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Theoretical Electrical Engineering and Electrophysics
UDC 621.3.022: 537.311.8: 621.313 doi: 10.20998/2074-272X.2016.6.08
M.I. Baranov, S.V. Rudakov
CALCULATION-EXPERIMENTAL METHOD OF RESEARCH IN A METALLIC CONDUCTOR WITH THE PULSE CURRENT OF ELECTRONIC WAVEPACKAGES AND DE BROGLIE ELECTRONIC HALF-WAVES
Purpose. Development of calculation-experimental method for a discovery and study of electronic wavepackages (EWP) and of de Broglie electronic half-waves in a metallic conductor with the pulse axial-flow current of high density. Methodology. Theoretical bases of the electrical engineering, bases of quantum physics, electrophysics bases of technique of high voltage and large pulse currents, and also bases of technique of measuring of permanent and variable electric value. Results. On the basis of generalization of results of research of features of the longitudinal wave periodic distributing of negatively charged transmitters of electric current of conductivity in the thin round continuous zincked steel wire offered and approved in the conditions of high-voltage laboratory method for a discovery and direct determination in him of geometrical parameters of «hot» and «cold» longitudinal areas quantized periodic longitudinal EWP and accordingly the mediated determination of values of the quantized lengths formative their de Broglie electronic half-waves. It is shown that results of close quantum mechanical calculations of EWP and quantized lengths Xenz/2 of longitudinal de Broglie half-waves for the probed wire long l0 well comport with the results of the executed high temperature experiments on the powerful high-voltage generator of homopolar large pulse current of millisecond duration. Originality. First calculation-experimental a way the important for the theory of electricity fact of existence is set in a round metallic explorer with the impulsive axial-flow current of the quantized coherent de Broglie electronic half-waves, amplitudes of which at the quantum number of n=1,3,9 correspond the middles of «hot» longitudinal areas of EWP. Calculation quantum mechanical correlation of type of lenz/2=l0/n got experimental confirmation, in obedience to which on length of l0 conductor the integer of quantized electronic half-waves is always laid de Broglie. Practical value. The use of the offered method allows to expose electro-technological possibilities of practical application offeatures sharply not homogeneous periodic wave longitudinal distributing of drifting lone electrons and accordingly by them the conditioned thermal field in round metallic conductors with the electric axial-flow current of high-slay. References 21, figures 8.
Key words: metallic conductor, pulse current, electronic wavepackage, de Broglie electronic half-wave, calculation-experimental investigation of electronic processes in the conductor.
Описан расчетно-экспериментальный метод для обнаружения и изучения в электропроводящей макроструктуре металлического проводника с импульсным аксиальным током большой плотности квантованных (с квантовым числом n=1,2,3,...) макроскопических «горячих» шириной Aznh и «холодных» шириной Aznci продольных участков, образующих шаг шириной (Aznh+Aznc¡) периодически размещенных вдоль проводника квантованных продольных волновых электронных пакетов (ВЭП). Показано, что при протекании в круглом сплошном стальном оцинкованном проводе радиусом r0=0,8 мм и длиной l0=320 мм апериодического импульса тока временной формы tm/zp~9 мс/160 мс с амплитудой его плотности S0m~0,37 кА/мм2 в исследуемом проводе стохастическим путем от одного протекания по нему указанного тока к другому возникают квантованные продольные ВЭП, имеющие один (n=1), три (n=3) и девять (n=9) «горячих» продольных участков одинаковой ширины Aznh. Места расположения середин данных «горячих» продольных участков ВЭП шириной Aznh~7 мм вдоль провода соответствуют амплитудам распространяющихся вдоль него квантованных электронных полуволн де Бройля, характеризующихся в проведенных экспериментах квантовым числом n=1,3,9 и квантованной длиной полуволны lenz/2~lo/n, равной 320, 107 и 34 мм соответственно. Полученные экспериментальные результаты соответствуют расчетным квантовоме-ханическим данным применительно к дрейфующим свободным электронам электропроводящего материала провода, базирующимся на фундаментальном соотношении неопределенности Гейзенберга и установленных закономерностях волнового продольного распределения в структуре провода этих электронов. Библ. 21, рис. 8. Ключевые слова: металлический проводник, импульсный ток, волновой электронный пакет, электронная полуволна де Бройля, расчетно-экспериментальное исследование электронных процессов в металле.
