On the causes of electrothermal destruction of fiber-optic communication lines placed on the structures of AC overhead wires

. The paper analyses the impact of the electromagnetic field of an alternating current catenary section on a fiber-optic cable suspended on the structures of the catenary system or on the overhead wires of the Centralised Traffic Control (CTC). Based on this calculation, conclusions have been made about the negative impact of alternating current electric fields with high vorticity.


Introduction
On the network of electrified railways, the method of laying communication lines with a fiber-optic cable, where the cable suspension is carried out from the field side of the catenary structures or the Centralised Traffic control supports has become widespread. A few years later, after the start of such lines operation, failures of fiber-optic cable (FOC) were recorded, they were expressed in local breaks and burns. As one of the reasons causing such problems, the result of exposure to a powerful alternating electromagnetic field of the catenary system was named [1]. It should be noted that, in contrast to the cases of laying such communication lines along the supports of high voltage power transmission lines of 35, 110, 220 kV, the degree of negative impact of electromagnetic fields will obviously be lower, due to the fact that the catenary system is an integral part of the traction network of an electrified railway, it is an electrically uncompensated power transmission line [2], where the wires of forward and reverse current are spaced apart by a significant distance.

Methods and results
For a detailed analysis of the exposure degree to the electromagnetic field, it is necessary, first of all, to focus on typical damages caused by the so-called electrothermal degradation that occurs during long-term operation of the FOC. The following typical cases of damage should be distinguished: cable breakage caused by its burning at the bottom of the supporting clip, burnout of the shell and Kevlar threads at the bottom of the supporting clip without cable breakage, the occurrence of "blisters" along the cable axis.
As the practice of FOC operation shows, cable damage does not begin to manifest itself immediately, but after several years. Moreover, according to statistics, cable breaks, as a rule, occur most often in wet weather. The peculiarities of cable accidents caused by electrothermal degradation of the cable also include their concentration.
Thus, based on the above-mentioned facts, it can be assumed that at least three factors have a decisive influence on the process of electrothermal degradation of a fiber-optic cable suspended on the supports of the catenary system: the service life of FOC, the humidity of the environment, the configuration of the bearing and supporting structures of the catenary system section and the two-wires-rail (TWR) system on which FOC is located.
Each of the influencing factors is considered separately below. During operation, the surface of the cable loses its original luster and becomes rough, as a result of which dust particles in the air begin to linger on the cable sheath. Over time, a thin conductive layer forms on the surface of the cable, that changes its resistance depending on weather conditions and air humidity. Provided that the cable has an electrical contact with the supporting clip (SC), and this SC is attached to the support without additional insulation, the cable begins to have an effect on the electric field of the traction network. This effect is similar to the effect of a grounded conductor suspended instead of FOC. The degree of similarity will be the higher the lower the surface resistance of the cable sheath and the lower the transition resistance between SC and grounded objects. The latter one is worth focusing in more details. The fixing bracket to which the supporting clip is attached, provided TWR system located above it, must necessarily be grounded.
Thus, in this case, the SC-ground transient resistance is close to zero. The situation is different in the absence of TWR system, and in this case, humidity is obviously crucial. It is the humidity of the air, not the rain.
In case of rain, the resistance of the rough and dirty surface of the cable becomes very small, as a result of which the entire surface of the cable is connected to the body of the wet support. FOC in this state is equivalent to a conductor grounded on both sides to the ground. Obviously, the time required for the cable to be dried is significantly less than the time required for complete evaporation of moisture from the concrete support. Therefore, in the time interval when the cable has already started to dry out, and the moisture from the concrete has not yet evaporated, the supporting clip will be at a potential close to the potential of the ground, and the potential of the fiber-optic cable will be determined mainly by the potential of the catenary field induced on it. The same effect can be observed at high humidity, when the concrete of the overhead wire supports absorbs moisture much more strongly than a thin layer of cable contamination.
As it was mentioned above, the third factor is the configuration of the load-bearing and supporting structures of the catenary section and TWR, where FOC is located. Currently, two main types of consoles are used on the Russian railway network, which serve to attach the wires of the catenary system. On the sections that were electrified a long time ago, noninsulated or, as they are also called, grounded consoles have been applied. Isolated consoles are used on the new sections. The difference is in the fact that in the case of using an isolated console, the points under the potential of the catenary system are close to the support body by a minimum distance of about 0.5 meters, which obviously greatly increases the induced potential on FOC near the support. In cases where grounded consoles are used, this distance much more increases, in addition, the console itself has a shielding effect.
