. The real conductivity can have strong fluctuations, including any spatial fluctuations inside the layer, differing from the “average” ones by several times.
It should be noted that the above estimate of the increased conductivity should be considered only as the preliminary stage. For example, it did not consider the absorption of free ions by the water droplets, ice particles, aerosols in the thundercloud, or reverse processes. The role of collisions of high-velocity electrons with the same particles and the entire chain of changes in the comprehensive physical and chemical processes occurring in the clouds have not been studied. However, it is possible that all these processes are slower than the MRB.
Micro runaway breakdowns
and fractals [2]
The data show that within 100–500 ms prior to occurrence of the first lightning strike, an activity occurs in a wide area of clouds with the width of a kilometer or several kilometers.
This process can be represented as the slowly drifting multiple small discharge currents. Each radiation burst is localized within the resolution region of the interferometer (50 m), however, the centers of the radiation regions are constantly shifted. The activity of the bursts is increased until there is a strong burst of radiation. During this period of time, the radiation intensity initially continues to increase rapidly, and then, in a time of less than 1 ms, falls sharply.
Moreover, there is a sharp decrease in the electric field, apparently related to the first lightning strike. Such processes with a typical development time of about 0.1–1 s precede the main discharge that usually contains several lightning strikes both inside the clouds and on the Earth.
The lightning discharge associated with the development of a highly conductive channel and collection of the thundercloud electrical charge from an area of 1–100 km2 during the period of 1–10 s is a very comprehensive process that has been studied in numerous publications. Let us note only a few points related to the role of runaway breakdown.
This is, firstly, the above-mentioned abnormal increase in conductivity caused by the MRB. An increase in conductivity should naturally contribute to the rapid transfer process of electric charge distributed in the cloud. Although this increase in conductivity is rather high, “on average” it is apparently not enough to collect an electric charge. Secondly, it can be increased significantly due to the highly inhomogeneous random structure of the conducting area, noted above. The latter can contribute to the generation of efficient conductive channels.
It is possible that it is precisely this “fractal” nature of conductivity in the cloud layer prior to the first lightning discharge caused by the MRB that is partially reflected by the radio interferometric observations [2]. The possible occurrence of a fractal conductivity structure in the cloud, caused by small ordinary discharges should be noted.
Gamma radiation bursts of the RB [2]
The important role of RB in the high-altitude discharges can be confirmed by the intense bursts of gamma radiation observed on the Compton satellite [2]. It has been established that the gamma bursts [6] come from the Earth from the regions with the most intense thunderstorm formation [2]. The duration of gamma bursts is several milliseconds, the energy spectrum corresponds to the spectrum that appears during the RB.
It can be noted that, in comparison with the observations of X-ray radiation in a thundercloud, the gamma radiation spectrum is shifted towards the higher energies (its maximum is about 300–500 keV) [2].
This fact indicates a large electron acceleration length and significant losses of γ-radiation in the atmosphere that directly corresponds to the theory. The radiation intensity is very high (about 100 photons (cm2s)−1). The results of model RB calculations are in the sufficient compliance with the observational data of γ-bursts [2].
It should be emphasized that currently the unambiguous connection of high-altitude discharges with the powerful gamma radiation pulses is only a hypothesis, although a very plausible one. Any findings about the direct and simultaneous observations of optical and gamma radiation of the high-altitude discharges are not yet available.
Cherenkov radiation
In 1934 P. A. Cherenkov performed researches on the fluid luminescence under the influence of gamma radiation in the S. I. Vavilov’s laboratory and discovered weak blue radiation of an unknown nature [6]. Already the first experiments of P. A. Cherenkov, undertaken on the initiative of S. I. Vavilov, revealed a number of inexplicable features of such a radiation: the luminescence was observed in all transparent liquids, and the brightness depended little on their chemical composition and chemical nature, the radiation was polarized with the predominant direction of an electric vector along the particle propagation direction, while, in contrast to luminescence, there was no phenomenon of thermal or impurity quenching. Based on these findings, S. I. Vavilov made the fundamental statement that the discovered phenomenon was not luminescence, and the light was emitted by high-velocity electrons moving in the liquid.
The relativity theory states that no material body, including the high-velocity elementary particles with high energies, can move at a speed exceeding the speed of light in a vacuum. However, in the optically transparent media, the velocity of fast charged particles can be greater than the phase speed of light in this medium. Indeed, the phase speed of light in a medium cm is equal to the speed of light in a vacuum c divided by the medium refractive index n:
cm = c / n.
Moreover, for example, water has a refractive index of 1.33, and the refractive indices of various brands of optical glass range from 1.43 to 2.1. Accordingly, the phase speed of light in such media is 50–75% of the speed of light in the vacuum. Therefore, it turns out that the relativistic particles which speed is close to the speed of light in vacuum, move in such media with a speed exceeding the phase speed of light. The high-velocity electrons are knocked out of the atomic envelopes in the medium by gamma radiation.
If a particle moves faster than the speed of light in the medium, then it overtakes the light waves. The set of tangent lines to the spherical wave fronts drawn from a point passing through the particle generates a circular cone, namely the wave front of Cherenkov radiation.
