RU2552518C2 - Method of generation of broadband electromagnetic radiation of uhf range - Google Patents

Abstract

FIELD: electricity.

SUBSTANCE: method of generation of broadband electromagnetic radiation of UHF range can be used in radio engineering and electronic industry, in particular, in devices of generation of powerful broadband electromagnetic impulses (EMI) in the centimetric, millimetric and submillimetric ranges. The photo diode electrodes are powered by voltage impulse, the photocathode with a shape of the focusing mirror for laser radiation is obliquely irradiated with the pulse laser radiation therefore from the cathode electrons are emitted which are accelerated in the vacuumised inter-electrode interval, using the anode, transparent for the generated electromagnetic radiation.

EFFECT: improvement of efficiency of transformation of electrostatic energy into energy of electromagnetic radiation.

4 dwg

Description

The invention relates to microwave technology and can be used in the development of generators of powerful broadband electromagnetic pulses (EMP) in the centimeter, millimeter and submillimeter wavelength ranges.

A known method of generating pulses of microwave radiation in a device with a virtual cathode (VK) [1] (Hwang GS, Wu MW, Song PS, Hou WS, "High power microwave generation from a tunable radially extracted vircator", J. Appl. Phys. 1991, No. 69 (3), P.1247). This generation method consists in creating a pulsed electron beam with a current above the limiting current in the diode region of the device, which is injected through the mesh anode into the drift space, where a virtual cathode is formed due to the action of the space charge of the electrons. A part of the electrons is reflected from the VC and oscillates between the real and virtual cathodes. The energy of these electrons is transferred to the electromagnetic field. The parameters and position of the virtual cathode oscillate in time and also contribute to the radiation energy. The disadvantage of this method is the low (about several percent) efficiency of converting the energy of the electron beam into radiation energy.

Closest to the proposed method and selected as a prototype is the method of generating electromagnetic radiation of the microwave range, described in [2] (Yu.N. Lazarev, PV Petrov, "Generator of electromagnetic radiation of the microwave range based on superlight source", JETP, 1999, T.115, C.1689), based on the use for the generation of electromagnetic radiation propagating with a superluminal speed current pulse arising above the anode in the discharge of a high-voltage photodiode initiated by laser radiation. It allows you to get a powerful broadband directional pulse of electromagnetic radiation.

The disadvantage of this technical solution is the relatively low (approximately 12%) conversion efficiency of the stored electrostatic energy into electromagnetic energy. To achieve higher conversion efficiency values, a significantly higher level of radiation intensity is required.

In the prototype under consideration, an anode opaque to EMR is used and an electromagnetic wave leaving the source is generated in the region above the anode. In this case [3, 4] (A.V. Soldatov, A.A. Soloviev, M.S. Terekhina, Plasma Physics, 2007, Vol.33, P.795, Yu.N. Lazarev, Yu.G. Syrtsova, ZhETF, 2012, T.141, S.177) the surface density of the dipole moment, its time derivatives change in proportion to cos ² θ, θ is the angle of incidence of the laser radiation initiating the discharge of the photodiode, which leads to a significant decrease in the power and energy of EMP at angles θ≥45 °. The culprit of this, as shown in [4], is an electromagnetic wave inside the discharge gap, the amplitude of which increases significantly due to repeated reflection from the electrodes and which noticeably slows down the accelerating electrons, reducing their energy ∝cos ² θ. If the anode is opaque to the EMP but transparent to the electrons, the radiation is emitted only from the region above the anode, the internal electromagnetic wave locked inside the photodiode makes no contribution to the EMP coming from the photodiode, and at the same time takes a significant fraction of the electron energy. Reducing the energy characteristics of the source can be avoided by using a photodiode with an transparent EMR anode to generate EMP, in which there is no negative influence of the internal electromagnetic wave, since its reflection from the anode is excluded. In the case of an anode transparent to EMR, the unhindered output of the internal wave reduces its amplitude. However, in general, the amplitude of the wave leaving the source increases. Due to the expansion of the generation region, which now includes both the internal and external regions of the photodiode, and the increase in the electron energy above the anode, the efficiency of converting electrostatic energy to electromagnetic energy increases significantly.

