RU2411662C1 - Method for directional transportation of microwave electromagnet radiation - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method for directional transportation of microwave electromagnet radiation in gas medium consists in the fact that plasma wave guide of tubular shape is created by passage of laser radiation of ultraviolet range in specified direction along walls of created wave guide, existence of specified wave guide is maintained for the time of transportation by passing of additional laser radiation of visible range in direction along walls of specified wave guide, and microwave radiation is transported along wave guide in regime of sliding mode of vibrations, at the same time train of pulses of filament laser radiation of ultraviolet range following each other with an interval of 2-10 ns is let through in specified direction, so that specified train serves to create tubular wave guide, and at the same time capacity of specified train pulses and their number are selected from the following condition: distances between filaments of laser radiation of ultraviolet range are less than length of wave of transported microwave radiation at any section of perimetre of tubular wave guide in its any section.

EFFECT: invention provides for high accuracy in selection of transfer direction and transportation of electromagnet radiation and selectiveness with respect to localisation of receivers of transmitted information and transported pulses of electromagnet radiation.

13 cl, 6 dwg

Description

The invention relates to techniques for microwave radiation and can be used in systems for transmitting information and transporting pulses of electromagnetic radiation (EMP), in particular to ensure high accuracy when choosing the direction of these transmission and transport and selectivity with respect to the localization of receivers of transmitted information and transported EMP pulses. Known methods for directional transmission of microwave signals by using parabolic or segmented transmitting antennas [1].

The disadvantages of these known methods are, as a rule, insufficiently high accuracy when choosing the direction of the indicated transmission and transportation and insufficient selectivity with respect to the localization of transmitters of transmitted information and transported pulses of electromagnetic radiation, and, as a consequence, insufficiently high signal intensity at receivers of transmitted microwave radiation.

There is also a method proposed in [2] for the directed transportation of microwave electromagnetic radiation, including the creation of a plasma waveguide of a tubular shape by transmitting in the specified direction the laser radiation of the ultraviolet range along the walls of the specified waveguide, maintaining the existence of the specified waveguide during the time of said transportation by transmitting additional laser radiation to the wavelength range of visible light in the specified direction along the walls of the specified wave novoda and transportation of the specified microwave radiation through the specified waveguide in the mode of the moving oscillation mode, which is selected as a prototype of this invention.

The disadvantage of this proposed method of the prototype is that the sliding mode of propagation of microwave radiation is predicted based on simple estimates that do not give the propagation range of the transmitted radiation on the specified waveguide, and without taking into account the then unknown filamentation effect of laser beams for ultrashort pulses (femto and picosecond ) duration, which leads to low reliability of the directional transportation of microwave radiation when implementing this method.

The aim of this invention is to remedy these disadvantages and increase the reliability of directional transportation of microwave - electromagnetic radiation. The goal is achieved in this proposed invention due to the fact that in the known method, including the creation of a plasma waveguide of a tubular shape by transmitting in the specified direction the laser radiation of the ultraviolet range along the walls of the specified waveguide, maintaining the existence of the specified waveguide during the time of this transportation by passing an additional laser visible radiation in the indicated direction along the walls of the specified waveguide and transporter alignment of the specified microwave radiation along the specified waveguide in the mode of sliding oscillation mode, in the specified direction, a train of successive 2-10 non-pulsed filament laser radiation of the ultraviolet range is passed in such a way that the said train serves to create the specified tubular waveguide and the power the pulses of the specified train and their number is selected from the condition: the distance between the filaments of the specified laser radiation in the ultraviolet range is less than the wavelength of the specified protractor UHV radiation at any part of the perimeter of the specified tubular waveguide in any of its sections; and also due to the fact that in the known method, including the creation of a plasma waveguide of a tubular shape by transmitting in a given direction the laser radiation of the ultraviolet range along the walls of the specified generated waveguide, maintaining the existence of the specified waveguide during the time of said transportation by passing additional laser radiation in the specified direction along the walls of the specified waveguide and transportation of the specified microwave radiation through the specified waveguide in the sliding mode modes of oscillations, in the indicated direction, a train of pulses of the ultraviolet filament laser radiation following one after another with an interval of 2-10 ns is passed so that the first few pulses of the indicated train serve to create the specified tubular waveguide, and subsequent pulses of the specified train support the existence of the specified microwave transport channel radiation and the power of the pulses of the specified train and their number is selected from the condition: the distance between the filaments of the specified laser radiation trafioletovogo range smaller than the wavelength of said transported microwave radiation in any portion of the perimeter of said tubular waveguide in any of its section and by the fact that to maintain the existence of said waveguide using a train of laser radiation pulses of UV power range sufficient to suppress electron trapping effect to molecules About ₂ and due to the fact that the indicated train of pulses of filamented laser radiation consists of pulses with a duration of about 1 picosecond and with a wavelength λ of 353 nm or 308 nm, or 248 nm, or 222 nm, or 193 nm with a wavelength spread of about 2 nm.