The detectors that record Cherenkov radiation are widely used in the high-energy physics to record the relativistic particles and determine their velocities and directions of motion. If the mass of particles generating Cherenkov radiation is known, then their kinetic energy is immediately determined.
This phenomenon can be explained by analogy with the Huygens waves; a spherical front of the light wave emanates from each point along the motion path of a high-velocity particle, propagating through the medium at the speed of light, and each subsequent spherical wave is emitted from the next point along the path of the particle. The theoretical explanation of this phenomenon was given by I. E. Tamm and I. M. Frank in 1937.
In 1958, P. A. Cherenkov, I. E. Tamm and I. M. Frank were awarded the Nobel Prize in physics with the wording: “For the discovery and interpretation of the Cherenkov effect”. Manne Siegbahn from the Royal Swedish Academy of Sciences noted in his acceptance speech that “the discovery of phenomenon currently known as the Cherenkov effect provides an interesting example of how a relatively simple physical observation, if done correctly, can lead to the important discoveries and break new paths for further research”.
The Cherenkov-Vavilov radiation or Cherenkov radiation is a glow caused in a transparent medium by a charged particle moving at a speed exceeding the phase speed of light propagation in this medium.
The occurrence of Cherenkov radiation is similar to the occurrence of a shock wave in the form of a Mach cone from a body moving at the supersonic speed in a gas or liquid, for example, a cone-shaped shock wave in the air from a supersonic aircraft or bullet.
Conclusions: part 1
Under the conditions of micro runaway breakdown (MRB) in a thundercloud, the ion concentration is increased by one and a half to two orders of magnitude over several tens of seconds. A layer of anomalously high conductivity occurs that, naturally, should greatly affect the electrodynamic processes in the thundercloud. The phenomenon of an anomalously increased conductivity at E > Ec has been predicted and called the “fast charge transfer”. Let us note only a few points related to the role of runaway breakdown.
Firstly, it is the above-mentioned abnormal increase in conductivity caused by the MRB. An increase in conductivity should naturally contribute to the rapid transfer process of electric charge distributed in the cloud. Although this increase in conductivity is rather high, “on average” it is apparently not enough to collect an electric charge. Secondly, it can be increased significantly due to the highly inhomogeneous random structure of the conducting area (“fractals”) noted above. The latter can contribute to the generation of efficient conducting channels on the “fractals”.
It is possible that precisely this “fractal” nature of conductivity in the cloud layer prior to the first lightning discharge caused by the MRB is partially reflected by the radio interferometric observations. It is possible that the fractal conductivity structure in the cloud may occur due to the small ordinary discharges.
Since the thunderclouds have a plane-layered structure, the average electric field in them is close in direction to the vertical z and each secondary electron of cosmic rays generates an avalanche of runaway electrons in the thundercloud. In this case, the number of high-velocity electrons is increased greatly. This process, called MRB, is responsible for the observed X-ray burst.
Two conclusions significant for observation follow from the calculation results of anomalous X-ray bursts caused by the MRB:
the spectrum has a standard form with a typical maximum in the region of 50–60 keV;
an intense radiation can be observed only within 1–1.5 km at a height from the electric field maximum.
The optical radiation from the Sprite high-altitude discharges (Red Sprite) has the shape of a cone (Fig. 1). However, there is a peculiarity, since the cone of radiation is predominantly directed towards the source of high-energy seed particles (cosmic rays), i. e. it is a reciprocal vector to the direction of particle propagation, rather than along the flow of particles towards the Earth.
It should be noted that the Sprite high-altitude discharges observed in the upper atmosphere differ not only in the optical glow color at various altitudes (Red Sprite and Blue Jet), but also in the glow cone direction in relation to the flow of seed cosmic particles that depends on the properties of fractals in which the MRB occurs.
It should be emphasized that currently the unambiguous connection of high-altitude discharges with the powerful gamma radiation pulses is only a hypothesis, although a very plausible one. Any findings about the direct and simultaneous observations of optical and gamma radiation of the high-altitude discharges are not yet available. The RB existence is confirmed by the cyclotron researches, but with due regard to some limitations during the experiment.
The question arises about possible development of the nature-like “fractals” for the formation and study of high-altitude discharges in the laboratory conditions on Earth.
In the continuation of the review (Part II), the properties of metamaterials will be considered, and an analysis of publications that indicate the possibility of low–field emission of various semiconductor and polymer materials at the size of nanogreens or points 20–30 nm is carried out. We will show that for the manufacture of a source of high-energy seed fast electrons and the realization of breakdown on escaping electrons, it is sufficient to use a thread 30-50 m long with fractals of aluminum nanostructures (nanodrops) with a size of 10–30 nm.
Financing of the study
The study was supported by the grant provided by the Russian Science Foundation No. 24-29-00129,
https://rscf.ru/project/24–29–00129/.
AUTHOR
Maltsev Petr P., Doctor of Technical Sciences, Professor, Chief Researcher,
V. G. Mokerov Institute of Ultra High Frequency Semiconductor
Electronics of the Russian Academy of Sciences (IUHFSE RAS),
Moscow, Russia.
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