Introduction. In [1-9] presented the results of many years of theoretical and experimental studies to establish the basic laws of quantum mechanical wave longitudinal and radial distributions drift of free electrons in the nonmagnetic metal circular solid cylindrical conductor of radius r0 and length l0>>r0 in which longitudinally runs pulse axial current i0(t) of arbitrary amplitude-time parameters (ATP). These results were obtained under the condition A,/r0>>1, where Ai is the thickness of the skin layer of the current in the conductor, and its use in the averaged current density d0(t)~i0(t)/S0, where S0=nr02 is
the cross section of mentioned conductor. The results obtained in [1-9] data show that in a homogeneous conductive metal conductor structure comprising quantum number n = 1,2,3... of de Broglie electronic half-waves there are stochastic by longitudinal and radial quantized periodic electronic wavepackets (EWP) each of which contains one relatively «hot» and «cold» areas of the longitudinal or radial macroscopic dimensions. These sites give rise to a metal conductor macrostructure inhomogeneous temperature fields, periodically changing along its length
© M.I. Baranov, S.V. Rudakov
or radius. Moreover, the temperature levels in the «hot» and «cold» longitudinal sections conductor at the manifestation of it EWP may vary up to 3.5 times [4, 7]. The stochastic nature of the formation of the quantized data is determined by EWP quantized energy states of free electrons trapped in the microstructure of the conductor material at the time of supplying a voltage and start the flow of electric current through it or that kind [6]. We point out that the wave packets, resulting in the propagation of monochromatic electromagnetic waves in dielectric media, at one time have been described in the theory of elec-tromagnetism and today electrophysics they studied well enough [10] as for the EWP metallic conductors with an electrical DC, AC and pulse current of different ATP formed in electrically conductive structures with their drifting free electrons as a result of the interference (superposition) of coherent electronic half-waves of de Broglie, they are currently in the theory of electricity are practically unexplored. That's why so far quantum-physical features of the spatial distribution of the main carriers of electricity in these structures - drift of free electrons, manifested most dramatically in the case of occurrence on them in regular (high-current discharges in circuits of high-voltage electrical installations [7, 11]), abnormal and emergency operating modes (overcurrent, short-circuit and direct linear lightning strikes [8, 12]) of high current density (108 A/m2 or more), and thus new areas of application in electrotechnology remain poorly understood. In this context, the development and practical use of new computational and experimental methods for the detection and study of quantized periodic EWP and quantized electronic half-waves of de Broglie in metal conductors with said electrical conduction current densities are actual scientific and technical problems.
The goal of the paper is development of computational and experimental method for the detection and study of quantized EWP and de Broglie electron half-waves in the metal conductor with a high density pulsed axial current.
1. Problem definition of investigation of EWP and de Broglie electron half-waves in the metal conductor with pulse current. Consider still housed outdoors straight round solid non-magnetic metallic conductor radius r0 and l0>>r0 length. Let air environment parameters correspond to normal atmospheric conditions (air pressure is 1.013105 Pa and its temperature T0 is 0 °C [10]), and the opposite ends of the conductor under consideration with the conductivity material y0 its electrical potential difference is applied, in varying unipolarly time t by an arbitrary law. We suppose that on the test conductor cross-section S0=nr02 along its longitudinal axis takes pulse unipolar conduction current i0(t) of amplitude I0m characterized by the average density of d0(t). We restrict ourselves to the case for which the thickness of the skin layer of the current A, in the conductor material substantially greater than its radius r0. For an approximate description of the behavior of drifting free conductor of electrons, as in [1-9], we use the well-known one-electron approximation, neglect their mutual influence on each
other, as well as the influence of the crystal lattice of the metal ion conductor on his itinerant electrons [10]. We adhere to the view that the longitudinal (radial) distribution of free electrons drifting in the test conductor subject to temporary Schrodinger wave equation, and according to their own quantized decisions [10]. It required on the basis of generalization obtained earlier in [1-9] quantum mechanical results concerning the electrical characteristics of the wave carrier distribution in the conduction current uniform conductive structures to formulate and test the in vitro methods to assess research EWP and electronic half-waves of de Broglie in thin circular metallic conductors with pulsed axial current i0(t) aperiodic temporary shape and high density d0(t).
