rus
Issue #7/2024
P. P. Maltsev
Pulsed Optical and X-ray Radiation of Fractals: Review of Hypotheses. Part II. Micro-Breakdown of Fractals made of Metamaterials
Pulsed Optical and X-ray Radiation of Fractals: Review of Hypotheses. Part II. Micro-Breakdown of Fractals made of Metamaterials
DOI: 10.22184/1993-7296.FRos.2024.18.7.522.534
In the continuation of the review, the properties of metamaterials are 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.
In the continuation of the review, the properties of metamaterials are 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.
Теги: fractals from the nano-sized aluminum droplets off-surface highly conductive condition plasma polymer filaments made of aromatic polyamide fiber 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 II. Micro-Breakdown of Fractals made of Metamaterials
P. P. Maltsev
Institute of Microwave Frequencies of the RAS, Moscow, Russia
In the continuation of the review, the properties of metamaterials are 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.
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
Properties of metamaterials [7]
In 1962, V. G. Veselago systematically described the hypothesis about the unusual properties of “left-handed” media. In [7], in particular, it is shown that such medica have negative dielectric εm and magnetic μm permeability, and should also have a negative refractive index n.
A metamaterial is a composite material which properties are determined not so much by the properties of its constituent elements, but by an artificially developed periodic structure of macroscopic elements with the arbitrary dimensions and shape. An artificial periodic structure modifies the dielectric and magnetic permeability of the source material [7, 8].
Thus, the metamaterials are artificially generated and specially structured media with the electromagnetic properties that are difficult to achieve technologically or that do not occur in nature. The prefix “meta” is translated from Greek as “beyond” that allows us to interpret the term “metamaterials” as the structures which efficient electromagnetic properties go beyond the properties of constituent components.
The most famous example of a natural ENG medium (εm is negative) that can be either transparent or opaque to the electromagnetic waves depending on the excitation frequency ω, is plasma, the dielectric constant of which is determined according to the following formula in the absence of an external magnetic field:
εм(ω) = 1 − ωр2 / ω2,
where ωp is a parameter called the radial plasma frequency (radial frequency of plasma natural oscillations) that depends on the density, charge magnitude and mass of charge carriers.
Below the plasma frequency, the dielectric constant is negative and the electromagnetic waves cannot propagate due to the loss of transparency in the medium. At ω > ωp the value εm > 0 and electromagnetic waves can pass through the ionized medium. A well-known example of electromagnetic plasma is the Earth’s ionosphere, from which the low-frequency radiation is reflected (at ε(ω) < 0), and the high-frequency electromagnetic waves pass with little absorption.
Among the artificial SNG media (single negative) with negative εm (ENG, εm is negative), a system of thin metal wires arranged in parallel was one of the first to describe. Such a medium (as an artificial dielectric for microwave applications) was indicated in the work of John Brown back in 1953. He obtained the relation for the plasma frequency of a given metamaterial.
It was later confirmed by Walter Rothman who in 1961 demonstrated the possible application of multiple thin conductors to simulate plasma, since their efficient dielectric constant was expressed by the same formula. In particular, for a metastructure based on the aluminum conductors with a radius r = 1 μm and an interval between them a = 5 mm, the radial plasma frequency is approximately 8.2 GHz (Fig. 6a).
The seminal work [7] contained a theoretical description of the medium properties with simultaneously negative values of εm and μm, as well as a study of the solution of Maxwell’s equations for this case. When interpreting the Maxwell’s equations, V. G. Veselago was the first to use the expression for εm, μm < 0 as the refractive index n that was a rather unexpected logical method. While noting the hypothetical nature of the relevant medium, V. G. Veselago pointed out the indisputable fact that its existence is not excluded by the Maxwell’s equations, and theoretically analyzed the propagation process of electromagnetic waves in such media.
It should be noted that while propagating in the medium, the wave has two velocities, namely phase velocity Vph and group velocity Vgr. The phase velocity is the wave phase speed, for example, the maximum or minimum of the oscillatory process, and the group velocity is the speed at which the pulse envelope moves. They do not have to be identical and directed to the same side.
The energy flow carried by an electromagnetic wave is determined by the Umov–Poynting vector S, and, consequently, Vgr always generates a right-hand triple of vectors with the electromagnetic wave vectors E and H. Thus, for the “right-handed” media the phase and group velocities are always directed to the same side, and for the “left-handed” media the vectors Vgr and Vph are located in different directions, that is, these are the media with negative group velocity.
For the “left-handed” media, the wave vector of radiation k will be directed along the motion path of the particle υ, and the radiation cone will be directed back in relation to the particle motion, i. e., towards the source.
The beginning of the 2000s was rich in events in the field of metamaterial development with a negative refractive index of electromagnetic waves. The effect of negative refraction is due to the simultaneously negative values of dielectric and magnetic permeability (εm < 0 and μm < 0). Such materials are often called the double negative media (DNG). Until recently, this class of materials was represented only by the artificial structures. However, in 2006 it was found that the La2/3Ca1/3Mn3 crystals have a negative refractive index of electromagnetic waves at approximately 150 GHz.
