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Theoretical Electrical Engineering and Electrophysics
UDC 621.3.01: 621.313 doi: 10.20998/2074-272X.2020.2.05
M.I. Baranov, S.V. Rudakov
CALCULATION-EXPERIMENTAL DETERMINATION OF THE AVERAGE NUMBER OF QUANTIZED LONGITUDINAL ELECTRON DE BROGLIE HALF WAVES IN A CYLINDRICAL CONDUCTOR WITH PULSED AXIAL CURRENT
Purpose. Implementation of calculation-experimental determination of average number n0m of the quantized longitudinal electron de Broglie half waves of length lew/2 in the metal cylindrical conductor with the pulsed axial current of high density. Methodology. Scientific bases of theoretical electrophysics and quantum physics, theoretical bases of the electrical engineering, electrophysics bases of technique of high-voltage and high pulsed currents. Results. The results of calculation-experimental estimations of average number n0m of the quantized longitudinal electron de Broglie half waves in the round continuous zincked steel wire of radius 0.8mm and of length 320 mm with aperiodic pulsed axial current i0(t) of temporal shape 9 ms/160 ms of high density (at its amplitude of S0m=0.37 kA/mm2). It is shown that in examined case the numeral value of the average quantized number from data of calculation and experiment makes n0m=9, and test average length of quantized longitudinal electron de Broglie half waves in the indicated steel wire appears approximately equal to lezm/2~34 mm. Electrophysical results are confirmed during the high current high temperature experiment conducted by a powerful high-voltage equipment calculation information on the choice of average value of quantized number n0m for longitudinal «hot» areas of the width Az of the wire, different anomalous enhanceable concentration of drifting lone electrons and accordingly temperature of Joule heating. Originality. On the basis of the known conformities to the law of atomic and quantum physics new quantum-mechanical calculation correlation is obtained for determination in a metallic conductor with axial current of conductivity i0(t) of different type (direct, alternating and pulsed) of average number n0m of the quantized longitudinal electron de Broglie half waves and accordingly longitudinal «hot» areas of the width Az of periodic localization along the conductor of drifting lone electrons. Practical value. Obtained results allow to make an evaluation prognosis on finding of possible places of longitudinal periodic localization of drifting lone electrons on narrow areas of the width Az of current-carrying parts of power wires and cables of objects of electrical power energy, production and dwellings apartments, showing up most strongly (expressed) in malfunctions of operation of cable-conductor products with the currents of short-circuit and high current density. References 26, figures 4.
Key words: metal conductor, pulsed current, calculation-experimental determination of the average number of quantized longitudinal electron de Broglie half waves and electron localization zones in a conductor.
Представлеш результати теоретичних i експериментальних дослiджень, ят пов 'язат з визначенням усередненого числа n0m квантованих подовжнк електронних твхвиль де Бройля в металевому провiднику з 1мпульсним акпальним струмом провiдностi великоТ щшьност1 Отриман результати вказывют на квантово-хвилевий характер протiкання мпульсного струму провiдностi в цьому провЫнику, що приводить до виникнення в його структурi квантованоТ подовжньоТ перюдичноТлокатзаци втьних електротв, що дрейфують, на дтянках шириною Az. Дан зони локажзаци електронв вiдрiзняються тдвищеною температурою нагрiву. Бiбл. 26, рис. 4.
Ключовi слова: металевий проввдник, 1мпульсний струм, розрахунково-експериментальне визначення усередненого числа квантованих подовжшх електронних швхвиль де Бройля i зон локал1защ1 електрошв в пров1днику.
Представлены результаты теоретических и экспериментальных исследований, связанных с определением усредненного числа n0m квантованных продольных электронных полуволн де Бройля в металлическом проводнике с импульсным аксиальным током проводимости большой плотности. Полученные результаты указывют на квантово-волновой характер протекания импульсного тока проводимости в этом проводнике, приводящий к возникновению в его структуре квантованной продольной периодической локализации дрейфующих свободных электронов на участках шириной Az. Данные зоны локализации электронов отличаются повышенной температурой нагрева. Библ. 26, рис. 4.