2. A proposed method of detection in metal conductor with a pulse current of EWP and de Broglie electronic half-waves. For clarity and better understanding of the problem under consideration electrophysical give first approximate quantum mechanical ratio for the smallest width Aznh «hot» longitudinal section through a conducting wire structure with pulsed axial current i0(t) causing the appearance in it the average current density with amplitude d0m~I0m/S0 [7, 9]:
_1 2 —1
Aznh ~ e0ne0h(me$0m) [8 + (n _ 2) ] , (1)
where e0=1.602-10-19 C is the module of the electron electric charge [10]; me=9.109-10-31 kg is the electron rest mass [10]; ne0 is the average density of free electrons in the metal conductor to the test exposure to the electric current pulse [10]; h=6.626-10-34 J-s is the Plank constant [10].
From (1) obtained using the fundamental Heisenberg uncertainty relation [10], it follows that the width of Aznh «hot» longitudinal portion of the conductor is practically determined by the numerical value of the amplitude of the pulse current density d0m in his material. So, taking into account (1) for copper conductor (ne0=16.86-1028 m-3 [10]) at c>0m=4T06 A/m2 typical for normal operation of industrial electric alternating current networks [13], we find that it Aznh width is approximately equal to 0.53 m. At c>0m=4T08 A/m2 corresponding to the emergency mode of operation of industrial electric networks with the flow of their current distributors fault currents [13] or the normal operation of high-current circuits of high-voltage electro installations [11], the estimated width Aznh takes the numerical value of about 5.3 mm. c>0m=4T0n A/m2 which is characteristic for a quick electric explosion (EE) of thin metal wires [14] the width Aznh «hot» longitudinal section in a copper conductor according to (1) is numerically equal to about 5.3 ^m. Such microscopic value of Aznh is in good agreement with the linear dimensions of the conductive fine fractions resulting from EE (sublimation of conductive parts) of thin metal wires [11, 14]. In addition, according to [15] in the experimental study of the phenomenon of rapid EE in the air thin round copper wires 60 mm long and 100 mm in diameter by passing them from the high-voltage generator of pulse currents (GPC) sinusoidal decaying exponentially bit high density pulse current (¿0m~6.4T012 A/m2) dispersed in the products the
explosive destruction of solid copper (in the «metal» plasma) by the high-speed photoregistration were fixed longitudinal periodic strata consisting of a layered discshaped longitudinal periodic structures of different luminosities, comprising alternating between a «light» in width Azh (34 pcs) and the «dark» width Azc (34 pcs) longitudinal sections. These areas formed in pairs in the discharge of said air gap with high-current circuit GPC «me-tallic» plasma step periodic structure EWP length about (Azh+Azc)~1.76 mm [11, 15]. One can reasonably assume that in the case of research [15] EV thin copper wires «light» longitudinal sections of the plasma «metal» products of the explosion in the discharge air gap correspond to «hot» areas of EWP, and their «dark» longitudinal sections - «cold» areas EWP. Experimental data from [15] indicate the accuracy of the quantum of provisions used in the basis of these estimations [1-9] of the wave distributions drift of free electrons and EWP respectively in thin metal conductors.
The above estimates indicate that identify in vitro particular longitudinal wave current distribution in the metal conductors can only mode transmission there through of DC, AC or pulse current i0(t) which provide a flow in cross sections S0 of conductive material a relatively large current densities ^0m. According to the experimental data of [16] to the DC level of density in a thin galvanized steel wire (r0=0.15 mm; A0=5 ^m is the thickness of the outer protective zinc coating) in an experimental study of its EWP is about 6.8108 A/m2. From own
experience in the study of quantized EWP and electronic half-waves of de Broglie in a thin circular galvanized steel wire (r0=0.8 mm; A0=5 ^m) with aperiodic pulsed axial current i0(t) millisecond duration in a research laboratory, equipped powerful high-voltage GPC to form a long-term load on the electric C- component of artificial lightning current [12], it follows that the values S0m numerically equal about 3.7108 A/m2 [3, 7].