Modern science has approached understanding the DNG media physics gradually. As judged by the available publications, the garland of the practical statement of a question related to the existence of waves with the negative group velocity should be given to Arthur Schuster, an English physicist (1851–1934). The conclusion that the negative group velocity is possible due to anomalous wave dispersion was confirmed in 1905 by Max Theodor Felix von Laue (1879–1960). In the same year, Pocklington once again showed in a short note that in a certain medium where a backward wave is possible, an activated source of oscillations generatesa wave with a group velocity directed away from the source, while its phase velocity is oriented towards it.
Let us note the consequences of the fact that in the left-handed media the phase velocity is opposite to the flow of energy. First of all, in the left-handed media the reversed effects will be observed: the Doppler effect and Cherenkov-Vavilov radiation!
For example, any change in the oscillation frequency due to the movement of a source or receiver is called the Doppler effect. Let the radiation receiver B moves with the speed V relative to the emitter A that emits the frequency. In this case, for the frequency perceived by the receiver due to the Doppler shift, the following expression can be obtained:
ω = ω0 ( 1 + р ( V / Vgr ).
In the “left-handed” medium (р = −1), the receiver will catch up with the wave points relevant to a specific phase. Moreover, in the formula, the velocities V and Vgr move in various directions. Therefore, due to the Doppler effect, in the “right-handed” medium an object approaching us will become more “blue”, while in the “left-handed” medium it will appear more “red”.
It can be assumed that this phenomenon is observed during the runaway breakdown in the high-altitude discharges of the Red Sprites (Fig. 1 and Fig. 4) under the influence of penetrating cosmic particles through the “left-handed” metamedium in the form of fractals.
Low-field emission of nanodots
Let us provide an analysis of publications that indicate the possible low-field emission of various semiconductor and polymer materials with the nanograin or nanotip dimensions of 20–30 nm.
It was shown in [9] that in the case of a positive bias on the probe (negative potential on the semiconductor), the electrons were emitted from protrusions on the semiconductor surface being the nanoobjects in nature (the protrusion tip size for emission could reach 10–20 nm).
The emission of electrons from a semiconductor occurs with the participation of (one or more) quantized electron energy levels in the near-surface area of the material, namely in the parts of the rough surface protrusions facing the probe.
Obviously, the main peak position is determined by the forbidden band gap of the semiconductor and the Fermi level position, as well as by the possible initial distortion of bands near the surface relevant to the electron enhancement mode of the semiconductor surface. The estimated linear dimensions of such quantum dots turn out to be in the range from 10 to 20 nm that is quite consistent with the analytical estimates for InSb.
The quantum dot, formed by the protruded part on the rough semiconductor surface acts as a kind of “filter” for the emission electron flow from the semiconductor into the vacuum and further to the tunnel microscope probe.
It was shown in [10] that the obtained low values of barriers for emission from the InSb and InAs micrograins suggest its low-field nature.
The current-voltage curves observed in relation to them indicate that the current is limited by the charge localized in the near-surface layer of the semiconductor.
A specific feature of InSb and InAs is the very small values of the effective mass m (light electrons, m ≈ 0.01m0) and energy Є (<0.2 eV) of electrons. This fact leads to the relatively large values of the de Broglie wavelength for the electron – λ = h(2m Є)–1/2 up to 30 nm (for other semiconductors it is about one nanometer).
The action area of the near-surface localized emission states should approximately correspond to the size λ. According to the experimental conditions, the emission surface area of the grain is ≈ 3 μm2. In this case, the volume of localized states in the micrograin is v ≈ 0–13 cm‑3, the concentration of localized emission centers is NS / v = (1017–1018) cm‑3, the average distances between the centers are (NS/v)–3 ≈ (10–30) nm.
In [11], a deviation from the Fowler-Nordheim formula for the field emission current from the nanoparticles was demonstrated when analyzing experimental data of the pointed field cathodes made of carbon nanotubes. It is noted that in order to obtain a current value during an experiment, the voltage must be at least 10 times greater, i. e. we observe not the field emission for the produced pointed field emission cathodes with a height reduced to the submicron dimensions, but the so-called low-field emission.
One of the reasons for the low-field emission is supposed to be a decrease in the electronic state density of the nanoparticle due to the size quantization of the spectrum. This will lead to a contact potential difference between the nanoparticle and the bulk substrate. The nanoparticle charge will then develop a field at the substrate surface near the nanoparticle junction with the bulk substrate that is sufficient for the electron tunneling into the nanoparticle through the vacuum. The external voltage will only change the motion path of the emitted electrons.
Another possible model is the surface layer deformation by the external electrical forces. Deformations in this case can be enhanced by the levers composed of nanoparticles.
The paper [12] demonstrated the capabilities of electrostatic AFM methods with a conducting probe for studying electrical specifications of the surface of polymer materials and changing the boundary conditions at the polymer-metal interface.
The thickness reduction of the dielectric polymer film leads to a situation when the charges concentrated near the boundaries of contact with metal electrodes begin to interact with each other while leading to a change in the shape of the potential barrier.