Ключевые слова: металлический проводник, импульсный ток, расчетно-экспериментальное определение усредненного числа квантованных продольных электронных полуволн де Бройля и зон локализации электронов в проводнике.
Introduction. A number of scientific publications in recognized domestic and foreign Journals and monographs have been devoted to theoretical and experimental studies of the quantum-wave nature of the electric conduction current in cylindrical metal conductors [1-11]. The results of these studies are fundamental in nature and allow to take a fresh look at the quantum mechanical processes of propagation and localization in the crystal structure of the metal of the indicated conductors of their drifting collectivized free electrons, which possess wave properties and are characterized by
their de Broglie wavelengths Ae [12, 13]. As is known, for the wavelengths Àe of electron waves propagating in a metal of a cylindrical conductor with current in its longitudinal and radial directions, the fundamental relation from the field of wave mechanics (quantum physics) holds, obtained in 1924 by the outstanding French theoretical physicist Louis de Broglie and having the following classic form [12, 13]:
Xe = h l(meve ), (1)
where h = 6.626-10-34 J-s is the Planck constant;
© M.I. Baranov, S.V. Rudakov
me = 9.109-10- kg is the rest mass of the electron; ve is the velocity of motion (drift) of free electrons in the crystalline structure of the material of the conductor.
According to [1-13], the behavior of free electrons in a metal conductor of a cylindrical shape is described by the corresponding Schrodinger wave ^-functions (they were first proposed and obtained in an analytical form at the beginning for coupled electrons of hydrogen-like atoms when solving the corresponding wave equation (it entered the history of modern physics as Schrodinger equation) by the outstanding Austrian theoretical physicist Erwin Schrodinger in 1926 [14]), varying in space and time according to the harmonic law and square whose module determines the probability density of their (electrons) being in a particular place in the cylindrical volume of the conductor. In this regard, the most probable places of drift of free electrons under the action of applied to the opposite ends of the conductor constant, alternating, or pulsed electric voltage of free electrons in the conductor metal will be those that correspond to the amplitudes of the Schrodinger wave ^-functions and, accordingly, the amplitudes of the electron waves of length Ae, spatio-temporal changes of which also occur in harmonic law. In addition, the wave distributions of drifting free electrons in the metal structure of any conductor obey the fundamental principle of quantum mechanics - the Heisenberg uncertainty relation [12, 13], formulated by the outstanding German theoretical physicist Werner Heisenberg in 1927 [14] and having for longitudinal z and radial r coordinates of a cylindrical conductor with current the following canonical form:
(2)
me Avez Az > h / 4n ; meAver Ar > h / 4n ,
(3)
where Az, Ar are, respectively, the uncertainties of the longitudinal and radial coordinates of free electrons drifting in the structure of the material of the conductor; Avez, Aver are the uncertainties of the longitudinal and radial components of the drift velocity ve of the electrons in the conductor material, respectively.
It follows from (2) and (3) that even for known (numerically specified) values of the velocities Avez and Aver of drifting free electrons, their spatial location in the cylindrical volume of the material of the conductor with current remains undefined and quantitatively determined by the quantities Az and Ar, respectively. Taking into account the above physical (statistical) interpretation of Schrodinger wave ^-functions, proposed in 1926 by the outstanding German theoretical physicist Max Born [14], the midpoints of the indicated Az and Ar values for drifting free electrons will correspond to the amplitudes of electron waves of length Xe.