The objective of the present invention is to provide a method that allows to obtain pulses of broadband electromagnetic radiation of the microwave range with significantly higher values of the radiation intensity and, as a result, with a higher efficiency of converting electrostatic energy into electromagnetic energy.

The problem is solved in that in a method for generating broadband electromagnetic radiation (EMP) of the microwave range, namely, that a voltage pulse is applied to the electrodes of the photodiode, the photocathode, in the form of a focusing mirror for laser radiation, is obliquely irradiated with pulsed laser radiation, as a result of which cathode emitted electrons, which are accelerated in the evacuated interelectrode gap, according to the invention, use an anode that is transparent to the generated electromagnetic radiation.

The technical result of the proposed method consists in obtaining a much more intense generation of electromagnetic radiation and a significant increase in the efficiency of conversion of electrostatic energy into electromagnetic energy due to an increase in the size of the electromagnetic radiation generation region and the electron energy above the anode. Laser radiation provides the formation of the required number of electrons and, thanks to the cathode in the form of a focusing LI mirror, synchronizes the radiation emitted by various parts of the photodiode.

The presence in the claimed invention features that distinguish it from the prototype, allows us to consider it appropriate to the condition of "novelty."

New features (namely, that they use an anode that is transparent to the generated EMR) are not identified in technical solutions for a similar purpose. On this basis, we can conclude that the claimed invention meets the condition of "inventive step".

The present invention is illustrated by specific examples, which, however, are not the only possible, but clearly demonstrate the ability to achieve the above sets of essential features of the desired result.

Figure 1 shows the data of a numerical calculation of the dependence of the amplitude dp / dτ on θ during the discharge of a photodiode with an anode transparent to electrons and EMR. ο-γ-1 = 0.04, □ -γ-1 = 0.2

- η_t=0.48(γ-1)^0.45; θ=45°, + - численный расчет,

- η_t=0.77(γ-1)^0.35; θ=60°, □ - численный расчет,

- η_t=0.92(γ-1)^0.25.Figure 2 presents the results of a numerical calculation of the dependence of η _t on γ-1 for a photodiode with an anode transparent to EMR and electrons for different incidence angles of the LI. θ = 30 °, ο - numerical calculation,

- η _t = 0.48 (γ-1) ^0.45 ; θ = 45 °, + - numerical calculation,

- η _t = 0.77 (γ-1) ^0.35 ; θ = 60 °, □ - numerical calculation,

- η _t = 0.92 (γ-1) ^0.25 .

Figure 3 shows the results of calculating the dependence of the amplitude dp ⁱⁿ / dτ on θ for two versions of the anode: ο - the anode is opaque to EMR, □ - the anode is transparent to EMR. γ-1 = 0.2.

Figure 4 presents the results of calculating the dependence of the conversion efficiency of electrostatic energy into electromagnetic energy η _in on γ-1 for various angles of incidence of radiation. The anode is transparent for EMR and opaque for electrons, θ = 60 ° -ο, θ = 45 ° - +, θ = 30 °.

The physical basis of the proposed invention is explained below.

Since the dimensions of the source under consideration are much larger than the characteristic radiation wavelength, the study of such a source reduces to the study of the discharge of a planar photodiode.

The electromagnetic field of an infinite flat dipole layer.

The simplest photoemissive EMR source is an infinite flat photodiode with an anode transparent to light and electrons, irradiated with a flat stream of pulsed light radiation, for example, laser. The electrons knocked out by light radiation are accelerated in the interelectrode electric field and, flying through the anode grid, form a radiating dipole layer in the supergrid space. If light radiation forms a superluminal current pulse near the surface of the photocathode, then the accelerated electron pulse above the anode will also be superluminal:

θ is the angle of incidence of light radiation.

The electromagnetic wave generated by this current distribution is the solution to the following problem:

as z → ∞, the outgoing electromagnetic wave.