It was noted in [12] that the thin films of polyarylenephthalides (polymers with a wide forbidden band) with a submicron thickness become a current-carrying conductor with high electrical conductivity, comparable to the conductivity of some metals, not as a result of the doping procedure, but when two critical conditions are met:
the thickness of films made of such material must be less than a certain critical (nano-sized) thickness;
the availability of an initiating relatively small external influence or electric field.
Thus, the dimensions of 20–30 nm (nanograins, nanotips, nanoroughnesses and nanoislands) are one of the conditions for low-field emission occurrence in various semiconductor and polymer materials in the presence of bias voltage and pulsed voltage.
Low-field emission of fractals
Let us consider the study results of fractals made of the chains of irregular aluminum nanoislands (nanodroplets) with the dimensions of 30–1 000 nm deposited on an aramid polymer thread made of the fibers of carbon benzene rings [13–15].
The aluminum nanoislands (nanodroplets) were applied to an aramid thread (aromatic polyamide of the Rusar type) that was wound on a drum and processed in a vacuum installation for magnetron aluminum sputtering at the MIR‑2 process unit in the Research Institute of Elastomeric Materials and Products LLC.
To obtain the experimental samples, a polymer thread with a length of 30 m and a diameter of 1 000 µm is used. It is tightly wound with 137 turns on a cylinder (reel-drum) with a radius of 3.5 cm and a length of 13.7 cm [13] for the aluminum application.
During the metallization process, the following modes are set in the vacuum chamber:
The thread is an aromatic polyamide (aramid), where 85% of the amide bonds are attached directly to two benzene rings. The aromatic carbon ring, namely benzene (C6H6), is designated as a hexagon with an inscribed circle (its outer diameter is 0.28 nm), thereby emphasizing the absence of fixed double bonds and availability of a single electron cloud covering all six atoms of the carbon cycle. The chains of two benzene rings line up in a fiber through a chlorine compound, and the interweaving of several fibers generates aramid (Fig. 6, b). It should be noted that the radius of an aluminum atom is 0.143 nm (its diameter is 0.286 nm).
Thereupon, the properties of thread samples with the length of 1 cm have been studied.
The photographs of polymer threads with the chains of irregular aluminum nanoislands (nanodroplets) with the dimensions of 30–1 000 nm (Fig. 6b and Fig. 7) are made by the scanning electron microscope CAMSCAN–S4 with the energy-dispersive and wavelength-dispersive attachments: Oxford INCA Energy 350 and INCA Wave 700 (Cambridge, England) at the High Technology Center of the Synchrotron Shared Use Center of the Federal State Unitary Enterprise “Lukin Research Institute of Physical Problems” of the National Research Center “Kurchatov Institute” [13, 14].
Based on the analysis of images in Fig. 7, obtained by an electron microscope, it can be considered that the polymer thread made of aramid fibers (from carbon benzene rings) with the chains of irregular aluminum nanoislands (nanodroplets) does not have a regular topology and can be classified as the nature-like fractals (aluminum is indicated in red in Fig. 7a and in white in Fig. 7b).
It should be noted that in mathematics, the fractals are considered as the sets of points in the Euclidean space that have a metric dimension that is different from the topological one, therefore, they should be distinguished from other geometric figures limited by a finite number of links.
The natural objects (quasi-fractals) differ from the ideal abstract fractals due to the incompleteness and imprecision of structure repetitions.
The study of the electrical specifications of polymer threads was performed after formation of the indium contacts to the polymer threads with the chains of irregular aluminum nanoislands (nanoproplets); the current-voltage characteristics (CVC) of the samples were taken by a L2–56 curve tracer. In addition to the CVC, the sample resistance was also assessed using the L2–56 curve tracer by the slope of the current-voltage dependence curve. A Hewlett Packard 4284A LCR meter was used to estimate the capacitance.
When measuring the CVC of samples with a length of 10 cm and 1 cm, no current occurred when the voltage was changed to 12 V. It has been experimentally established that at the low constant voltages a polymer thread made of aramid fibers with the chains of irregular aluminum nanoislands is an insulator [13–15].
When a high voltage of up to 1.6 kV is smoothly applied (for 1 second) to a polymer thread with the nanoisland metallization by aluminum, there is no breakdown.
When a pulsed high voltage is applied to the thread, the situation is changed: an electrical discharge occurs and an off-surface highly conductive state is obtained above a polymer thread made of aramid fibers with the chains of irregular aluminum nanoislands, possibly in the resulting plasma. It has been experimentally established that when a voltage pulse of 1.6 kV is applied to the electrodes connected to a polymer thread with the length of 1 cm, an electrical discharge occurs.
Fig. 7a shows the aluminum nanoislands (nanodroplets) with the dimensions of 30–1000 nm that can unite several tens to hundreds of carbon benzene rings and develop the aluminum/carbon structures. In some part of such a structure, a “nanodot” can be formed, in which the conditions will be developed for the occurrence of low-field emission of electrons from the benzene rings when a pulsed voltage is applied to the polymer thread.