In connection with the above, the proposed settlement and the experimental method of research in the macrostructure selected based on visualization of the expected electro manifestations (quantized longitudinal EWP and forming their electronic half-waves of de Broglie) metallic conductor with a pulsed axial current i0(t) is based on the use of these quantum-physical laws and circuitry High discharge circuit of mentioned GPC-C shown in Fig. 1. As test samples (TS) of the conductor to be included as shown in Fig. 1 and 2 in the high-current high-voltage circuit GPC-C use the straight portions of commercially available galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; S0=2.01 mm2) [17]. The presence in such TS in a relatively thin coating of fusible and refractory enough massive wire base provides in its intensive local Joule heating (to temperatures of about 1500 °C) indirect detection by a sphere-like swelling on the cover of «hot» sections of longitudinal wires quantized longitudinal EWP and accordingly electronic de Broglie half-waves forming such EWP [7, 9].
0
if
TS
cs
GPC-C
Fig. 1. Schematic diagram of high-current discharge circuit powerful high voltage GPC-C applied to the study of quantized periodic longitudinal VEP and electronic half-waves of de Broglie in the test piece of metal wire (GHIP - generator of highvoltage ignition pulses of amplitude up to ±100 kV; F1, F2 - respectively, three and two-electrode spark high air switches;
Cd - dividing capacity of 180 pF and a pulse voltage up to ±120 kV in the GHIP circuit controlling actuation air spark switches F1 and F2; TS - test sample of the metallic conductor; CS - coaxial shunt type ^K-300 for measurement of pulse current in the conductor; ±^CC - charging voltage of capacitors GPC-C; ±UCA - charging voltage of capacitors of another GPC of existing artificial lightning current generator; LC~11.43 mH, RC~4.74 Q, CC~45.36 mF - respectively, inductance, active resistance and capacitance of the discharge circuit of GPC-C)
Used a powerful single-module GPC-C at rated stores electric energy WC0=567 kJ arranged according to the scheme of Fig. 1 through 324 parallel-connected highvoltage pulse capacitors HM-5-140 (rated voltage U0=±5
kV; nominal capacity C0=140 ^F) has the following own electrical parameters [12]: Cc~45.36 mF; Rc~4.74 Q; ZC~11.43 mH. Note that in the GPC-C was applied resistive protect it from accidental over-current capacitors
implemented by placing on their high conclusions permanent protective bulk graphite-ceramic resistors TB0-60-100 Q [12, 18]. After charging to constant voltage Uœ<±4.2 kV capacitors GPC-C (at Uca=0) and the supply of high voltage generator of ignition pulses (GHIP) control microsecond pulse amplitude voltage of ±100 kV high-voltage electrode is controlled three-electrode spark air switch F1 cascade type hemispherical steel working
electrodes and the spacing length of 4 mm and 9 mm which is part of the present at the Scientific-&-Research Planning-&-Design Institute «Molniya» of the NTU «KhPI» artificial lightning current generator [12], due to the TS formed wire surge pulse occurs triggering high voltage two-electrode spark air switch F2 rectangular graphite electrodes and insulating the working gap of 3 mm in length.
■ v
Fig. 2. General view of the continuous round galvanized steel wires (r0=0.8 mm; /0=320 mm; A0=5 ^m; S0=2.01 mm ) included its ends by means of a bolted joint in high-power high-voltage discharge circuit GPC-C and placed on a thermal asbestos cloth, before subjecting it to an aperiodic pulse axial current i0(t) of high density
As a result, through the TS wires will flow current pulse required ATP. ATP measurement pulse wires running through the TS current i0(t) is performed using a digital storage oscilloscope Tektronix TDS 1012 and attorney metrological service measuring coaxial shunt (CS) fflK-300 type with its own internal resistance of 0.185 mfi and fixable nano-, micro- and millisecond current pulse amplitude of 10 A to 200 kA [12], is included as shown in Fig. 1 nonpotential (grounded) part of the high-current discharge circuit GPC-C. We use CS at regular measurement in the discharge circuit GPC-C long aperiodic component of artificial lightning current conversion ratio was equal to approximately 56.42-102 A/V [7, 12].