, то и все другие величины должны зависеть от x и t аналогично. Это позволяет снизить размерность задачи, перейдя от переменных t, x, z к переменным

В этих переменных для компоненты поля E_x справедливо следующее уравнение:Since the current density j _z , which is the only cause of the field, and the boundary conditions depend on x and t only in combination

, then all other quantities must depend on x and t in a similar way. This allows you to reduce the dimension of the problem by moving from variables t, x, z to variables

In these variables, the following equation holds for the field component E _x :

The solution to the problem (3, 4) (which is easy to verify by substitution) can be represented as:

If the current density is localized within a certain interval Δz, then for z> Δz:

где

- средняя скорость электронов излучающего слоя, T_j - характерное время изменения тока, тоAs

Where

is the average electron velocity of the radiating layer, T _j is the characteristic time of the current change, then

and therefore, the delay in expression (6) can be neglected

поверхностная плотность дипольного момента, n_e(z,t) - плотность электронов в слое,

here

surface density of the dipole moment, n _e (z, t) is the electron density in the layer,

Using (7), we obtain

Expressions (7, 8) for the fields of the generated electromagnetic wave show that it propagates in the mirror direction to the direction of light incidence.

Outside the region of localization of the current density, the values of the generated fields depend only on the first time derivative of the surface density of the dipole moment.

In the case of a planar source of finite dimensions, the obtained expressions for the fields are valid in the near zone of the source. With the characteristic transverse size of the source D and the interelectrode gap L, the possible error is small, ~ 4L / D << 1.

The surface density of the dipole moment.

To calculate the surface density of the dipole moment, the trajectories of the electrons both inside and outside the photodiode are necessary. The simplest way is to obtain a solution of the equations of motion for a normal incidence of light on an infinite plane photocathode. In this case, the generation of electromagnetic radiation is absent and the electrons knocked out by light move only in the external accelerating field and the space charge field. The density of the dipole moment obtained for θ = 0 can be used for an approximate description of the radiation field at θ ≠ 0, which will be more accurate the smaller the influence of the electromagnetic field on the motion of electrons.

The problem has two time scales: T _p is the characteristic time of the natural oscillations of the electron plasma (space charge formation time), T ₀ is the electron motion time between the electrodes at the initial potential difference. At low electron emission current densities T _p >> T ₀ and the dynamics of the process of discharge of the photodiode and the generation of EMR is determined by T _p (T _j = T _p ). At high emission current densities T _p << T ₀ and the role of the characteristic task time is T ₀ .

The radiation field is expressed in terms of the time derivatives of the density of the dipole moment. This means that the radiation power will be the higher, the shorter the characteristic task time and, therefore, the maximum radiation power can be obtained only in the mode of limiting the current by the space charge, when T _p << T ₀ . This area is considered in the future.

Consider an infinite flat diode with an anode transparent to electrons, charged to a voltage of φ ₀ , eφ ₀ / mc ² = γ-1 << 1. The z axis is directed normal to the surfaces of the cathode (z = 0) and the anode (z = L). The cathode is irradiated by a light pulse with a flat front, normally incident on the cathode surface and knocking electrons out of it with a current density j _k (t). Despite the fact that the field E _z varies both in time and in space, at the beginning of the discharge there is a sufficiently large period of time during which each electron moves under the action of a constant force that experiences a jump when passing through the anode. The charge dσ = -j _k (t ₁ ) dt emitted from the cathode surface at time t = t ₁ , for t> t ₁ , an electric field acts inside the diode

directed along z. This is the value of the electric field that was on the cathode at the time the electron appeared. It consists of an external field -E ₀ and a space charge field already emitted by this point in time electrons. Outside the diode, only the space charge field

Thus, the electric field acting on the electron and the electron trajectory are described by the following equations:

For definiteness, let the current density of emitted electrons vary linearly with time

In the case of using laser radiation (LI), this approximately corresponds to the behavior of the emission current density at short times (t <τ _F , τ _F is the width of the front of the laser pulse).

We write equations (15, 16) in a dimensionless form.

характерное время собственных колебаний электронной плазмы,

- время движения электрона между электродами при начальной разности потенциалов φ₀.Here u = E / E ₀ , τ = t / T ₀ , b = T ₀ / T _p , z = Z / L,

characteristic time of natural oscillations of the electron plasma,

- the time of motion of the electron between the electrodes at the initial potential difference φ ₀ .

Equations (18, 19) have the following solution:

- момент времени, когда электрон, испущенный при τ=τ₁ попадает на анод и покидает межэлектродный промежуток. Этот электрон вновь пересечет анод и возвратится в межэлектродный промежуток в момент времени

.

- the point in time when the electron emitted at τ = τ ₁ hits the anode and leaves the interelectrode gap. This electron will again cross the anode and return to the interelectrode gap at time

.