It should be noted that the distance “broken” by a spark in the air depends on the electric field strength at the electrode surface and their shape. For the spheres which radius is much larger than the discharge gap, it is considered equal to 30 kV per centimeter, and for the needles it will be 10 kV per centimeter [3].
The electrical strength of a gas strongly depends on its density (i. e., on pressure if the temperature is constant). In the case of small changes in gas temperature and pressure, the breakdown voltage is proportional to the gas density. Under the normal conditions, i. e. at a pressure of 0.1 MPa and at a temperature of 20 °C, the electrical strength of air at a distance between the electrodes of 1 cm is approximately 3.2 MV/m. The breakdown development depends on the homogeneity degree of the electric field in which the gas is broken down. If in a homogeneous field the field strength is constant, then in a significantly inhomogeneous field it is changed by several orders of magnitude along the field line [3].
The papers [14, 16] show the photographs of a cone-shaped discharge along a polymer thread with the length of 30 m and the chains of irregular aluminum nanoislands (nanodroplets) (Fig. 8a) that is similar to the optical radiation of micro runaway breakdown of a high-altitude discharge given in [2] (Fig. 8b), and not to the shape of the ordinary zigzag electric lightning over the Earth.
An experiment and photograph of an electric discharge in the direction of an electromagnetic wave propagation along a polymer thread made of aramid fibers with the aluminum nanoislands (thread length 30 m; electric field voltage E = 30 kV/m) were performed and made at a high-voltage stand of the All-Russian Electrotechnical Institute [16]. The experiment established that during the electrical breakdown in air, the polymer threads with nanoisland metallization by aluminum do not burn out.
It can be assumed that the occurrence of low-field electron emission on the long fibers of carbon benzene ring compounds under the pulsed voltage through the aluminum nanoislands (nanoproplets) leads to the plasma development and formation of an off-surface high-conducting state (OSHCS) that facilitates the occurrence of high-energy electrons at an applied high electrical voltage, capable of replacing the seed cosmic rays.
It should be noted that the formation of an off-surface high-conducting state (OSHCS) above the thread surface in the form of plasma preserves it, therefore, it does not burn out [13–15]. This state is similar to the anomalous increase in conductivity at Е > Ес that was called the “fast charge transfer” during the MRB in the high-altitude discharges in the papers [1, 2].
It has been experimentally established that the breakdown of a thread made of aramid fibers with the irregular chains of aluminum nanoislands under the room conditions is 1.6 kV/cm [13–15] that is even less than that required for the runaway breakdown (2.16 kV/cm) [2]. The lower breakdown voltage may influence the reduction of the exponential growth length of the runaway electron avalanche from a theoretical length of 50 m [2] to 30 m at a pressure of 1 atm [15, 16]. For reference, at a pressure of 1 atm, the threshold field for an ordinary breakdown is 23–30 kV/cm [2, 3].
The papers [13–15] show that the threads made of aramid fibers with the aluminum nanoislands with the dimensions of 10–1000 nm can have the properties of metamaterials and the plasma frequency value for the metamaterial under study is estimated at the level of 1–10 THz.
It can be assumed that the metamaterials based on the fractals of aluminum nanoislands are a source of high-energy seed fast electrons for the implementation of runaway breakdown in the laboratory conditions at the thread length of 30 m and an electric field strength of 30 kV/m.
Conclusions: part 2.
Hypothetically, it can be assumed that when a pulsed high voltage is applied to the polymer thread made of aramid fibers, consisting of benzene carbon rings, with the chains of irregular aluminum nanoislands (nanodroplets) (its dimensions are 10–100 nm), a fractal microbreakdown through plasma formed by the low-field electron emission occurs, with the generation of an off-surface high-conducting state (OSHCS) over the polymer thread.
It has been experimentally established that the micro breakdown of a fractal with the irregular chains of aluminum nanoislands on the aramid fiber threads is 1.6 kV/cm (under the room conditions) that is less than the estimated value for the micro runaway breakdown equal to 2.16 kV/cm. Thus, to produce a source of high-energy seed fast electrons and implement the runaway breakdown, it is sufficient to use a thread with the fractals of aluminum nanoislands (nanodroplets) with the length of 30–50 m.
The wave front of the high-altitude discharge propagation in the form of a cone directed to the source of cosmic radiation can only be implemented on the fractals made of metamaterials (having negative dielectric and magnetic constants), for example, the aluminum nanodroplets on the surface of polymer threads made of fibers of carbon benzene rings. The estimated value of the plasma frequency for the developed metamaterial is 1–10 THz.
The photograph of a cone-shaped micro breakdown of a fractal made of aluminum nanoislands (nanodroplets) along a polymer thread with the length of 30 m is similar in shape to the optical radiation of a micro runaway breakdown of a high-altitude discharge.
In addition, the high-altitude discharges observed in the upper atmosphere differ in the optical glow color at various altitudes due to the different types of fractals in which the MRB occurs: Red Sprites occur in the meta-medium, and Blue Jets are developed in the ordinary medium. As a result, the MRB differ in the luminescence cone direction in relation to the flow of seed cosmic particles during the MRB, i. e. the Doppler effect will be «reversed» for the Red Sprites on the metamaterial fractals.