The surface of the cable is subjected to various kinds of atmospheric influences, as a result of which it deteriorates and changes the resistance of the FOC surface. Thus, the cable becomes conductive, and in order to simulate the processes in it correctly, it is necessary to correct the picture of the influencing electric field. The limiting case of degradation of the cable sheath (for solving the problem of calculating the electric field) is the case when its sheath acquires a resistance close to zero. Such a regime can take place in reality on the sections with prolonged ascents or descents. In such areas, the surface of the cable over time is covered with a layer of metal dust formed when the pads of electric rolling stock (ERS) are erased. In addition, both on hilly and flat sections, the surface of a cable that has served for several years loses the property of repelling water, and after precipitation, a conductive film forms on the surface of the cable.
When simulating the field of the section under the specified conditions, there is no need to calculate the potential of the FOC sheath, it is set ones, assuming FOC to be a grounded conductor. The feeder wire will be denoted by the index "k", the index "c" is the carrier cable, and the index "f" is the fiber optic cable. Using the first group of Maxwell formulas, the application of which is permissible under the conditions being considered in the paper [3], it is possible to create a system of equations that allow to calculate the electric field pattern for a single-track section of an electrified railway, where there are no other feeder and grounded conductors. Thus, the system of equations will have the form: In these expressions, the following notations are accepted: τkthe linear charge density on the surface of the contact wire, [ From all of above mentioned it follows, that with severe degradation of the cable, the potential of its surface becomes minimal, however, as follows from the picture of the field presented in Figure 8, the potential rises sharply moving away from the wire, and at a distance of several meters from FOC the pattern of the potential field is practically the same as that shown in Figure 2.
The situation is different with the pattern of the field vorticity near FOC. As it was mentioned earlier, the potential on the surface of the cable will be close to zero, and, in addition, it will increase very sharply moving away from the cable. It is known [3] that to determine the electric field vorticity, one can use the ratio: ̄= =̄+̄. (2) In this case, the value of the rate of potential change near the cable will be significant, and therefore the field vorticity near the cable will be high. The pattern of the vorticity field of the section under consideration, shown in Figure 2, confirms the statement that, under the condition of complete degradation of the sheath, a significant increase in the electric field vorticity will be observed near FOC. The investigation of changes in the field pattern of potentials and vorticities for variants of the state of the fiber-optic cable sheath, which differ from the two boundary cases considered earlier, is of particular interest, since it is in these modes, as studies have shown, that the processes of partial and complete destruction of the sheath and the cable body begin to occur. It is obvious, the main difficulty in this case can cause the construction of the potentials field pattern, since the field of vorticities is reconstructed on the basis of a given field of potentials as the sum of partial derivatives in two coordinates [4][5][6][7][8][9].
The presence of FOC in the electric field, with a finite value of the sheath resistance, will be taken into account on the basis of the following considerations. With a decrease in the surface resistance of the cable, the potential on its surface will decrease, in the extreme case tending to zero. Thus, by varying the potential value at the cable suspension point from the maximum possible value to zero, it becomes possible to simulate the degree of degradation of the cable sheath. In addition to the previously made designations, the potential of the fiberoptic cable sheath will be denoted by the variable φf. Thus, the system of equations will have the form: The maximum possible value of the potential is defined as the potential of the suspension point of the cable with the resistance of its sheath tending to infinity. The pattern of the potentials field and vorticities for cases of gradual degradation of FOC will be simulated below. The changing of the field pattern for the case when there is only a catenary system will be considered. The figures below show the dynamics of changes in the pattern of the potential field with gradual degradation of the cable. Figures 3 and 4 show how the potential and field vorticity will be changed with a sufficiently large, but already finite resistance of the cable sheath. When simulating the field pattern, it is assumed that the potential of FOC surface is reduced relative to the maximum possible value by 200 volts. The potential, provided there is no influence, was calculated and is 5200 V, the set value is 5000 V. In Figure 3 (a), there are no significant changes in the determination of the potential field compared to Figure 2 (a). In the area of the cable suspension point, with coordinates X = 1000, Y= 7000, a slight deformation of the equipotential line is observed.
