ISSN 10642269, Journal of Communications Technology and Electronics, 2015, Vol. 60, No. 2, pp. 204–207. © Pleiades Publishing, Inc., 2015. Original Russian Text © E.N. Kozyrev, I.N. Goncharov, A.I. Maldzigati, Yu.F. Shevrikuko, 2015, published in Radiotekhnika i Elektronika, 2015, Vol. 60, No. 2, pp. 213–216.

ELECTRON AND ION OPTICS

Modeling of the Behavior of Reflected Electrons in Image Converters E. N. Kozyrev, I. N. Goncharov, A. I. Maldzigati, and Yu. F. Shevrikuko NorthCaucasian Institute of Mining and Metallurgy (State Technological University), ul. Nikolaeva 44, Vladikavkaz, 362021 Russia email: goncharov[email protected] Received November 30, 2013

Abstract—Approaches to modeling of the electric field arising at the input of the channels of microchannel plates (MCPs) mounted in image converters (ICs) used in the nighvision technique are proposed. A proce dure for determining the boundary conditions of the model, which allows one to adequately compute paths of the electrons emitted by the photocathode of the 2nd+generation IC and then interacting with the end surface of the MCP is presented. The developed model is used to study the behavior of the electrons reflected by the input surface of the MCP. DOI: 10.1134/S1064226915020060

Microchannel plates (MCPs) (see Fig. 1), namely, glass vacuum multichannel detectors and electron image amplifiers are widely used in different areas of technology, in particular, in nightvision devices. The design of such a device is shown in Fig. 2. The elec tronic signal that carries the visual information and requires amplification is transmitted to the MCP input from the surface of the photocathode. The photocath ode of the image converter (IC) is located in parallel to the MCP at the distance lpc–IC = 0.25 mm. The poten tial difference maintained between them correspond to Upc–IC = 500 V.

of the channels with consideration for the boundary conditions and the model of electron behavior in con ditions of this field. Let us consider principles of mod eling of the electric field in regions located in front of the end surface of the MCP and in the initial part of the channels with consideration for the boundary con ditions. Since the photocathode and the surface of the MCP have relatively large areas (about 2.5 cm2) and are located at a small distance from one another, the electric field formed between them can be considered

It should be noted that the electron multiplication factor and the degree of completeness of the electron image transmission are in many respects determined by the ratio of the areas of the MCP open surface and the channeltochannel partitions (see Fig. 3). This parameter of the MCP is called transparence ω and, according to the product specification, is about 0.58– 0.6. The closer the value of ω to unity, the higher com pleteness of the electronic signal transmitted through the MCP and the lower the degree of sampling of this signal. As a result, the image formed on the IC screen will have higher brightness, resolution, and lower noise characteristics. It is also necessary to have information on the behavior of the electrons emitted by the photocathode and subsequently held by the input end (nonfunc tional) surface of the plate. To study in detail this phe nomenon, it is necessary to develop computer aids for studying the behavior of the electrons emitted from the input end of the MCP. These aids use the model of the electric field formed in the region of the input part 204

Fig. 1. Microchannel plate in the transport container.

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8 Fig. 2. Block diagram of a nighvision device with the 2+generation IC: (1) objective lens, (2) photocathode, (3) 2+generation IC vacuum unit, (4) multichannel plate, (5) cathodoluminescent screen, (6) eyepiece, (7) eye, (8) power supply electrodes of the IC, and (9) input surface of the MCP.

as flat. The mathematical model of this field can be based on the Laplace equation, which is written as [1]:

∂ U + ∂ U = 0, (1) 2 2 ∂x ∂y where x and y are the coordinates, and U is the poten tial of the field. Let us consider in more detail the design of the region between the photocathode and the IC MCP input. A fragment of the section of this region is shown in Fig. 4. Note that, when the Laplace equation is solved by the finitedifference method, the calculated domain should be closed [2]. Assume that a real electronoptical system (EPS) of the region between the photocathode and the MCP input includes a great number of channels with cross section diameter d = 10 µm, which are periodically repeated along the plate diameter equal to 20 mm. The distance from the photocathode to the MCP is 0.25 mm and the channel length is 0.4 mm. The anal ysis of the problem shows that, when a grid method is used in the process of the computeraided calculation of the electric field distribution with the optimum grid step h = 1 µm, storing the information in 2D arrays requires a large volume of the computer RAM [3]. It is evident that the boundaries of the investigation area should be reduced as much as possible; however, this reduction should be made so that the adequacy of the calculation results is not decreased. It was found that the design of the IC (first of all, its periodicity) and the conditions of its operation allow one to perform this reduction. It is necessary to reduce and enclose the region based on physical considerations so that the 2

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segments of the boundary introduced for calculation do not affect the conditions determining the behavior of electrons. Let us consider the potential distribution in region 2–3 between the photocathode and the MCP input (see Fig. 4). The larger the distance from the sur face of the plate, the smaller the influence of channels on the gap field. Taking into account the channel diameter (d = 10 µm), it is possible to consider that, at a distance of (2–3)d from segment 2–7 and farther toward the cathode, the potential distribution between the cathode and the MCP corresponds to the potential distribution between two flat electrodes,

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Fig. 3. Configuration of the MCP surface: (h) period of the structure, (d) diameter of the channel, and (k) width of the channeltochannel partition.