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 use of developed fractals with the chains of irregular aluminum nanoislands (nanodroplets) on a polymer thread made of aramid fibers (based on the aromatic carbon rings – benzene) makes it possible to study simultaneously optical and X-ray radiation in the laboratory conditions on the Earth’s surface.
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/.
P. P. Maltsev
Institute of Microwave Frequencies of the RAS, Moscow, Russia
In the continuation of the review, the properties of metamaterials are 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.
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
Properties of metamaterials [7]
In 1962, V. G. Veselago systematically described the hypothesis about the unusual properties of “left-handed” media. In [7], in particular, it is shown that such medica have negative dielectric εm and magnetic μm permeability, and should also have a negative refractive index n.
A metamaterial is a composite material which properties are determined not so much by the properties of its constituent elements, but by an artificially developed periodic structure of macroscopic elements with the arbitrary dimensions and shape. An artificial periodic structure modifies the dielectric and magnetic permeability of the source material [7, 8].
Thus, the metamaterials are artificially generated and specially structured media with the electromagnetic properties that are difficult to achieve technologically or that do not occur in nature. The prefix “meta” is translated from Greek as “beyond” that allows us to interpret the term “metamaterials” as the structures which efficient electromagnetic properties go beyond the properties of constituent components.
The most famous example of a natural ENG medium (εm is negative) that can be either transparent or opaque to the electromagnetic waves depending on the excitation frequency ω, is plasma, the dielectric constant of which is determined according to the following formula in the absence of an external magnetic field:
εм(ω) = 1 − ωр2 / ω2,
where ωp is a parameter called the radial plasma frequency (radial frequency of plasma natural oscillations) that depends on the density, charge magnitude and mass of charge carriers.
Below the plasma frequency, the dielectric constant is negative and the electromagnetic waves cannot propagate due to the loss of transparency in the medium. At ω > ωp the value εm > 0 and electromagnetic waves can pass through the ionized medium. A well-known example of electromagnetic plasma is the Earth’s ionosphere, from which the low-frequency radiation is reflected (at ε(ω) < 0), and the high-frequency electromagnetic waves pass with little absorption.
Among the artificial SNG media (single negative) with negative εm (ENG, εm is negative), a system of thin metal wires arranged in parallel was one of the first to describe. Such a medium (as an artificial dielectric for microwave applications) was indicated in the work of John Brown back in 1953. He obtained the relation for the plasma frequency of a given metamaterial.
It was later confirmed by Walter Rothman who in 1961 demonstrated the possible application of multiple thin conductors to simulate plasma, since their efficient dielectric constant was expressed by the same formula. In particular, for a metastructure based on the aluminum conductors with a radius r = 1 μm and an interval between them a = 5 mm, the radial plasma frequency is approximately 8.2 GHz (Fig. 6a).
The seminal work [7] contained a theoretical description of the medium properties with simultaneously negative values of εm and μm, as well as a study of the solution of Maxwell’s equations for this case. When interpreting the Maxwell’s equations, V. G. Veselago was the first to use the expression for εm, μm < 0 as the refractive index n that was a rather unexpected logical method. While noting the hypothetical nature of the relevant medium, V. G. Veselago pointed out the indisputable fact that its existence is not excluded by the Maxwell’s equations, and theoretically analyzed the propagation process of electromagnetic waves in such media.
It should be noted that while propagating in the medium, the wave has two velocities, namely phase velocity Vph and group velocity Vgr. The phase velocity is the wave phase speed, for example, the maximum or minimum of the oscillatory process, and the group velocity is the speed at which the pulse envelope moves. They do not have to be identical and directed to the same side.
The energy flow carried by an electromagnetic wave is determined by the Umov–Poynting vector S, and, consequently, Vgr always generates a right-hand triple of vectors with the electromagnetic wave vectors E and H. Thus, for the “right-handed” media the phase and group velocities are always directed to the same side, and for the “left-handed” media the vectors Vgr and Vph are located in different directions, that is, these are the media with negative group velocity.
For the “left-handed” media, the wave vector of radiation k will be directed along the motion path of the particle υ, and the radiation cone will be directed back in relation to the particle motion, i. e., towards the source.
The beginning of the 2000s was rich in events in the field of metamaterial development with a negative refractive index of electromagnetic waves. The effect of negative refraction is due to the simultaneously negative values of dielectric and magnetic permeability (εm < 0 and μm < 0). Such materials are often called the double negative media (DNG). Until recently, this class of materials was represented only by the artificial structures. However, in 2006 it was found that the La2/3Ca1/3Mn3 crystals have a negative refractive index of electromagnetic waves at approximately 150 GHz.
Modern science has approached understanding the DNG media physics gradually. As judged by the available publications, the garland of the practical statement of a question related to the existence of waves with the negative group velocity should be given to Arthur Schuster, an English physicist (1851–1934). The conclusion that the negative group velocity is possible due to anomalous wave dispersion was confirmed in 1905 by Max Theodor Felix von Laue (1879–1960). In the same year, Pocklington once again showed in a short note that in a certain medium where a backward wave is possible, an activated source of oscillations generatesa wave with a group velocity directed away from the source, while its phase velocity is oriented towards it.