что свидетельствует о пересечении электронных траекторий при достаточно больших временах, порядка

или более.The function τ _A (τ ₁ ) is a monotonically increasing function of τ ₁ , while τ _R (τ ₁ ) has a minimum

which indicates the intersection of electronic trajectories at sufficiently large times, of the order

or more.

. Обозначим τ_m минимальное из всех возможных значений τ_i:τ_m=min(τ_i).The moment of time τ _i at which two electron trajectories intersect is found from the solution of the equation

. Denote by τ _{m the} minimum of all possible values of τ _i : τ _m = min (τ _i ).

Для задач, изучающих генерацию электромагнитного поля, это достаточно большое время, поскольку к этому моменту генерация практически заканчивается.An unambiguous relationship between the time when the electron was emitted and the field acting on it exists only until the electron trajectories intersect. Therefore, expressions (13, 14) for an electric field acting on an electron are valid only for τ≤τ _m . Then it is possible to use expressions (22, 23) for the electron trajectories. At

For tasks studying the generation of an electromagnetic field, this is a fairly long time, because by this moment the generation is almost over.

электрическое поле на катоде обращается в 0 и электроны, выбитые световыми квантами при τ≥τ_b, не могут покинуть поверхность катода и внести вклад в разрядный ток;From the obtained solution of the equations of motion it also follows that for

the electric field at the cathode turns to 0 and the electrons knocked out by light quanta at τ≥τ _b cannot leave the cathode surface and contribute to the discharge current;

at τ≤1, all emitted electrons are inside the diode.

Knowing the electron trajectory, we can calculate the density of the dipole moment and its time derivatives inside and outside the diode (the minus sign is omitted in the expressions for p and its derivatives later in this section):

единичная функция: η=1, если x≥0, η=0, если x<0.τ _b <1, 0 <τ≤τ _b ⇒ α = 0, β = τ, τ _b <τ <1 ⇒ α = 0, β = τ _b ; τ≥1 ⇒ α = τ _L , β = τ _b , where τ _{L is the} solution of the equation

unit function: η = 1 if x≥0, η = 0 if x <0.

p = P / P ₀ - dimensionless density dipole moment, P ₀ = mc ² [γ-1) / 4πe, P ₀ · q (τ) = P ₀ b ³ τ ^2/2 - charge emitted from the cathode to the time τ, q = q ⁱⁿ + q ^out , q ⁱⁿ is the dimensionless charge inside the diode, q ^out is outside.

As already noted, in studying the process of electromagnetic wave emission, the derivatives of the density of the dipole moment are of interest, since the generated electromagnetic fields are expressed through these quantities.

The maximum values of the dimensionless functions dp ⁱⁿ / dτ, dp ^out / dτ, with an error of ≤3% are described by the following formulas (b >> 1):

Thus, at sufficiently large values of the emission current density (b >> 1), the amplitude values of the derivatives of the density of the dipole moment with respect to time are proportional to the corresponding scale factors:

and, therefore, depend only on the energy mc ² (γ-1), which the electrons can gain when passing through the diode, and the length of the interelectrode gap L. Details of the behavior of the emission current do not play a role. The main thing is that it be so large that b >> 1.

Power and energy source

The easiest way to estimate the energy U and power Φ of a source is by considering its radiation in the near field. In the source zone, the divergence of the radiation beam is still negligible, the beam front is flat and the cross-sectional area of the radiation beam is equal to the projection area of the emitting surface onto a plane perpendicular to the direction of radiation propagation, and the magnetic field is proportional to the first time derivative of the surface density of the dipole moment

Photodiode with an opaque EMR anode

In the case of an anode that is opaque to the EMR, a wave leaving the source is generated in the region above the anode and, therefore, P = P ^out . Since, according to [3, 4], P ^out (θ) ≈cos ² θP ^out (θ = 0), using the solution to the discharge problem of an infinite flat diode, we can represent dP ^{out /} dt in the following form:

where the dimensionless function p ^out (τ) = dp ^out / dτ.

получим:After substituting (31) into (30) and performing the necessary calculations

we get:

V = SL,, [S] = cm ² , [L] = cm.

sin²θ_m cos³θ_m≈0.186.The function sin ² θcos ³ θ в has a maximum at the point θ = θ _m ,

sin ² θ _m cos ³ θ _m ≈ 0.186.