Fig. 3 shows the waveform of an aperiodic pulse of negative polarity in the discharge current circuit GPC-C if its TS instead of regular steel wire equivalent electrical load in the form of an aluminum sheet 2 mm thick and in terms 0.5 m x 0.5 m. It can be seen that when the amplitude of the module I0m^835 A generated in this case (WC~400 kJ; UCC~-42 kV) aperiodic pulse wave current time tm/zp~9 ms/160 ms (tm is time corresponding I0m; Tp is the duration 0.5I0m current pulse level) is characterized by a complete duration t0~1000 ms and transfers in high-current discharge circuit GPC-C large electric charge, whose magnitude is approximately qC~191 C.
Fig. 4 shows the negative polarity in the discharge circuit GPC-C waveform i0(t) aperiodic current pulse in the presence of its TS investigated galvanized steel wire, losing at t>380 ms its metallic conductivity due to intense local Joule heating and electro-thermal destruction of its structure.
1 1 1 1 1 ■ ■ ■+
:
4
■ 1 1 1 1 i i i v 1 1 1 1 1 1 1 1 1 i i i i + i l l l 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I-
;
Fig. 3. Waveform of aperiodic current pulse i0(t) negative polarity of temporary form tmhp~9 ms/160 ms flowing in the discharge circuit GPC-C with the equivalent electrical load in the form of a flat aluminum plate of 2 mm thick and in terms 500 mm x 500 mm (WC=400 kJ; UCC=-4.2 kV; I0m~-835 A; tm~9 ms; xp~\60 ms; t0=1000 ms; qC=-191 C; the vertical scale -282 A/cell; the horizontal scale - 100 ms/cell)
For this reason, the total duration of the flow in the wires of the TS aperiodic current pulse temporal shape tm/tp~9 ms/160 ms in our ongoing experiments did not exceed t0^576 ms. Note that the conductive structures IO wires with these TS use of current pulses is carried out under the terms of the required research the relationship between the variables Ai and r0 [7]: Ailr(^2r0'l[tml(n^0y()]y2~42, where ,«0=4n-10-7 H/m is the
magnetic constant [10] and y0~8-106 S/m is the conductivity base metal wires used in experiments [10]. Current waveform in Fig. 4 (WC~310 kJ; UCC~-3.7 kV; Im-745 A) is a characteristic of all executed by us on GPC-C experiments intense Joule heating TS galvanized steel wire, caused by weak scattering in the crystal lattice of metal atoms it electronic half-waves of de Broglie [10, 19]. Averaged amplitude of the critical current density pulse i0(t) as shown in Fig. 4 is not exceed d0m~0.37 kA/mm2. The experiments on the GPC-C showed that when ¿0m>0.37 kA/mm2, there is a complete sublimation of the electrically conductive material of the TS steel wire, eliminating any visual observations it EWP and electronic half-waves of de Broglie [7-9].
Fig. 5-7 show external views of the TS galvanized steel wire immediately after exposure to the high-current discharge circuit in the high-voltage GPC-C single aperiodic current pulse i0(t) of negative polarity according to the Fig. 4 (UCC~-3.7 kV; I0m=-745 A; ¿0m~0.37 kA/mm2).