With the numerical value of the longitudinal velocity vez of the drift of free electrons in the copper conductor (respectively, and the numerical value of its uncertainty Avez), in the limit of, for example, for the short circuit (SC) mode in the electric circuit (with a longitudinal current density dez of about 1 kA/mm2 [15]), about 37 mm/s, it follows from (1) and (2) that the length XJ2 of
the de Broglie electron half wave in this metal of the conductor will be numerically about 9.8 mm, and the Az value of the longitudinal localization of drifting free electrons in a conductor - about 1.56 mm. It can be seen that in the case under consideration (in the SC mode), the quantities XJ2 and Az take macro-sizes commensurate with the transverse dimensions of the real conductors used in electrical engineering and the electric power industry. In this regard, for this case, wave manifestations in the conductor metal of drifting free electrons, leading to local periodic overheating of the conductor metal in sections of width Az, can be physically detected and recorded using measuring equipment (for example, a thermal imager or camera). As for the random (thermal) motion of free electrons in a copper conductor without conduction current (before applying an electric voltage to it), then in this case their highest speed, determined according to the Fermi-Dirac quantum statistics by the Fermi energy WF [12, 13], takes numerical value of about 1.6-106 m/s. Substituting this value of the electron velocity in (1) and (2), we find that for this case (the initial state of the «electron cloud» of the conductor), the desired values of XJ2 and Az take nano-sizes, respectively, equal to approximately 0.23 nm and 0.036 nm. Therefore, it is not possible for the researcher to identify local manifestations of the wave properties of free electrons randomly moving in its interatomic space and their influence on macroscopic electrophysical processes (for example, on the contact potential difference of metals, thermoelectricity [12], etc.) that occur in conductors.
The above quantitative estimates indicate that, due to the relatively small values of the drift velocities v,, of free electrons in the crystalline structure of the metal of the conductor (for electric power industry, not more than 1 m/s), their wave properties will significantly affect the processes of their spatial distribution in metal conductors and, accordingly, on the processes of Joule heat release in their material.
When studying the behavior of drifting free electrons in conductor metal with conduction current, it is imperative that the quantum nature of all processes occurring in the microworld of matter be taken into account. Therefore, solutions of partial differential equations describing the wave distributions of these electrons in a conductor will be characterized by eigenvalues integers n0 = 1, 2, 3, ... which are called quantum numbers in quantum physics [12-14].
When studying the processes of formation and propagation of drifting free electrons in a metal conductor, one should also take into account the fundamental «principle of prohibition» formulated in 1925 by the outstanding Austrian theoretical physicist Wolfgang Pauli [14] regarding the properties of bound electrons in an atom of any substance. According to the «Pauli principle of prohibition», only one bound electron can be on the electron shells of an atom of matter, having a corresponding and characteristic quantitative set of four quantum numbers [12, 13]: the main quantum number n, the orbital quantum number l, the magnetic quantum
number m¡ and the spin quantum number ms. Therefore, bound electrons even in the same atom of matter differ from each other in energy, the shape of the electron orbital, the position of the electron orbital in atomic space, and the direction of its rotation around its own axis [12, 13]. Having left its atom due to its ionization processes, these bound electrons of various properties become free, forming in the interatomic space an «electron cloud» with an averaged volumetric density (concentration) nem, numerically equal for the main conductive materials (copper, aluminum, etc.) to a value of about 1029 m-3 [12].
At present, in experimental physics, a number of experimentally discovered new electrophysical effects (for example, the presence of longitudinal and radial microstrata in a «metal plasma» during the electric explosion of thin metal wires in a gas medium and vacuum by pulsed current of high density [16, 17], the presence on the axis a high-current plasma channel during a high-voltage spark discharge in a gaseous medium of cylindrical zones with significantly higher volumetric density of free electrons (a thousand or more times) compared with its peripheral zones [18] and others) did not find their theoretical justification based on the laws of classical physics. In this regard, further deepening on the basis of the laws of quantum physics of our ideas about the nature of the longitudinal-radial flow of wave processes in metal conductors of a cylindrical configuration with electric conduction current of various types (DC, AC and pulsed) and amplitude-temporal parameters (ATPs) used in modern electrical engineering, electric power industry and high pulsed current technology, is an urgent scientific and technical task. One of the steps in solving this problem is to find the number of quantized de Broglie electron half waves of average length Xezm/2 located along the indicated conductors with pulsed current and determining in them the corresponding average number of zones of width Az that differ in their increased volumetric density according to the laws of quantum physics of free electrons and correspondingly elevated temperature.