Let us note the consequences of the fact that in the left-handed media the phase velocity is opposite to the flow of energy. First of all, in the left-handed media the reversed effects will be observed: the Doppler effect and Cherenkov-Vavilov radiation!
For example, any change in the oscillation frequency due to the movement of a source or receiver is called the Doppler effect. Let the radiation receiver B moves with the speed V relative to the emitter A that emits the frequency. In this case, for the frequency perceived by the receiver due to the Doppler shift, the following expression can be obtained:
ω = ω0 ( 1 + р ( V / Vgr ).
In the “left-handed” medium (р = −1), the receiver will catch up with the wave points relevant to a specific phase. Moreover, in the formula, the velocities V and Vgr move in various directions. Therefore, due to the Doppler effect, in the “right-handed” medium an object approaching us will become more “blue”, while in the “left-handed” medium it will appear more “red”.
It can be assumed that this phenomenon is observed during the runaway breakdown in the high-altitude discharges of the Red Sprites (Fig. 1 and Fig. 4) under the influence of penetrating cosmic particles through the “left-handed” metamedium in the form of fractals.
Low-field emission of nanodots
Let us provide an analysis of publications that indicate the possible low-field emission of various semiconductor and polymer materials with the nanograin or nanotip dimensions of 20–30 nm.
It was shown in [9] that in the case of a positive bias on the probe (negative potential on the semiconductor), the electrons were emitted from protrusions on the semiconductor surface being the nanoobjects in nature (the protrusion tip size for emission could reach 10–20 nm).
The emission of electrons from a semiconductor occurs with the participation of (one or more) quantized electron energy levels in the near-surface area of the material, namely in the parts of the rough surface protrusions facing the probe.
Obviously, the main peak position is determined by the forbidden band gap of the semiconductor and the Fermi level position, as well as by the possible initial distortion of bands near the surface relevant to the electron enhancement mode of the semiconductor surface. The estimated linear dimensions of such quantum dots turn out to be in the range from 10 to 20 nm that is quite consistent with the analytical estimates for InSb.
The quantum dot, formed by the protruded part on the rough semiconductor surface acts as a kind of “filter” for the emission electron flow from the semiconductor into the vacuum and further to the tunnel microscope probe.
It was shown in [10] that the obtained low values of barriers for emission from the InSb and InAs micrograins suggest its low-field nature.
The current-voltage curves observed in relation to them indicate that the current is limited by the charge localized in the near-surface layer of the semiconductor.
A specific feature of InSb and InAs is the very small values of the effective mass m (light electrons, m ≈ 0.01m0) and energy Є (<0.2 eV) of electrons. This fact leads to the relatively large values of the de Broglie wavelength for the electron – λ = h(2m Є)–1/2 up to 30 nm (for other semiconductors it is about one nanometer).
The action area of the near-surface localized emission states should approximately correspond to the size λ. According to the experimental conditions, the emission surface area of the grain is ≈ 3 μm2. In this case, the volume of localized states in the micrograin is v ≈ 0–13 cm‑3, the concentration of localized emission centers is NS / v = (1017–1018) cm‑3, the average distances between the centers are (NS/v)–3 ≈ (10–30) nm.
In [11], a deviation from the Fowler-Nordheim formula for the field emission current from the nanoparticles was demonstrated when analyzing experimental data of the pointed field cathodes made of carbon nanotubes. It is noted that in order to obtain a current value during an experiment, the voltage must be at least 10 times greater, i. e. we observe not the field emission for the produced pointed field emission cathodes with a height reduced to the submicron dimensions, but the so-called low-field emission.
One of the reasons for the low-field emission is supposed to be a decrease in the electronic state density of the nanoparticle due to the size quantization of the spectrum. This will lead to a contact potential difference between the nanoparticle and the bulk substrate. The nanoparticle charge will then develop a field at the substrate surface near the nanoparticle junction with the bulk substrate that is sufficient for the electron tunneling into the nanoparticle through the vacuum. The external voltage will only change the motion path of the emitted electrons.
Another possible model is the surface layer deformation by the external electrical forces. Deformations in this case can be enhanced by the levers composed of nanoparticles.
The paper [12] demonstrated the capabilities of electrostatic AFM methods with a conducting probe for studying electrical specifications of the surface of polymer materials and changing the boundary conditions at the polymer-metal interface.
The thickness reduction of the dielectric polymer film leads to a situation when the charges concentrated near the boundaries of contact with metal electrodes begin to interact with each other while leading to a change in the shape of the potential barrier.
It was noted in [12] that the thin films of polyarylenephthalides (polymers with a wide forbidden band) with a submicron thickness become a current-carrying conductor with high electrical conductivity, comparable to the conductivity of some metals, not as a result of the doping procedure, but when two critical conditions are met:
the thickness of films made of such material must be less than a certain critical (nano-sized) thickness;
the availability of an initiating relatively small external influence or electric field.
Thus, the dimensions of 20–30 nm (nanograins, nanotips, nanoroughnesses and nanoislands) are one of the conditions for low-field emission occurrence in various semiconductor and polymer materials in the presence of bias voltage and pulsed voltage.