■ ■
:
- +
■ 1 1 1 1 1 1wTI 1 1 1 1 1 1 1 1 1 1 1 1 + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i i i i i i i i -
: :
:
Fig. 4. Waveform of affecting the electrothermal locally destroyed analyzed straight round galvanized steel wire (r0=0.8 mm; /0=320 mm; A0=5 ^m; S0=2.01 mm2) aperiodic pulse axial current i0(t) negative polarity of temporary form tjTp~9 ms/160 ms of high density (WC~310 kJ; UCC=-3.7 kV; I0m~-745 A; S0m~0.37 kA/mm2; tm~9 ms; xp~160 ms; t0=576 ms) (the vertical scale - 282 A/cell; the horizontal scale - 100 ms/cell)
Fig. 5. External view of experimental distribution along the galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; S0=2.01 mm2) of cooling air and heatproof asbestos cloth macroscopic one «hot» (high-temperature zone width EWP Aznh~7 mm in the middle of the wire) and two extreme «cold» (width Aznce~ 156.5 mm at partial sublimation of one of them) longitudinal portions after flowing through it a current pulse aperiodic i0(t) negative polarity temporary form tm/rp~9 ms/160 ms of high density (I0m~-745 A;
Som~0.37 kA/mm2; n=1; t0=576 ms) [20]
BpSt
Fig. 6. External view of experimental distribution along the galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; S0=2.01 mm2) of cooling air and heatproof asbestos cloth macroscopic three «hot» (high-temperature zone width EWP Aznh~7 mm) and four «cold» (two extreme of width Aznce~50 mm at full sublimation of one of them and two internal of width Aznc~100 mm) longitudinal portions
after flowing through it a current pulse aperiodic i0(t) negative polarity temporary form tjtp~9 ms/160 ms of high density (I0m~-745 A; 80m~0.37 kA/mm2; n=3; t0=576 ms) [20]
yfr
< v-iis«
mm
■■ - I jM ■ '-/
^f^/fr'/y
'isTJWTf
E0W
Fig. 7. External view of experimental distribution along the galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; S0=2.01 mm ) of cooling air and heatproof asbestos cloth macroscopic four «hot» (high-temperature zone width EWP Aznh~7 mm) and two internal «cold» (width Az„cl~27 mm) longitudinal portions after flowing through it a current pulse aperiodic i0(t) negative polarity temporary form tm/rp~9 ms/160 ms of high density (I0m=-745 A; S0m~0.37 kA/mm2; n=9; t0=576 ms; the other five are «hot» and eight «cold» areas of the longitudinal wires have undergone complete sublimation) [20]
Thermal state of cooling air and heatproof asbestos cloth thickness 3 mm, made of chrysotile asbestos (its melting point is about 1500 °C [21]), the TS of the test wire indicates a partial sublimation of the electrically conductive structures (for zinc coating melting temperature is about 419 °C and the boiling point - 907 °C [10]; for the steel base, these temperatures are about 1535 and 2735 °C, respectively [10]) and the presence of a stochastic manner arising along the galvanized steel wire from one of said impulse current exposure to other meltblown brightly glowing sphere-like quantized «entities» the same in all cases, the width Aznh~7 mm.
The number of these «entities» in Fig. 5-7 corresponds to the quantum number n = 1,3,9. Between these sphere-like «formations» that have white-hot steel and, accordingly, the temperature of not less than 1200 °C [7, 16], located cylindrical «necks» in diameter 2r0=1.6 mm and width of quantized Aznc with visually intact due to the pulsed heating zinc coating on them. Because of the heat indicated «necks», together with their surviving zinc coating acquired dark color.
Metallographic examination under an optical microscope MEC-9 type of cooled and carefully cleaned with a soft cloth cylindrical «isthmus» TS wires showed that they contain a uniform, shiny and adherent to a steel base wires zinc coating [7]. These experimental data indicate that the maximum heating temperature on cylindrical «isthmuses» TS wire does not exceed the melting temperature of the zinc coating (not more than 419 °C) [10]. With regard to the results of the survey on the optical microscope MEC-9, the cooled sphere-like «formations» TS wires inside them contained hardened fraction of the boiled and molten zinc coating steel wire base [7]. In this regard, the maximum heating temperature of the spherelike «formations» TS wire is not less than the melting point of its steel base (>1535 °C [10]). This conclusion is confirmed by the fact that under all natural cooled air sphere-like «formations» TS wires occurred keyhole heat
cloth, made of chrysotile asbestos not less than 1500 °C with a melting point [21]. The above thermal results obtained with use of a powerful high-voltage GPC-C and line segments of thin galvanized steel wire high experiments indicate that the quantized sphere-like «formations» in the TS wires correspond to the «hot» longitudinal sections of its quantized periodic longitudinal EWP and cylindrical «necks» wire in the TS - «cold» longitudinal sections of these EWP.