Figure 1 shows a schematic representation of the propagation of microwave radiation in a cylindrical plasma waveguide.

Figure 2 shows the attenuation length of the sliding mode in a plasma waveguide with different radii R for a wavelength of microwave radiation λ _microwave = 8 mm

Figure 3 shows the attenuation length of the sliding mode in a plasma waveguide in the submillimeter wavelength range at an electron density of N _e = 5 * 10 ¹³ cm ^-3 (a), 10 ¹³ cm ^-3 (b) and 10 ¹² cm ^-3 (s )

Figure 4 shows the ratio of the intensities of microwave radiation (λ _microwave = 8 mm) in the virtual waveguide to the intensity during free propagation for various sizes of the transmitting antenna (emitter).

Figure 5 shows a diagram of an experiment to demonstrate the directional transportation of microwave radiation in a hollow plasma waveguide, where

1 and 2 - positive and negative lenses of the telescope;

3 and 4 - a telescope from conical axicon lenses;

5 - magnetron with a waveguide and horn emitter;

6 - microwave radiation detector;

7 - laser radiation receiver.

Figure 6 shows a schematic representation of the process of electron accumulation (below) in a plasma with multiphoton ionization of air by a train of picosecond pulses (above).

Traditional methods for ensuring the necessary directivity of microwave radiation are based on the use of large transmitting antennas, the characteristic size of which for a mobile installation can be set to D ~ 2 m. The divergence of the microwave beam (at half the maximum intensity) due to diffraction at the output aperture of the antenna is in this case β _microwave ≈λ _microwave / D. For the wavelength of microwave radiation λ _microwave ~ 1 cm, we have β _microwave = 5 * 10 ^-3 rad. To reduce the divergence, an increase in D is required. However, an increase in the aperture of the transmitting antenna inevitably leads to a decrease in the flux density of the transmitted power (intensity), which can be compensated by increasing the power of the microwave generator only to a certain limit determined by the threshold for air breakdown by microwave radiation. The range L of such a generator can be estimated based on the formula [3]

where d is the characteristic size of the microwave emitter (usually does not exceed ~ 10 cm), and P _D / P _eff is the ratio of the maximum signal power density (limited by air breakdown) to its effective value required for a beneficial effect, and is of the order of several tens meters, if a sufficiently high power density is to be delivered to the object.

An alternative to the traditional approach is the transportation of microwave radiation through an artificial waveguide created in atmospheric air by UV laser radiation having an annular beam cross section [2]. Since the refractive index in ionized air is less than in the original air, the effect of total internal reflection of radiation will be observed at sliding angles of incidence of electromagnetic radiation at the interface. In a cylindrical waveguide, the qualitative condition for channeling microwave radiation in the geometric approximation (valid, strictly speaking, when the diameter of the waveguide is D _B >> λ _microwave ) is satisfied if the diffraction angle of divergence of the microwave radiation β _microwave is less than the total internal reflection angle θ defined by the relation Cosθ = n, where n is the refractive index of the ionized gas relative to air, which is set by the density of free electrons in the ionized air N _e (see Figure 1). That, in turn, is determined by the balance of electron production in multiphoton ionization processes and their death upon adherence to oxygen molecules, electron-ion or associative recombination. Thus, the electron concentration depends on the intensity and wavelength of the UV laser radiation, as well as the pulse duration.