From the unit area of the considered source of electromagnetic radiation can be removed (θ = θ _m ):

Knowing the energy of microwave radiation and the energy stored in the interelectrode gap

can find source efficiency

Photodiode with an EMP transparent anode

In the general case, when a photodiode is discharged, the movement of electrons occurs both inside and outside the photodiode (above the anode). Accordingly, two areas of electromagnetic wave generation arise: internal and external, with a common boundary between them - the anode. It is clear that the characteristics of the generated electromagnetic waves should depend on the properties of this boundary. However, until recently, this circumstance was not given due importance. We studied only the version of the source with an opaque EMR anode, in which the electromagnetic wave leaving the source was a wave generated in the region above the anode. The discovered strong dependence of the energy characteristics of the generated EMR on the angle of incidence of the LI was an unpleasant surprise, which forced us to look for a way out of this situation.

According to [3, 4], a decrease in the amplitude of the density of the dipole moment is a consequence of the deceleration of accelerating electrons in the field of the wave they generate. The amplitude of this wave reaches values comparable to the accelerating field due to the addition of waves reflected from the electrodes of the photodiode. It follows that this unwanted increase in the amplitude of the electromagnetic wave inside the photodiode can be prevented or reduced if the wave is completely or partially deprived of the ability to be reflected from the electrodes. To do this, it is enough to use an anode transparent to EMR. There are at least two cases where the anode will be transparent to EMR.

When the thickness of the anode is less than the thickness of the skin layer

When the wires of the mesh anode are perpendicular to the plane of incidence of light.

So, suppose that an electromagnetic wave passes through the anode of a photodiode, which is also transparent to electrons. Integrating the Maxwell equation for the field component E _z over the localization region of the electron current density L _j ≈2L

we get:

As shown earlier, outside the current density localization region

(it is assumed that L _j cosθ / s << T ₀ ). Hence

отсутствует cos²θ и оно совпадает с аналогичным выражением при θ=0, когда генерации электромагнитной волны вообще нет. Следовательно, можно считать, что

и для компоненты поля E_z справедлива следующая оценка:Thus, in the expression linking E _Z and

cos ² θ is absent and it coincides with a similar expression for θ = 0, when there is no electromagnetic wave generation at all. Therefore, we can assume that

and for the field component E _{z the} following estimate holds:

влиянием электромагнитной волны на движение электронов можно пренебречь.From this estimate it follows that in the case under consideration at sufficiently low accelerating voltages and / or sufficiently small angles of incidence, when

the influence of an electromagnetic wave on the motion of electrons can be neglected.

Both internal and external regions of the photodiode take part in wave generation. Therefore, the surface density of the dipole moment is the sum of the internal and external densities:

P = P ⁱⁿ + P ^out .

Respectively

dP / dt = dP ⁱⁿ / dt + dP ^out / dt.

From the solution of the discharge problem of an infinite flat diode it follows that dP / dt can be represented in the following form:

where the dimensionless function p (τ) = dp / dτ has an amplitude of ≈1.

a (dp/dτ)_max≈1.17, получим выражения для характеристик рассматриваемого источника излучения.Substituting (36) into (30), given that

a (dp / dτ) _max ≈1.17, we obtain expressions for the characteristics of the considered radiation source.

From the unit area of the photoemission source under consideration, EMR can be removed:

source efficiency

The obtained analytical results are based on the assumption that the strong inequality L _j cosθ / s << T ₀ is satisfied. In addition, it is assumed that L _j ≈ 2L. As a result, the original inequality reduces to inequality

В этот момент, согласно выражению для траектории электрона (23), все электроны находятся внутри отрезка 0≤z≤2L. Учет поля волны не может увеличить размер этого промежутка, поскольку волна тормозит электроны. Следовательно, выбор L_j≈2L обоснован и неравенство (40) выполняется всегда, когда γ-1<<1.which for γ-1 << 1 (for example, γ-1 is less than or of the order of 0.01) is satisfied for all angles. Thus, for γ-1 << 1, the results are applicable if the assumption L _j ≈2L is true. The size of the region where the electrons are localized varies during the discharge and, generally speaking, can be noticeably larger than 2L. However, to estimate the limiting characteristics, the times after the time moment τ _max , when the derivative dp / dτ, and with it the field amplitudes reaches a maximum, are of no interest. At

At this moment, according to the expression for the electron trajectory (23), all the electrons are inside the interval 0≤z≤2L. Taking into account the wave field cannot increase the size of this gap, since the wave slows down the electrons. Therefore, the choice of L _j ≈ 2L is justified and inequality (40) is always satisfied when γ-1 << 1.