For the case when n=1 (Fig. 5), the quantized width AznxK each of the two extremes of «cold» longitudinal sections of the EWP, the right of which was subjected to partial sublimation, in these experiments was found to be about 156.5 mm. The widths of these areas together with the wide Aznfp7 mm single «hot» longitudinal section EWP, located in the middle of the TS wire, according to those in [1-9] for the laws of EWP in a metallic conductor with an electrical conduction current form for the case n=1 the length of the quantized Xenz/2 of one half-wave electronic de Broglie, numerically equal XeJ2~2Aznce+Aznh ~ 320 mm. The amplitude of this half-wave electronic de Broglie corresponds to the width of the middle Aznh «hot» longitudinal portion EWP. Obtained for n=1 the experimental data for the quantized longitudinal EWP and electron de Broglie half-wave in the identity of the test wire is schematically illustrated in Fig. 8,a. From (1) at ne0=16.82-1028 m-3 [10] and c>0m=3.7T08 A/m2 we find that the estimated width of the «hot» longitudinal portion of said EWP in the test wire is about Aznh~5.7 mm. The estimated width of the quantum-mechanical assessment of the extreme «cold» longitudinal portion of the quantized longitudinal EWP in the test steel wire can be made according to the following analytical relationships [6]:
2
Aznoe ~ V(2n) - 0,5e0ne0h /(me8{)m )[8 + (n - 2) ]. (2)
From (2) at n=1, ne0=16.82-1028 m-3 and ¿0m=3.7-108 A/m2 it follows that Aznce~157.1 mm. Then, for the calculated length Xenz/2~2Aznce+Aznh of electron half-wave
of de Broglie studied in the quantum case («=1) we have: Xenz/2-2x 157.1 mm + 5.7 mm-319.9 mm. It can be seen that the results of experiments performed by highquantum case n=1 is fully correspond to the data of quantum-mechanical calculation of EWP in the studied steel galvanized wire.
For the case of n=3 (Fig. 6) Aznce quantized width of each of the two extremes of «cold» longitudinal portions quantized longitudinal EWP, the left of which has undergone a complete sublimation is about 50 mm (if the width calculated by (2) 50.5 mm). Two internal «cold» longitu-
dinal sections located in this case between the neighboring «hot» sections of the longitudinal width Aznh -7 mm, had a quantized width Aznci -100 mm. It can be seen that the experimental width Aznci internal «cold» longitudinal sections twice the width Aznce experienced extreme «cold» longitudinal sections TS steel wire. Therefore, the quantum case n=3, the length of the quantized experienced XeJ2 half-wave of de Broglie in TS wires will be numerically Aenz/2-Aznci+Aznh-107 mm. The experimental data obtained for the quantum case n=3 is schematically shown in Fig. 8,b.
Fig. 8. Simplified schematic representation of the experimental data for the «hot» (Aznh~7 mm) and «cold» longitudinal sections quantized periodic longitudinal EWP and electronic half-waves of de Broglie in TS round galvanized steel wire radius r0=0.8 mm and length l0=320 mm experiencing in the high-voltage high-current discharge circuit GPC-C single exposure time aperiodic pulse current form tm/zp~9 ms/160 ms of high density S0m-0.37 kA/mm2 (1 - «hot» EWP part; 2 - «cold» EWP part; 3 - electronic half-wave of de Broglie length Xenz/2; for a - n=1 and Xenz/2~320 mm; for b - n=3 and 2enz/2~107 mm; for c - n=9 and 2enz/2-34 mm)
From the estimated settlement of (1) at ne0=16.82-1028 m-3 and ¿0m=3,7-108 A/m2 width Az^ «hot» longitudinal portion EWP follows that it is equal to about 5.7 mm. Settlement quantum mechanical estimate for n=3 width Aznci internal «cold» longitudinal portion EWP in the test conductor will perform the analytical relation of the form [6]:
_1 2 _1
^0/ n _ e0ne0h(meS0m ) [8 + (o _ 2) ] -
(3)
From (3) for n=3, ne0=16.82-1028 m-3 and ^0m=3.7-108 A/m2 we obtain that Aznci-101 mm. As a result, the estimated length Xenz/2-Aznci+Aznh electronic half-wave of de Broglie relation to the quantum case n=3, we find: Xenz/2-101 mm + 5.7 mm-106.7 mm. Therefore, we can say that the experimental results on the GPC-C by indirect detection of a thin galvanized steel wire quantized longitudinal EWP and electronic de Broglie half-waves in
the quantum case n=3, and correlate well with the calculated data.
