2020-06-30

Dynamic skin-effect and new opportunities in the energy sector

Our discovery, which we presented in the previous part of this work, can have a very wide range of applications, but in this part we restrict ourselves to the energy component of this phenomenon. Dynamic skin effect is different from the static (classical) is quite complicated processes in the depth of the conductor through which flows an alternating current.

In the following diagrams (Fig. 9-10), as in the previous part of this work, is represented a longitudinal section of the wire from its surface to its center. Thus, the bottom figure is the lower surface of the conductor, and the top of the picture — its middle. Axis \(x\) here the delay time, one period of oscillations (\(0..2\pi\)). We also remind you that while we are considering the sinusoidal current flowing through this conductor. Therefore, the chart you need to look from left to right: the first time the sine is zero and the current is almost absent, about one-quarter of the oscillation current and the maximum current density is higher; in half of the oscillations of the sine is again equal to zero and there is no current, then the reverse process, the other polarity. By the end of the period (\(2\pi\)), the sine will again be zero, as the flowing current, and then the whole process repeated again.

Fig.9. The current density distribution in the wire when d = 3Λ at one period of oscillations | Fig.10. The current density distribution in the wire at d = 5Λ in one period of oscillation |

Although such diagrams are beautiful and clear, but it is not visible energy of the whole process. Next, we will try to fix this drawback and for this we can use another basic principle of graphing. Figure (11) represented by this variant. This graph vkluchaet several curves, each of which displays a process of changing the current density in one layer of wires during one period of oscillation. For example, the red solid line is the \(j(\alpha, 0)\) — indicates a current density on the conductor surface. As you can see, it coincides with the sine wave current from the source.

Next, drill into the wire at the depth from 0.5 transverse wavelength (about it told in the previous part of this work). This curve displays a blue dotted line \(j(\alpha, 0.5)\), which is already slightly different from the sine wave. Going thus forth, inside of a guide, we see the picture change of the current density at a distance of 1, 2 and 3, the transverse wavelength. Of course it is assumed that the wire has sufficient diameter.

Fig.11. The current density distribution in the wire when d = 0Λ, 0.5 Λ, 1Λ, 2Λ, 3Λ in one period of oscillation |

We should be interested in the latest curves, where one can clearly see oscillatory process with a frequency greater than the main one. Moreover, the frequency value increases in the interval from the maximum (minimum) of the sine wave until it is zero. This time we will continue to use.

Wire of the power plant

If we take as a basis the classical skin effect and measure the potential difference between the surface of the conductor and its middle, we get the classical sine with an amplitude equal to the amplitude at its surface. For energy is of no interest. But let us now consider the dynamic skin-effect and let's measure the potential difference between the surface of the conductor and its various layers. Mathematically, this difference can be obtain by subtracting from the density of the surface layer, we need the deep layer. For example, finding the potential difference for the depth that is half the length of the shear wave is done as follows: \(j(\alpha, 0) - j(\alpha, 0.5)\). Such potential difference, shown in figure (12).

Fig.12. The potential difference in the wire when the depth of 0Λ, 0.5 Λ, 1Λ, 2Λ, 3Λ in one period of oscillation |

The figure clearly shows that the maximum of some capabilities than unity, it means that on these sites (hereafter, we call them slices) we can obtain the gain efficiency of the second kind is greater than one. To calculate the energy gain we compare the RMS amplitudes on the surface of provodnika and the potential difference on its depth, for the same period: \[ K_{\eta 2} = {A_d \over A_s} \qquad (2.1)\] \[ A_d = \int \limits_0^{\pi} [j(\alpha, 0) - j(\alpha, k)]^2\, \Bbb{d} \alpha, \quad A_s = \int \limits_0^{\pi} [j(\alpha, 0)]^2\, \Bbb{d} \alpha \] Where \(k\) here is the ratio of the length of the shear wave. From the graph (12) can immediately say that the increase in efficiency more unit begins at a depth of more than or equal to 3Λ. It can be estimated that there are \(K_{\eta 2} (3Λ) = 1.28\). There will be other interesting depth: \[ K_{\eta 2} (3Λ) = 1.28 \] \[ K_{\eta 2} (/4Λ) = 1.48 \] \[ K_{\eta 2} (5Λ) = 1.45 \] \[ K_{\eta 2} (6Λ) = 1.35 \] Recall that the interval at which do these integrals: \(0..\pi\). If the integration we take the only part of this interval: \(\pi / 2..\pi\), the layout will be slightly different: \[ K_{\eta 2} (3Λ) = 1.88 \] \[ K_{\eta 2} (/4Λ) = 2.18 \] \[ K_{\eta 2} (5Λ) = 2.05 \] \[ K_{\eta 2} (6Λ) = 1.81 \] This part of the interval and potential difference in a conductor, in the above proportions with the length of the shear wave, graphically represented in figure (13).

Fig.13. The potential difference in the wire at a depth of 3Λ, / 4Λ, 5Λ, 6Λ on the part of the oscillation period |

Insights

From the last figure, whereby is obtained the energy gain. This approach could be attributed to the methods of pulse compression in time, but still it was a rather complicated and energy-intensive technologies, for example [1]. Due to the dynamic skin-effect, with proper engineering treatment can be simplified to a single generator and a specially prepared wire!

Dynamic skin-effect means that in alternating current, the depth of the conductor, there are processes that in classical electrodynamics previously simply was not considered. It was believed that with the deepening of the thickness of the wire, the amplitude of the current density simply decreases exponentially. In fact, with the right formulation, in the depth of the conductor we can find and accurately estimate periodic processes with frequency higher than basic on the surface. This leads us to the concept of transverse wave length parameter, which is very convenient to handle in calculations.

Promising, in the author's opinion, can be considered research in the area of combined longitudinal and transverse waves, which can give large gains in efficiency and more optimal scheme of energy extraction.

A new approach to the problem of sin-the effect opens new possibilities in alternative energy, simplifies the development methodology and the energy used to manufacture generators. However, at this stage require research and engineering work theoretically obtained results. It concerns methods of energy extraction from the conductor corresponding to its design and material.

__The materials used__

- M. L. A. Magnetic pulse generators. 1968 [DJVU]