For values of γ-1 <1, for example, about 0.2 or more and angles θ not too close to 90 °, instead of strong inequality (40), only a weak inequality can be fulfilled:

A numerical study of the discharge of a photodiode with an anode transparent to EMR and electrons has shown that in this case all the conclusions of the analytical approach remain valid.

An analysis of expression (39) for the efficiency of conversion of electrostatic energy into electromagnetic energy, taking into account the restrictions that were made in the process of deriving this expression, shows that the considered version of the photoemissive source can have an efficiency significantly higher than 50%. This conclusion is confirmed by the results of numerical calculations.

что приводит к соответствующим изменениям в выражениях для характеристик источника:If the anode is opaque to electrons, then the characteristics of the generated electromagnetic field in the near field will be determined by dP ⁱⁿ / dt. In this case (dp ⁱⁿ / dτ) _max = 1,

which leads to corresponding changes in the expressions for the characteristics of the source:

Description of numerical calculations of the generation of electromagnetic radiation during the discharge of a planar photodiode

In a numerical study of the dynamics of a discharge of a planar photodiode in a two-dimensional formulation, the Maxwell equations and the equations of electron motion were solved. It was assumed that LI irradiates the photocathode passing through a transparent anode for LI. We studied the characteristics of the electromagnetic wave inside the photodiode for various values of the angle of incidence of the laser radiation. The length of the photodiode varied from L _x = 0.2 cm to L _x = 5 cm, the interelectrode gap was L = 0.1 cm, φ (z = -L) = - 100 kV, φ (z = 0) = 0. The calculation data in comparison with the corresponding analytical results are presented in the figures.

The results of an analytical and numerical study of the discharge of a planar photodiode initiated by a planar LI flux obliquely incident on the photocathode show that in the case of using an anode transparent to EMR

- at θ≥60 ° the flux density of electromagnetic energy is ten or more times higher than the flux density of the electromagnetic energy of a source with an anode that is opaque to the EMP;

- the efficiency of conversion of electrostatic energy into electromagnetic energy exceeds 50%.

(increase the efficiency and intensity of electromagnetic radiation). Thus, an electromagnetic radiation source that uses a photodiode discharge with an EMP transparent anode to generate an EMP has significantly higher energy characteristics than its counterpart in the known technical solution with an opaque EMP anode in which the EMP is generated by a dipole layer above the anode. When E ₀ = φ ₀ / L≈10 ⁶ V / cm, L = 0.1 cm θ = 60 °, the power taken from 1 cm ^{2 of the} radiating aperture of the proposed source will be ~ 10 ⁹ W.

Reducing the energy characteristics of the source can be avoided by using a photodiode with an transparent EMR anode to generate EMP, in which there is no negative influence of the internal electromagnetic wave, since its reflection from the anode is excluded. In the case of an anode transparent to EMR, the unhindered output of the internal wave reduces its amplitude. However, in general, the amplitude of the wave leaving the source increases. Due to the expansion of the generation region, which now includes both the internal and external regions of the photodiode, and the increase in the electron energy above the anode, the efficiency of converting electrostatic energy to electromagnetic energy increases significantly.

The use of this invention will allow to obtain more powerful pulses of a broadband EMP microwave range.

For the claimed invention, in the form described in the claims, the possibility of implementing a method for generating broadband electromagnetic radiation of the microwave range and the ability to achieve the technical result perceived by the applicant is confirmed.

Therefore, the claimed invention meets the condition of "industrial applicability".

Claims (1)

A method for generating broadband electromagnetic radiation of the microwave range, namely, that a voltage pulse is applied to the electrodes of the photodiode, a photocathode in the form of a focusing mirror for laser radiation is obliquely irradiated with pulsed laser radiation, as a result of which electrons are emitted from the cathode, which are accelerated in the evacuated interelectrode gap characterized in that they use an anode that is transparent to the generated electromagnetic radiation.

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