The formation of extended plasma structures with a high electron density N _e = 10 ¹⁴ ÷ 10 ¹⁵ cm ^-3 and higher, in principle, allows the realization of microwave plasma waveguides with excitation of volume modes similar to those transmitted via metal waveguides [4, 5], and also coaxial lines and waveguides of surface waves [6]. Recent experiments [7] demonstrated channeling of microwave radiation through a hollow tubular waveguide with a diameter of 45 mm, the plasma walls of which consisted of numerous filaments arising from the propagation of an ultrashort laser pulse with a radiation wavelength λ = 800 nm. However, the propagation length of the volume mode of microwave radiation in such a plasma waveguide was only 16 cm and was determined by the high specific resistance of the plasma as compared with the metal. The duration of the microwave signal transmitted through this waveguide was about 10 ns and was determined by the characteristic lifetime of free electrons in the filaments.

The new method of directional transportation of microwave electromagnetic radiation proposed in this application combines the advantages of ultrashort ultraviolet laser pulses for efficient ionization of air and the creation of virtual plasma waveguides with a theoretically justified and experimentally verified sliding mode of microwave radiation propagation along the specified waveguide. The method includes the following operations.

1. The creation of a tubular plasma waveguide by transmitting laser radiation of the ultraviolet range along the walls of the specified waveguide. Air ionization under the influence of ultraviolet radiation with a wavelength of λ = 248 nm and a quantum energy of hν = 5 eV, as our experiments have shown, in the range of intensities 10 ¹¹ ≥I≥3 * 10 ⁸ W / cm ² occurs mainly due to the two-stage process of molecular ionization oxygen O ₂ having an ionization potential I _i = 12.08 eV:

Here O ₂ ^* is some intermediate resonant excited state of the molecule. At higher intensities I≥10 ¹¹ W / cm ² (but below the avalanche ionization threshold, which depends on the pulse duration), direct three-photon oxygen ionization dominates:

In both cases, the laser radiation energy of ~ 15 eV is expended for the ionization of one molecule and the formation of one free electron.

To form the specified hollow plasma waveguide of a tubular shape, a laser beam with an annular cross section, formed by two telescopes located one after another, is transmitted through the air. The first compresses the original laser beam into a beam with a small radius equal to the required wall thickness of the plasma waveguide ΔR. The second telescope forms the desired tubular laser beam with a radius R.

An annular laser beam with an inner radius R and a ring width ΔR, having a radiation divergence θ, gradually “spreads out” as it propagates: its radius at a distance L is R _L ≈R + θ · L, and its width ΔR _L = ΔR + θL. At θ ~ 10 ^-5 rad (which is much larger than the diffraction limit, θ _diff = 0.61 λ / R = 5 · 10 ^-7 rad) and L = 1 km, the value θ · L = 1 cm. For the initial radius R = 30 cm and ΔR = 1 ÷ 2 cm, the radius of the channel remains almost unchanged (R _L ≈R), and the ring width increases approximately two times, which leads to a decrease in the average electron concentration in the walls of the waveguide. As a result, the sharp initial boundary of the ring and the stepwise radial distribution of the electron concentration spread out, and losses due to absorption of microwave radiation in the walls of the plasma waveguide increase. However, as long as the width of the blur region of the waveguide does not exceed the wavelength of the microwave radiation, the attenuation length of the microwave signal along the plasma waveguide does not substantially decrease. To compensate for phase distortions introduced by the optical elements of the laser circuit, a laser beam correction system using an adaptive mirror is used.

In the longitudinal (along the plasma waveguide) direction (z), the electron concentration gradually decreases in accordance with the law of attenuation of radiation intensity:

in the case of the dominance of the stepwise ionization process through the intermediate level (2) and

in the case of direct three-photon ionization (3).

, I₀=I(z=0) - начальное значение интенсивности лазерных импульсов, которое находится из условия наработки требуемой концентрации электронов. В случае доминирования процесса ступенчатой ионизации с константой К₂=100 см/Вт²с [8], полагая, что прилипание электронов к молекуле О₂ полностью скомпенсировано обратным процессом фотоотрыва электронов (что справедливо для интенсивности лазерного излучения I≥3*10⁷ Вт/см²), получаем, что для создания концентрации электронов N_e=10¹³ см^-3 цугом из n=50 импульсов с длительностью τ=1 пс необходима пиковая интенсивность импульсов:Here K ₂ and K ₃ are the rate constants of the corresponding photoionization processes

, I ₀ = I (z = 0) is the initial value of the intensity of the laser pulses, which is found from the condition for the production of the required electron concentration. In the case of the dominance of the stepwise ionization process with the constant K ₂ = 100 cm / W ² s [8], assuming that the attachment of electrons to the O ₂ molecule is completely compensated by the reverse process of electron photodetachment (which is true for the laser radiation intensity I≥3 * 10 ⁷ W / cm ² ), we find that to create an electron concentration N _e = 10 ¹³ cm ^{-3 in a} train of n = 50 pulses with a duration τ = 1 ps, the peak pulse intensity is necessary:

.