The goal of the paper is quantitative determination by calculation and experimentally of the average number n0m of quantized longitudinal de Broglie electron half waves of length Xezm/2 in a metal conductor of a cylindrical shape with pulsed axial current of high density.
1. Problem definition. Let us consider the case when axial pulsed current i0(t) of arbitrary ATPs with a large density d0(t)=i0(t)/S0 averaged over its cross section S0 flows through a thin rectilinear round continuous cylindrical conductor of radius r0 and length l0>>r0. We use the Hartree-Fock single electron approximation [12, 13], which does not take into account electron-ion interactions in the internal crystalline structure of the conductor. We assume that the spatio-temporal distributions along the longitudinal coordinate z and in time t of drifting free electrons in the material of the investigated conductor with pulsed current i0(t) will
approximately obey the corresponding one-dimensional Schrodinger wave equation [12, 13]. On the basis of the quantum-mechanical approach, it is required to carry out an approximate calculation of the averaged number n0m of quantized longitudinal de Broglie electron half waves of length Xezm/2 in the considered metal conductor of a cylindrical shape with pulsed axial current i0(t), and also to perform using a high-power high-voltage generator of aperiodic current pulses experimental verification of the results of calculating the number n0m of quantized longitudinal electron de Broglie half waves of length Xezm/2 in this conductor.
2. Calculation estimation of the average number of quantized longitudinal de Broglie electron half waves in a metal conductor. To begin with, it was shown in [1, 4, 6-9] for the first time in the field of theoretical electrophysics that on the length l0 of a metal conductor with conductivity current i0(t) of any kind (DC, AC, or pulsed) an integer quantum number n0 of longitudinal de Broglie electron half waves, satisfying the following relation always fits:
n0 = 2I0/ ^ez . (4)
Then from (4) for the desired value of the averaged number n0m of quantized longitudinal electron de Broglie half waves in the metal of the conductor it follows:
n0m = 2l0 / ^ezm , (5)
where Xzm is the average length of the quantized longitudinal de Broglie electron wave in the metal structure of a conductor with conduction current.
From (1) we find that for the quantity Xezm in a first approximation, an expression of the form is valid:
Kzm = h /(mevem X (6)
where vem is the average drift velocity of free electrons in a homogeneous conductor material.
It is known from atomic physics that, in the general case, vem can be determined by the formula [12]:
vem = S0m /(V2e0nem ^ (7)
where S0m/(2)1/2 is the root mean square value of the current pulse density i0(t) in the conductor with its amplitude 50m; S0m; e0=1.602-10-19 C is the modulus of the electric charge of an electron; nem is the averaged volumetric density of drifting free electrons in a conductor.
As a result, from (5)-(7) for the average number n0m of quantized longitudinal electron de Broglie half waves in a metal conductor with pulsed axial current i0(t) of various ATPs, we have:
n0m = J2meS0ml0 /(e0nemh) . (8)
We point out that the value of the averaged volumetric density nem of drifting free electrons in the conductor metal, included in (8), is equal to the concentration N0 of metal atoms multiplied by its valency, determined by the number of unpaired electrons on the valence electron subshells of the conductor metal atoms (for example, for copper, zinc and iron valency is equal to two [12, 19]). The concentration N0 (m-3) of atoms in the metal of the conductor with its mass density d0 (kg/m3)
before the pulsed current i0(t) flows through it is determined by the formula [12]:
= do(Ma
•1,6606 -10"27)"1,
(9)
where Ma is the atomic mass of the conductor material included in the D.I. Mendeleev periodic system of chemical elements and almost equal to the mass number of the nucleus of the atom of the metal of the conductor, calculated in atomic units of mass (in this case, one atomic unit of mass is numerically equal to 1.6606-10-27 kg [13]).