The situation is different with the vorticity of the field. Figure 3 (a) allows to see that the changes in the pattern of the field of vorticity are more significant. It is important to note that this pattern was caused by a change in the potential of the cable surface of about 4%. It is assumed a significant change in the potential of the cable surface and the processes that occur with a more significant degradation of the sheath are simulated further. Figure 4 shows patterns of fields constructed under the condition that the specified value of the sheath potential was 1000 V. The dynamics of the cable resistance influence on the pattern of the electric field is quite clearly traced. In Figure 4 (a), it is already possible to distinguish the place of the cable suspension, a strong distortion of the equipotential line is visible. The pattern of the field vorticity indicates that a decrease in the resistance of the cable results in an increase in vorticity around FOC. Thus, it can be argued that the magnitude of the vorticity near FOC and also the configuration of the field of potentials and vorticity for a particular section will be subject to a significant change with a decrease in the resistance of its sheath.
A further study conducted with a pattern of the field of vorticities corresponding to the case of severe degradation of the cable surface, Figure 4 (b), allows to conclude that there is a significant increase in the electric field vorticity near the suspension point of the fiber-optic cable. It is this fact that suggests that the increase in the electric field vorticity is decisive in the process of electrothermal degradation of existing fiber-optic communication lines.
To carry out the proposed assumption, an experiment was conducted, for which a sample of a 10 mm FOC was cut out and placed between two metallised geax plates. A uniform electric field was formed between the plates, created by a high-voltage installation of alternating sinusoidal current. The voltage between the plates was raised stepwise, at a rate of 1000 kV per minute. At each time interval, the current flowing through the fiber-optic cable sample was recorded using a microammeter. As a result of the experiment, it was found that when the test voltage was raised to values not exceeding 5 kV, the leakage current flowing through the test sample was insignificant and corresponded to 4 µA, which is commensurate with the leakage currents of insulation. However, with an increase in the test voltage to 6000 V, an increase in current was noted -12 µA, and with a further increase in voltage to 9000 V, the current reached a value of 0.1 mA, after which a breakdown of the fiber-optic cable sample occurred.
The study of individual structural elements of FOC, carried out after the completion of the sample tests in a high-vorticity field, showed that neither the polyethylene sheath, nor the central modular tube, nor the gel filling were subject to any damage, and only the Kevlar sheath was significantly damaged, Figure 5a. A thorough inspection of the Kevlar sheath, Figure 5 (b) showed that in some parts of the sheath there are strands of Kevlar, and in some of them there are whole significant bundles of Kevlar that have been charred, which contributed to the formation of conductive tracks with negligible resistance compared to the original Rorig = 5000 mOhm; Rchar = 7 kOhm.
The conducted experiment suggests the possibility of changing the structure of Kevlar filaments caused by a powerful alternating electric field of high vorticity. A high-vorticity electric field activates the processes of destruction of polyamides [10]. Under such conditions, "crosslinking" processes occur in the structure of polyamides, which are directly related to the destruction of weakly molecular bonds and the formation of molecules of certain chemical elements. In addition, the process of "crosslinking" is accompanied by the emergence of free radicals in the polyamide structure.

Conclusions
The results of the work described in this paper allow to draw a number of important conclusions regarding the issue of investigating the causes of electrothermal degradation of fiber-optic communication lines suspended on the supports of the catenary and CTC lines. According to the results of the experiment, a powerful electric field has a negative effect on the power part of FOCaramid threads (Kevlar), which is confirmed by the fact of burning a bundle of Kevlar threads inside the cable. A powerful external electric field vorticity will be present at the cable suspension points, provided that the outer sheath of FOC has degraded under the influence of wind, rain and solar radiation, as well as other external destructive factors. Degradation of the cable sheath will result in an increase of surface conductivity, and as a consequencethe formation of local points of forced reduction of the potential of the field induced by the catenary. The presence of a potential gradient at the suspension point of the cable will result in an increase in the electric field vorticity, which, as it was mentioned above, is the main cause of damage to the fiber-optic cable.