.

The characteristic length of depletion (at which the laser radiation intensity decreases by a factor of 2) L ₀ = (3hνK ₂ I ₀ ) ^-1 ≈ 930 m.

2. Maintaining the existence of a plasma waveguide for the required time for transportation of microwave radiation is ensured by transmission of additional laser radiation. Since the main cause of death of free electrons in air at concentrations of N _e ≤10 ¹⁶ cm ^-3 is their adhesion to an oxygen molecule with the formation of an electronegative molecular ion O ₂ ^- , it is proposed to use a second laser pulse to maintain ionization in a weakly ionized plasma due to the reverse bremsstrahlung absorption, or photodetachment of electrons, if the quantum energy is greater than the binding energy (affinity) of the electron in the molecular ion hν≥ε. For О ₂ ^- ε ~ 0.5 eV and therefore photodetachment of electrons is possible for visible radiation [9]. For UV radiation, compared with visible radiation, the cross section of the process increases several times.

3. Transportation of microwave radiation through a plasma waveguide in the mode of a sliding oscillation mode. Our theoretical calculations based on the solution of dispersion equations with the complex permittivity of air plasma determined the region of parameters in which the sliding mode of propagation of microwave radiation is realized. It is determined by the parameters α and β from the relations

- диэлектрическая проницаемость плазмы, характерный параметр задачи

. Здесь R есть радиус плазменного волновода,

- характерная плазменная частота, N_e есть плотность электронов в слабоионизованной плазме, ν_T - характерная транспортная частота столкновений электронов в плазме (с молекулами воздуха, ионами и электронами плазмы), ω и k₀ - частота и вакуумное волновое число СВЧ-излучения.Where

is the dielectric constant of the plasma, a characteristic parameter of the problem

. Here R is the radius of the plasma waveguide,

is the characteristic plasma frequency, N _e is the electron density in a weakly ionized plasma, ν _T is the characteristic transport frequency of electron collisions in plasma (with air molecules, plasma ions and electrons), ω and k ₀ are the frequency and vacuum wave number of microwave radiation.

и µ≥1.The values of α and β are determined from the numerical solution of the corresponding dispersion equation for the mode of transported radiation. In particular, for lower axially symmetric modes, depending on the values of the parameters of the problem, estimates give α ~ 1 ÷ 3 and β ~ 0.2 ÷ 0.5. The slip mode is obviously performed at

and µ≥1.

In the region of millimeter and submillimeter waves, ω << ν _T (characteristic values of the transport frequency of collisions of electrons of a weakly ionized plasma with neutral molecules of atmospheric air ν _T ~ (1 ÷ 10) × 10 ¹² s ^-1 depending on the electron temperature, (T _e ~ 0.026 ÷ 1.5 eV) and relations (6) can be represented in the form (assuming α = 1, β = 0)

In the high-frequency region ω >> ν _{T, the} first condition in (6) is always satisfied, and only the second condition remains, which can be represented (since μ no longer depends on the _microwave wavelength λ) in the form

The calculations performed for waveguides with different radii R and a wavelength of microwave radiation λ _microwave = 8 mm, are shown in figure 2. For a fixed radiation wavelength with λ _{microwave frequency} = 8 mm, the attenuation length (at which the microwave radiation intensity decreases by a factor of e) increases with increasing waveguide radius and electron concentration, reaching ~ 800 m at _Ne = 10 ¹³ cm ^-3 and R = 30 cm. It was also shown that for such electron concentrations the waveguide wall thickness can not exceed 1 cm. The attenuation length increases with decreasing wavelength and reaches several kilometers for submillimeter waves (Figure 3).

The exposure range in the case of channeling of microwave radiation in a plasma waveguide in the sliding mode mode is many times greater than the exposure range for free propagation obtained by formula (1).

The ratio of the intensities of microwave radiation transmitted through a virtual plasma waveguide to the intensity during propagation in free space for different sizes of the transmitting antenna and the same power of the microwave generator (λ _microwave = 8 mm) is shown in FIG. 4. It can be seen that even with large antenna sizes of ~ 2 m, in the case of transporting radiation through a virtual waveguide, a more than 10-fold gain in intensity is achieved, and the virtual waveguide has an advantage at distances of more than 1 km.