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Fig. 4. Scheme for specification of the boundary conditions in modeling of the electric field distribution in the region of the MCP input in the 2nd+generation IC: (I) to the photocathode, (II) emission region, and (III) input ends of the MCP.

i.e., it is linear. Thus, we can assume that, in this region, the boundary is located at a distance of 20 µm (segment 2–3) and goes along segment 3–6. The potential distribution over segment 2–3 is formed as a result of interaction between the electric fields of the MCP channels and the photocathode–MCP gap in accordance with values of Upc–MCP, lpc–MCP, and UMCP. The elastically reflected and secondary electrons under study, which are emitted by the input surface of the MCP end toward the photocathode, have an initial energy of no more than 10 eV. Under the action of the retarding field, arising due to voltage Upc–MCP, the electrons flying out from the end surface of the MCP fly back to the MCP input. By comparing values of the retarding field and the electron flight energy, it is pos sible to conclude that the heights of parabolic paths of electrons are small and do not exceed 5 µm. Thus, the problem of modeling of the behavior of the electrons flying out from the end surface of the MCP can also be solved by considering a limited domain of the gap between the photocathode and the MCP input. With out losing the accuracy of the results, it is sufficient to calculate the field picture at the distance selected ear lier, which is equal to 20 µm from the end surface (along segments 2–3 and 6–7 in Fig. 4). Since the accelerating voltage applied to the MCP linearly increases along its channels in accordance with the channel length and the resistance of the resis tiveemission layer, the distribution of the potential between the input and output surfaces of the plate

should be assumed linear by analogy with region 2–3. In this case, in the study, it is sufficient to consider only some portion of the channel (in this case, a quarter of the length, which is equal to 100 µm). Thus, in this region, the boundary passes along segment 1–8. The degree of the potential increment along segment 2–1 and its limiting value are determined in accordance with the total supply voltage of the MCP. Finally, it is necessary to enclose the studied region along segment of the MCP surface, i.e., to limit the length of segment 2–7 (see Fig. 4). Assume that it includes six channels partitioned by barriers. The obtained section with vertical boundaries 1–3 and 8⎯6 enables one to create a sufficiently exact field picture, which is typical of a real gap between the photocath ode and the microchannel plate. The closureness of the region is the necessary but not sufficient condition for solution of the Laplace equation by a finitedifference method [1]. The poten tial or its normal derivative should be known at each point of the boundary belonging to the elements of the plate design. In segments 3–6 and 1–8, potentials take constant values and they change linearly along the seg ments 2–3 and 7–6 and along the segments 2–1 and 7–8. The methods for determining these potentials were considered above. Thus, in all segments, bound ary conditions correspond to the Dirichlet problem (the potential is given at each point of the boundary of the studied region and it is necessary to determine its

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Fig. 5. Calculated paths of the end electrons of the MCP in the presence of an element of its side section at different initial con ditions of escaping electrons: (a) E = 1 eV and α = 0, (b) E = 3 eV and α = 67°, (c) E = 12 eV and α = 45°, and (d) E = 17 eV and α = 45°.

distribution inside the region). This problem should be solved numerically by a finitedifference method. After solving the problem of finding the field with consideration for the boundary conditions specified above, we should proceed to calculation of the paths of electrons in this field. The behavior of the electrons flying out from the end surface of the MCP toward the photocathode is described by the following system of equations [4]: ⎧V = dx , dV x = − e E , x ⎪ x dt dt m (2) ⎨ ⎪V y = dy , dV y = − e E y , ⎩ dt dt m where Vx and Vу are the projections of the velocity vec tors onto the х and уaxes, respectively; Ех and Еу are the calculated field intensities in projections onto the х and уaxes; and е and m are the charge and mass of the electron. When calculating the paths of electrons, it is neces sary to take into account the initial conditions, namely, the facts that the angular distribution relative to the perpendicular to the emission surface for the outgoing secondary electrons is cosineshaped and the electron flight energy Е corresponds to the range (1⎯15) eV [5, 6]. Figure 5 shows the results of calculations corre sponding to different initial conditions. They were performed using the developed tools of the computer aided analysis of calculations. The studies have shown that about 50% of the considered secondary and reflected electrons emitted from the end of the MCP fly back into the channels. According to the value of ω, on average about 40% of signal electrons interact with the MCP end, and, as a result, the transparency auto matically increases by on average 20%. Thus, using machine computations, we managed to find out that the actual transparency of the MCP is noticeably higher than the geometrical transparency determined by the MCP structure and indicated in the product specification. Hence, there is no need for changing the

plate design, i.e., to increase the value of ω in order to increase the gain of the input signal and, thus, to reduce its mechanical and electric strength. The depths of penetration into the channels of electrons of the considered category were also deter mined. Calculations have shown that, in most cases, these depths do no exceed 100 µm, which corresponds to the energy of impact against a wall in (10–200) eV (at UMCP = 800 V). It was revealed that the higher are flight angle α of the electron and its energy E, the nearer to the beginning of the channel is the point at which the electron interacts with the wall; the electron flightup angles decrease with penetration into the channel. These data are important for calculation and analysis of the secondaryemission efficiency of inter action between the electrons and the channel walls. ACKNOWLEDGMENTS The results of the study are obtained within the framework of State order no. 2014/207 of the Ministry of Education and Science of the Russian Federation, project no. 267 g/b. REFERENCES 1. I. N. Goncharov, Prib. Sist., No. 3, 38 (2009). 2. I. N. Goncharov, Gornyi Inf.Anal. Byull., No. 5, 125 (2009). 3. I. N. Goncharov, Vestn. Voronezh. Gos. Tekh. Univ. 8 (2), 41 (2012). 4. I. N. Goncharov, E. N. Kozyrev, and A. G. Mouraov, Izv. Vyssh. Uchebn. Zaved., Probl. Energ., No. 3–4, 94 (2009). 5. I. N. Goncharov, Izv. Vyssh. Uchebn. Zaved., Severo Kavkaz. Region. Tekh. Nauki, No. 5, 32–36 (2008). 6. I. N. Goncharov and E. N. Kozyrev, Vestn. Voronezh. Gos. Tekh. Univ. 5 (6), 114 (2009).

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Translated by N. Pakhomova

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