In formula (8), the quantities me, e0 and h are world constants [12, 13], while the values l0 and d0m characteristic of a particular conductor can be numerically specified or determined experimentally.
It should be noted that the computational relation (8), which is simple in form of writing, was obtained in a rather rigorous way based on the known quantum-mechanical laws characteristic of the wave distribution of drifting free electrons in the metal of a conductor with current i0(t) [10].
The calculation estimation by (8) of the average number n0m of quantized longitudinal de Broglie electron half waves in a steel wire (r0=0.8 mm; l0=320 mm; M)=8.43-1028 m-3; nem=16.86-1028 m-3 [10]), which is directly affected by axial aperiodic current pulse of a temporary shape 9 ms/160 ms (á0m=0.37 kA/mm2), shows that in this case the value of n0m turns out to be numerically equal to about 9.
It is important to note that a similar quantitative result for the value of the quantum number n0m in a steel wire (n=4) with current i0(t) was previously obtained on the basis of a calculated relation of the form [10]:
n0m = nm /ln nm , (10)
where nm=2n2 is the maximum value of the quantum number n0 for Schrodinger wave ^-functions describing the wave distributions of drifting free electrons in a metal conductor.
In obtaining analytical relation (10), it was assumed that the maximum number of varieties of free electrons (in their orbital l, magnetic ml, and spin ms quantum numbers) in a conductor metal is equal to the maximum number 2n2 of bound electrons in its atoms with the same principal quantum number n.
3. Experimental estimation of the average number of quantized longitudinal de Broglie electronic half waves in a metal conductor. For experimental verification of the obtained data on the choice of the averaged number n0m of quantized longitudinal de Broglie electronic half waves in the conductor metal with pulsed axial current i0(t), we used a high-power PCG-C high-voltage generator that generates on the RL-load an aperiodic current pulse with amplitude of I0m up to 1 kA of temporal shape tm/Tp=9 ms/160 ms (tm is the time corresponding to the current amplitude I0m; tp is the pulse duration at the level of 0.5 I0m) and the total duration t0 of the flow through the load (conductor) is up to 1000 ms (Fig. 1) [20] ].
Fig. 1. Oscillogram of an aperiodic current pulse i0(t) of negative polarity of the temporal shape Jxp =9 ms/160 ms flowing in the PCG-C discharge circuit with the equivalent of the electric load in the form of a square 2 mm thick aluminum sheet and plan size 500 mm x 500 mm (WC=400 kJ; UC~-42 kV;
I0m~ -835 A; tm~9 ms; rp~\60 ms; t0;
;1000 ms;
vertical scale - 282 A/cell; horizontal scale - 100 ms/cell) [22]
A straight round solid steel wire (r0=0.8 mm; l0 = 320 mm) with a thin zinc coating A0=5 ^m thick outside was chosen as a prototype of a metal conductor (Fig. 2). The presence of a zinc coating on the indicated wire was due to the authors' assumption related to visualization of the features of the process of intense Joule heating of the wire in quantized sections of width Az having a refractory steel base (with a melting point of up to 1536 °C [21]) and a relatively low-melting zinc coating (with its melting point up to 419 °C and boiling point up to 907 °C [21]).