The mode of creeping propagation of microwave radiation in a tubular plasma waveguide was experimentally confirmed in our experiments (see Figure 5). The radiation generated by a pulsed magnetron with a wavelength of λ _{microwave frequency} = 8 mm was introduced using a horn antenna into a plasma waveguide with R = 60 mm and ΔR = 10 mm, in the walls of which an electron concentration N was created using a KrF laser with a wavelength of λ = 248 nm _e ~ 10 ¹² cm ^-3 . During a 100 ns laser pulse at a microwave receiver installed at a distance of up to 60 m from the horn emitter, a significant increase in the amplitude of the microwave signal was observed due to the channeling of the radiation in the plasma waveguide.

4. To create a hollow plasma waveguide, a train of ultraviolet pulses of the picosecond range of durations and with a high peak intensity I ₀ ~ 4.5 * 10 ¹⁰ W / cm ² , following with an interval of 2-10 ns (see Figure 6), is used, which allows it is more efficient to ionize air in each of the train pulses, since the probabilities of multiphoton ionization processes (2) and (3) are proportional to ∞ I ² and ∞ I ³ , respectively, and to accumulate the electron concentration from pulse to pulse. The interval between train pulses was chosen so that, on the one hand, it was longer than the recovery time of population inversion (gain) in the active medium of an excimer amplifier (~ 2 ns) [10] used to amplify the train, and on the other hand, it was shorter characteristic time of electron attachment (~ 10 ns) to oxygen molecules, which is the main mechanism of electron loss in the concentration range _Ne <10 ¹⁶ cm ^-3 .

Since the peak power of individual pulses in the train P = 2πRΔRI ₀ = 8.5 TW (R = 30 cm, ΔR ~ 1 cm, I ₀ = 4.5 * 10 ¹⁰ W / cm ² ) is many orders of magnitude higher than the critical value for filamentation ultraviolet laser radiation P _cr ≈10 ⁸ W [11], then the tubular beam will consist of many filaments, the average distance between which is much less than the wavelength of the indicated transported microwave radiation at any part of the perimeter of the specified tubular waveguide in any section, and the local concentration of electrons in which N _e ~ 3 * 10 ¹⁵ ÷ 10 ¹⁶ cm ^-3 - will be significant o exceed the average value of N _e ~ 10 ¹³ cm ^-3 . In this case, the total energy of laser radiation in a train of 50 pulses is ~ 430 J.

5. The first few ultraviolet pulses from a train of picosecond pulses with a high intensity I ~ 4.5 * 10 ¹⁰ W / cm ² are used to create and accumulate the necessary electron concentration in a plasma waveguide using the filamentation of a laser beam, which develops when the radiation power is significantly higher than critical Р _кр ≈10 ⁸ W and, as a result, when the distance between the filaments is less than the microwave radiation wavelength. Subsequent pulses with a lower peak intensity I ~ 10 ⁸ W / cm ² serve to maintain ionization in the specified waveguide for the time required to transmit the microwave signal due to the effect of photodetachment of electrons from O ₂ ^- molecules.

6. To amplify the train of picosecond ultraviolet pulses generating a hollow plasma waveguide, wide-aperture amplifiers with electron beam pumping on various excimer molecules are used: ArF (wavelength λ = 193 nm), KrCl (λ = 222 nm), KrF (λ = 248 nm), XeCl (λ = 308 nm), XeF (λ = 353 nm). All of them have high gain efficiency and short gain recovery times in the active medium (of the order of several nsec), as well as a short radiation wavelength, which allows ionizing the air due to multiphoton ionization processes.

Implementation example

The proposed method is implemented as follows: a titanium-sapphire laser generates laser pulses with a duration of several tens of fs, a repetition rate of several Hz and a pulse energy of several mJ, and a wavelength of about 744 nm, which triple in frequency to a wavelength of 248 nm . These pulses are converted to a train, for example, in an optical resonator, following each other after a few ns. The trains of ultrashort laser pulses thus formed are sequentially amplified in two krypton-fluorine laser amplifiers, pumped, for example, by electron beams with a pulse duration of several hundred ns, as a result of which an output energy density of 10 mJ / cm ² for one ultrashort is achieved a laser pulse and of the order of 500 mJ for a train of, for example, 50 ultrashort laser pulses. The total energy of laser radiation in one train is about 500 J.