For quantum case n=9 (Fig. 7) surviving «hot» EWP quantized longitudinal portions also had Aznh—7 mm width (the width when calculated according to (1) of 5.7 mm). Quantized width Aznci internal «cold» TS in the longitudinal wire portions in this case was about 27 mm (when calculated on the width (3) 29.8 mm). In this regard, the length of the quantized experienced Xenz/2 half-wave of de Broglie in TS galvanized steel wires for the quantum case n=9 is approximately equal Aenz/2-Aznci+Aznh-34 mm. Fig. 8,c is illustrative in schematic form displayed corresponding experimental data for the TS considered in the case of quantum wires (n=9). In this case, as in the cases with the quantum numbers n=1 (see. Fig. 5) and n=3 (see. Fig. 6), the middle «hot» longitudinal portions quantized
periodic EWP correspond to the amplitudes TS investigated cylindrical propagated in conductive structure wire quantized coherent electron de Broglie half-waves. In view of the above data for the calculated value for n=9 length Xenz/2 electron de Broglie half-wave in the TS Xenz/2~29.8 mm + 5.7 mm~35.5 mm wires we have: Xenz/2~29.8 mm + 5.7 mm~35.5 mm. Therefore, we can say that in this quantum case (n=9) experienced the results for the geometric parameters of the «hot» and «cold» longitudinal sections quantized periodic longitudinal EWP and accordingly the electronic half-waves of de Broglie in thin galvanized steel wire with aperiodic pulse current temporary form tm/xp~9 ms/160 ms of high density (á0m~0.37 kA/mm2) in the range of 4% in line with the relevant data submitted by us quantum mechanical calculation estimates for the basic geometric characteristics of EWP and de Broglie electron half-waves in the investigated steel wire.
Conclusions.
1. The proposed and tested in a high-voltage laboratory of computational and experimental method for the detection and direct determination of geometric parameters (in particular, the widths Aznh, Azrue¡1 h Aznc) «hot» and «cold» longitudinal sections quantized periodic longitudinal EWP and thus indirectly determining the values of the quantized lengths Xenz/2 (n=1,2,3, ...) they form the electronic half-waves of de Broglie in a round galvanized steel wire (r0=0.8 mm; l0=320 mm; A0=5 ^m; 50=2.01 mm2), which in a single operation from the one described in brief high-voltage high-power GPC-C developed at the Scientific-&-Research Planning-&-Design Institute «Mol-niya» of the NTU «KhPI» unipolar momentum affects the axial current temporary form tm/rp^9 ms/160 ms of large average density (á0m~0.37 kA/mm2).
2. For the first time settlement and experimentally investigated for a round galvanized steel wires, is confirmed the important fundamentals of the theory of electricity electrophysical the fact that in this metal conductor used with aperiodic pulsed axial current conduction time form 9 ms/160 ms and high density (about 0.37 kA/mm2) in the longitudinal direction extend quantized coherent electronic half-wave of de Broglie length Xenz/2 defined during the investigations by the quantum numbers n=1,3,9.
3. The interference of de Broglie electron half-waves gives rise to the conductive structure of the investigated steel galvanized wire quantized periodic longitudinal WEP macroscopic size, mid experimentally identical fixed widths Aznh~7 mm «hot» longitudinal sections which correspond to the amplitudes of these half-waves quantized electron de Broglie length in accordance with the established contact ratio XeJ2~l(Jn with n=1,3,9 in the 320, 107 and 34 mm, as well as an appearance in the macrostructure of the longitudinal wires inhomogeneous periodic temperature field with a temperature difference between its «hot» and «cold» longitudinal in about 1000 °C.
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Received 01.06.2016
M.I. Baranov1, Doctor of Technical Science, Chief Researcher, 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 +38 057 7076841, e-mail: [email protected]
2 National University of Civil Protection of Ukraine, 94, Chernyshevska Str., Kharkiv, 61023, Ukraine, phone +38 057 7073438, e-mail: [email protected]
How to cite this article:
Baranov M.I., Rudakov S.V. Calculation-experimental method of research in a metallic conductor with the pulse current of electronic wavepackages and de Broglie electronic half-waves. Electrical engineering & electromechanics, 2016, no.6, pp. 45-53. doi: 10.20998/2074-272X.2016.6.08.