Fig. 2. General view of a round galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; S0=2.01 mm2) placed in air above a heat-shielding asbestos cloth and rigidly fixed in the
discharge circuit of the PCG-C generator (WC ~ 310 kJ; UC ~ -3.7 kV before an aperiodic current pulse of high density flows through it [9]
In the case of Joule heating with the indicated current pulse in the discharge circuit of the PCG-C type generator (with stored electric energy WC up to 570 kJ and charging voltage UC of its pulse capacitors HM2-5-140 up to ±5 kV) of the test wire up to temperature of about 1500 °C and higher along the wire in quantized sections of width Az, it is possible to boil the zinc coating and melt the steel base of the indicated wire. In this case, visualization of periodic formation along the wire in areas of width Az of expanded spheres consisting of products of boiling of a zinc coating and melting of the steel base of the wire becomes real. Running a little ahead, it can be noted that it was precisely this electrophysical phenomenon that was observed by electrophysicists on the desktop of the PCG-C type generator with a selected thin galvanized steel wire (Fig. 3).
Fig. 3. External view of the desktop of a powerful high-voltage
generator PCG-C and the thermal state of a galvanized steel wire (r0=0.8 mm; /0=320 mm; A0=5 ^m; S0=2.01 mm2) with four «hot» quantized zones with a width Az = 7 mm and two «cold» longitudinal sections (isthmuses) about 27 mm wide after exposure to the aperiodic wire under study of the current pulse i0(t) of the temporary shape tm/Tp=9 ms/160 ms of high density (70m=-745 A; |^0m|=0.37 kA/mm2; n0m=9) [9]
Figure 4 shows the oscillogram of the current pulse tm/Tp=9 ms/160 ms, used in the study of the quantum-wave nature of the current i0(t) in the wire.
Fig. 4. Oscillogram of an aperiodic current pulse i0(t) of negative polarity of the temporal shape tmkp= 9 ms/160 ms of high density (I0m=-745 A; |c>0m|=0.37 kA/mm2) which destroys the galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m;
S0=2.01 mm2; vertical scale - 282 A/cell; horizontal scale - 100 ms/cell) [22]
According to [1-11], the longitudinal sections with a width Az of the wire under consideration are called relatively «hot», and the longitudinal sections (isthmuses) periodically located between its zones of width Az are called «cold». We point out that in [7, 9] it was shown that the Joule heating temperatures of these longitudinal sections of a round metal wire with the conductivity current i i0(t) can differ up to 3.5 times. This is precisely the main danger of the thermal effect of large emergency SC currents on cable-conductor products (CCP) of electric power facilities, industrial and residential premises. Due to the localization of drifting free electrons in the current-carrying parts of the CCP in their narrow longitudinal sections of width Az, which is not more than (3-10) mm in SC [10], they can quickly be intensively heated by emergency current to the ignition temperature of the CCP insulation (up to 450 °C and higher) [23]. In our opinion, this circumstance may be the main cause of
many fires due to the onset of fire during sudden SCs of a power CCP not only at electric power facilities, but also in the everyday life of citizens using AC (DC) electric networks. In this regard, not only purely scientific, but also applied interests can motivate electrophysicists in solving the quantum-mechanical problem formulated above and, accordingly, achieving the previously set goals.
The main construction schemes, technical characteristics and principles of operation of a highvoltage generator of the PCG-C type were described in [20, 24-26]. The means of high-current measuring equipment (shunts, oscilloscopes, etc.) regularly verified in the State Metrological Service that are used as part of the PCG-C generator for the experimental determination of the ATPs of the current pulse i0(t) flowing through the tested wire were also described there. From the experimental results obtained using the indicated PCG-C generator and from data of Fig. 3 it follows that when flowing along a bimetallic wire (r0=0.8 mm; l0=320 mm) with a thin external zinc coating (A0=5 ^m) and the steel base of a powerful aperiodic current pulse of negative polarity (|á0m|~|/0m|/S0^0.37 kA/mm2), such a wave longitudinal distribution of drifting free electrons in the wire metal is observed, which potentially leads to the periodic appearance of nine brightly glowing «hot» longitudinal zones along the wire with a width of approximately Az = 7 mm, which take a spherical shape. Since the midpoints of each of these «hot» longitudinal zones of the wire correspond to the amplitudes of the quantized Schrodinger wave ^-function (n0=9) [8], their own quantized de Broglie electron half waves, characterized by quantum number n0m=9 will correspond to them (to the middle of zones of width Az).