Low-field emission of fractals
Let us consider the study results of fractals made of the chains of irregular aluminum nanoislands (nanodroplets) with the dimensions of 30–1 000 nm deposited on an aramid polymer thread made of the fibers of carbon benzene rings [13–15].
The aluminum nanoislands (nanodroplets) were applied to an aramid thread (aromatic polyamide of the Rusar type) that was wound on a drum and processed in a vacuum installation for magnetron aluminum sputtering at the MIR‑2 process unit in the Research Institute of Elastomeric Materials and Products LLC.
To obtain the experimental samples, a polymer thread with a length of 30 m and a diameter of 1 000 µm is used. It is tightly wound with 137 turns on a cylinder (reel-drum) with a radius of 3.5 cm and a length of 13.7 cm [13] for the aluminum application.
During the metallization process, the following modes are set in the vacuum chamber:
- rotation speed of the reel-drum: ≈5 rpm;
- spraying time for the reel-drum with the thread: ≈1–30 minutes;
- current strength in the magnetron: 2.5 A.
The thread is an aromatic polyamide (aramid), where 85% of the amide bonds are attached directly to two benzene rings. The aromatic carbon ring, namely benzene (C6H6), is designated as a hexagon with an inscribed circle (its outer diameter is 0.28 nm), thereby emphasizing the absence of fixed double bonds and availability of a single electron cloud covering all six atoms of the carbon cycle. The chains of two benzene rings line up in a fiber through a chlorine compound, and the interweaving of several fibers generates aramid (Fig. 6, b). It should be noted that the radius of an aluminum atom is 0.143 nm (its diameter is 0.286 nm).
Thereupon, the properties of thread samples with the length of 1 cm have been studied.
The photographs of polymer threads with the chains of irregular aluminum nanoislands (nanodroplets) with the dimensions of 30–1 000 nm (Fig. 6b and Fig. 7) are made by the scanning electron microscope CAMSCAN–S4 with the energy-dispersive and wavelength-dispersive attachments: Oxford INCA Energy 350 and INCA Wave 700 (Cambridge, England) at the High Technology Center of the Synchrotron Shared Use Center of the Federal State Unitary Enterprise “Lukin Research Institute of Physical Problems” of the National Research Center “Kurchatov Institute” [13, 14].
Based on the analysis of images in Fig. 7, obtained by an electron microscope, it can be considered that the polymer thread made of aramid fibers (from carbon benzene rings) with the chains of irregular aluminum nanoislands (nanodroplets) does not have a regular topology and can be classified as the nature-like fractals (aluminum is indicated in red in Fig. 7a and in white in Fig. 7b).
It should be noted that in mathematics, the fractals are considered as the sets of points in the Euclidean space that have a metric dimension that is different from the topological one, therefore, they should be distinguished from other geometric figures limited by a finite number of links.
The natural objects (quasi-fractals) differ from the ideal abstract fractals due to the incompleteness and imprecision of structure repetitions.
The study of the electrical specifications of polymer threads was performed after formation of the indium contacts to the polymer threads with the chains of irregular aluminum nanoislands (nanoproplets); the current-voltage characteristics (CVC) of the samples were taken by a L2–56 curve tracer. In addition to the CVC, the sample resistance was also assessed using the L2–56 curve tracer by the slope of the current-voltage dependence curve. A Hewlett Packard 4284A LCR meter was used to estimate the capacitance.
When measuring the CVC of samples with a length of 10 cm and 1 cm, no current occurred when the voltage was changed to 12 V. It has been experimentally established that at the low constant voltages a polymer thread made of aramid fibers with the chains of irregular aluminum nanoislands is an insulator [13–15].
When a high voltage of up to 1.6 kV is smoothly applied (for 1 second) to a polymer thread with the nanoisland metallization by aluminum, there is no breakdown.
When a pulsed high voltage is applied to the thread, the situation is changed: an electrical discharge occurs and an off-surface highly conductive state is obtained above a polymer thread made of aramid fibers with the chains of irregular aluminum nanoislands, possibly in the resulting plasma. It has been experimentally established that when a voltage pulse of 1.6 kV is applied to the electrodes connected to a polymer thread with the length of 1 cm, an electrical discharge occurs.
Fig. 7a shows the aluminum nanoislands (nanodroplets) with the dimensions of 30–1000 nm that can unite several tens to hundreds of carbon benzene rings and develop the aluminum/carbon structures. In some part of such a structure, a “nanodot” can be formed, in which the conditions will be developed for the occurrence of low-field emission of electrons from the benzene rings when a pulsed voltage is applied to the polymer thread.
It should be noted that the distance “broken” by a spark in the air depends on the electric field strength at the electrode surface and their shape. For the spheres which radius is much larger than the discharge gap, it is considered equal to 30 kV per centimeter, and for the needles it will be 10 kV per centimeter [3].