After excimer laser amplifiers, a tube laser beam is formed from the train of amplified pulses using optical elements. The formed tubular laser beam ionizes the air along the propagation path and creates a hollow plasma waveguide of circular cross section with a free electron density of the order of 10 ¹³ cm ^-3 , which is accumulated due to the action of a train of ultrashort laser pulses. Microwave radiation is directed into the indicated plasma waveguide using an input system. Using the mode transformer, the H ₁₁ microwave radiation volume mode is formed, which is closest to the sliding mode of the indicated plasma waveguide.

The distance over which microwave radiation is transported in the indicated plasma waveguide is about 1 km, and the power density at the receiver is about 10 times higher than the power density when microwave radiation propagates in free space, the duration of microwave radiation can reach several hundred ns.

A theoretical analysis of the operation of the generated plasma waveguide, confirmed experimentally, provides high reliability of directional transportation of microwave electromagnetic radiation performed by the proposed method.

Information sources

Claims (13)

1. The method of directional transportation of microwave electromagnetic radiation in a gas environment, including the creation of a plasma waveguide of a tubular shape by transmitting in the specified direction the laser radiation of the ultraviolet range along the walls of the specified generated waveguide, maintaining the existence of the specified waveguide during the time of said transportation by transmitting additional visible laser radiation in the specified direction along the walls of the specified waveguide and the transportation specified of microwave radiation through the specified waveguide in the mode of a moving oscillation mode, characterized in that a train of pulses of ultraviolet filamented laser radiation following one after another with an interval of 2-10 ns is passed in such a way that the train serves to create the specified tubular waveguide, and wherein the pulse power of the specified train and their number is selected from the condition: the distance between the filaments of the specified laser radiation in the ultraviolet range is less than the wavelength of the specified trans sporting microwave radiation at any part of the perimeter of the specified tubular waveguide in any section. 2. The method according to claim 1, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 353 nm with a wavelength spread of about 2 nm. 3. The method according to claim 1, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 308 nm with a wavelength spread of about 2 nm. 4. The method according to claim 1, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength of λ equal to 248 nm with a wavelength spread of about 2 nm. 5. The method according to claim 1, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 222 nm with a wavelength spread of about 2 nm. 6. The method according to claim 1, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 193 nm with a wavelength spread of about 2 nm. 7. A method for the directed transportation of microwave electromagnetic radiation in a gaseous medium, including the creation of a tubular plasma waveguide by transmitting ultraviolet laser radiation in a given direction along the walls of the waveguide to be created, maintaining the existence of the specified waveguide during the time of said transportation by transmitting additional laser radiation in the specified direction along the walls of the specified waveguide and transportation of the specified microwave radiation n about the specified waveguide in the mode of sliding oscillation mode, characterized in that in the indicated direction a train of pulses of ultraviolet filament laser radiation following one after another with an interval of 2-10 ns is passed so that the first few pulses of the specified train serve to create the specified tubular waveguide, and subsequent pulses of the specified train support the existence of the specified channel for the transportation of microwave radiation, and the pulse power of the specified train and their number are selected from I: the distance between the filaments of the specified laser radiation of the ultraviolet range is less than the wavelength of the indicated transported microwave radiation at any part of the perimeter of the specified tubular waveguide in any section thereof. 8. The method according to claim 2, characterized in that to maintain the existence of the specified waveguide use the following subsequent pulses of laser radiation of the ultraviolet range of lower power, sufficient to suppress the effect of electron attachment to O ₂ molecules. 9. The method according to claim 7 or 8, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 353 nm with a wavelength spread of about 2 nm. 10. The method according to claim 7 or 8, characterized in that said train consists of filaments of laser radiation with a duration of the order of 1 ps and a wavelength λ of 308 nm with a wavelength spread of about 2 nm. 11. The method according to claim 7 or 8, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 248 nm with a wavelength spread of about 2 nm. 12. The method according to claim 7 or 8, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 222 nm with a wavelength spread of about 2 nm. 13. The method according to claim 7 or 8, characterized in that said train consists of filaments of laser radiation with a duration of about 1 ps and a wavelength λ of 193 nm with a wavelength spread of about 2 nm.

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