It should be noted that due to different conditions of longitudinal heat removal from periodically arising along the studied thin cylindrical steel wire of relatively «hot» and «cold» longitudinal sections with a geometric step approximately equal to Xezm/2 ~ 34 mm without taking into account the two extreme «cold» and directly adjacent to the bolted joints of the sections (see Fig. 3), in the experiment performed five «hot» and eight «cold» longitudinal sections of galvanized steel wire were completely sublimated [21]. Violation of the metallic conductivity of the tested wire, caused by intense Joule heating of its current-carrying part, begins at a point in time corresponding to approximately 380 ms (see Fig. 4). Data in Fig. 4 shows that at a time from the beginning of the flow through the wire of the considered pulsed current i0(t) of about 570 ms, the metal structure of the wire is completely destroyed and the conduction current stops flowing through the wire.
The results obtained during a high-current and high-temperature experiment using a high-power PCG-C highvoltage generator and the indicated galvanized steel wire unambiguously indicate the operability of the recommended quantum-mechanical relation (8) with an approximate choice of the average number n0m of quantized longitudinal de Broglie electron half waves in a
cylindrical conductor with pulsed axial current i0(t) of various ATPs.
Conclusions.
1. For the estimated forecasting of possible places of the onset of longitudinal localization of drifting free electrons in narrow sections of width Az of current-carrying parts of power wires and cables of electric power facilities, industrial and residential premises, which is manifested most strongly in emergency operation of CCP with SC currents and high current densities, a new quantum-mechanical calculation relation (8) is proposed.
2. Experimental verification using powerful high-current high-voltage equipment and a prototype of bare galvanized steel wire with diameter of 1.6 mm and length of 320 mm (with density amplitude module of flowing for up to 570 ms through the wire an aperiodic current pulse of about ¿0m=0.37 kA/mm2 and widths Az of each of the longitudinal localization regions of drifting free electrons in it up to 7 mm) of the proposed relation (8), which determines, for the indicated numerical value 80m, the average number n0m= 9 of quantized longitudinal electron de Broglie half wave length Xezm/2 ~ 34 mm in the metal wire, has confirmed its operability.
3. To ensure the fire safety of the power CCP in emergency operation modes, accompanied by the flow in current-carrying parts of wires and cables of alternating currents of SC with their high densities (200 A/mm2 or more), it is necessary in the relevant regulatory documents that determine the conditions for reliable operation of the CCP in industrial and home conditions, to take into account the peculiarities of the influence of the wave nature of the distribution along the metal cores (shells) of the CCP of free electrons drifting in them on the possibility of occurrence in current-carrying parts of the CCP of short longitudinal zones of width Az with abnormally increased concentration of such electrons and accordingly the temperature of indicated CCP operation modes.
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Received 19.11.2019
M.I. Baranov1, Doctor of Technical Science, Professor, S.V. Rudakov2, Candidate of Technical Science, Associate Professor,
1 Scientific-&-Research Planning-&-Design Institute «Molniya», National Technical University «Kharkiv Polytechnic Institute», 47, Shevchenko Str., Kharkiv, 61013, Ukraine,
phone +380 57 7076841, e-mail: baranovmi@kpi.kharkov.ua
2 National University of Civil Protection of Ukraine, 94, Chernyshevska Str., Kharkiv, 61023, Ukraine, phone +380 57 7073438,
e-mail: serg_73@i.ua
How to cite this article:
Baranov M.I., Rudakov S.V. Calculation-experimental determination of the average number of quantized longitudinal electron de Broglie half waves in a cylindrical conductor with pulsed axial current. Electrical engineering & electromechanics, 2020, no.2, pp. 33-39. doi: 10.20998/2074-272X.2020.2.05.