The electrical strength of a gas strongly depends on its density (i. e., on pressure if the temperature is constant). In the case of small changes in gas temperature and pressure, the breakdown voltage is proportional to the gas density. Under the normal conditions, i. e. at a pressure of 0.1 MPa and at a temperature of 20 °C, the electrical strength of air at a distance between the electrodes of 1 cm is approximately 3.2 MV/m. The breakdown development depends on the homogeneity degree of the electric field in which the gas is broken down. If in a homogeneous field the field strength is constant, then in a significantly inhomogeneous field it is changed by several orders of magnitude along the field line [3].
The papers [14, 16] show the photographs of a cone-shaped discharge along a polymer thread with the length of 30 m and the chains of irregular aluminum nanoislands (nanodroplets) (Fig. 8a) that is similar to the optical radiation of micro runaway breakdown of a high-altitude discharge given in [2] (Fig. 8b), and not to the shape of the ordinary zigzag electric lightning over the Earth.
An experiment and photograph of an electric discharge in the direction of an electromagnetic wave propagation along a polymer thread made of aramid fibers with the aluminum nanoislands (thread length 30 m; electric field voltage E = 30 kV/m) were performed and made at a high-voltage stand of the All-Russian Electrotechnical Institute [16]. The experiment established that during the electrical breakdown in air, the polymer threads with nanoisland metallization by aluminum do not burn out.
It can be assumed that the occurrence of low-field electron emission on the long fibers of carbon benzene ring compounds under the pulsed voltage through the aluminum nanoislands (nanoproplets) leads to the plasma development and formation of an off-surface high-conducting state (OSHCS) that facilitates the occurrence of high-energy electrons at an applied high electrical voltage, capable of replacing the seed cosmic rays.
It should be noted that the formation of an off-surface high-conducting state (OSHCS) above the thread surface in the form of plasma preserves it, therefore, it does not burn out [13–15]. This state is similar to the anomalous increase in conductivity at Е > Ес that was called the “fast charge transfer” during the MRB in the high-altitude discharges in the papers [1, 2].
It has been experimentally established that the breakdown of a thread made of aramid fibers with the irregular chains of aluminum nanoislands under the room conditions is 1.6 kV/cm [13–15] that is even less than that required for the runaway breakdown (2.16 kV/cm) [2]. The lower breakdown voltage may influence the reduction of the exponential growth length of the runaway electron avalanche from a theoretical length of 50 m [2] to 30 m at a pressure of 1 atm [15, 16]. For reference, at a pressure of 1 atm, the threshold field for an ordinary breakdown is 23–30 kV/cm [2, 3].
The papers [13–15] show that the threads made of aramid fibers with the aluminum nanoislands with the dimensions of 10–1000 nm can have the properties of metamaterials and the plasma frequency value for the metamaterial under study is estimated at the level of 1–10 THz.
It can be assumed that the metamaterials based on the fractals of aluminum nanoislands are a source of high-energy seed fast electrons for the implementation of runaway breakdown in the laboratory conditions at the thread length of 30 m and an electric field strength of 30 kV/m.
Conclusions: part 2.
Hypothetically, it can be assumed that when a pulsed high voltage is applied to the polymer thread made of aramid fibers, consisting of benzene carbon rings, with the chains of irregular aluminum nanoislands (nanodroplets) (its dimensions are 10–100 nm), a fractal microbreakdown through plasma formed by the low-field electron emission occurs, with the generation of an off-surface high-conducting state (OSHCS) over the polymer thread.
It has been experimentally established that the micro breakdown of a fractal with the irregular chains of aluminum nanoislands on the aramid fiber threads is 1.6 kV/cm (under the room conditions) that is less than the estimated value for the micro runaway breakdown equal to 2.16 kV/cm. Thus, to produce a source of high-energy seed fast electrons and implement the runaway breakdown, it is sufficient to use a thread with the fractals of aluminum nanoislands (nanodroplets) with the length of 30–50 m.
The wave front of the high-altitude discharge propagation in the form of a cone directed to the source of cosmic radiation can only be implemented on the fractals made of metamaterials (having negative dielectric and magnetic constants), for example, the aluminum nanodroplets on the surface of polymer threads made of fibers of carbon benzene rings. The estimated value of the plasma frequency for the developed metamaterial is 1–10 THz.
The photograph of a cone-shaped micro breakdown of a fractal made of aluminum nanoislands (nanodroplets) along a polymer thread with the length of 30 m is similar in shape to the optical radiation of a micro runaway breakdown of a high-altitude discharge.
In addition, the high-altitude discharges observed in the upper atmosphere differ in the optical glow color at various altitudes due to the different types of fractals in which the MRB occurs: Red Sprites occur in the meta-medium, and Blue Jets are developed in the ordinary medium. As a result, the MRB differ in the luminescence cone direction in relation to the flow of seed cosmic particles during the MRB, i. e. the Doppler effect will be «reversed» for the Red Sprites on the metamaterial fractals.
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 use of developed fractals with the chains of irregular aluminum nanoislands (nanodroplets) on a polymer thread made of aramid fibers (based on the aromatic carbon rings – benzene) makes it possible to study simultaneously optical and X-ray radiation in the laboratory conditions on the Earth’s surface.
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/.
Readers feedback
