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2. The energy of the standing wave with displacement
Previously we have already compared the two standing waves: the center one of which moves along the x-axis and the center of the second is moved. We emphasize again that in the first and in the second case, we observe a standing wave.

Since the animation is built with maximum approximation to real lines on the page examples you need to wait for some time until a stationary regime.

In the previous section, we found a way of expressing the motion of the center of such a wave through the area of displacement or PSV. Now consider some of the effects associated with this unusual movement. Be our wave will be in perfect long line [1] (DL) — without loss and without attenuation in a wide frequency range. To shape the wave will be a special generator of Gw which can provide the required PSV. Next, we will consider private poluvalmovye case, and thus the opposite ends of the generator of DL — closed (not shown).
In figure 1, consider the operation of the reflected wave (it moves from the closed end to the generator). The rule of thumb [2] check the direction of force of the magnetic lines and will make their field a few non-magnetic conductors (depicted in orange). Will be hereinafter abbreviated to designate non-magnetic conductors of the NWO.

On the left-hand rule [3, 4], we define the direction of the current in NMP, and then check the same direction, but the movement of the direct wave (from the generator to the closed end of the DL). As you can see, the direction of the current in these conductors has not changed. In fact, the motion of the center of the wave, at the exit of the NWO, we get a pulsating DC voltage.

Figure 1 red and blue color depicts a symmetric (1.1) and asymmetric (1.3) DL, gray — magnetic lines, uranium — non-magnetic conductors. Outset that steel FOR the standard inclusion when the braid goes to the ground, and the pulse is supplied to the Central vein, has the external magnetic field. We will consider another method of inclusion, when the Central vein is ground, and the braid — momentum. As FOR steel can be ordinary wire, in this case a common wire Gw, and the second end of the wire connected with the earth.

Симметричная и несимметричная ДЛ. Внесение немагнитных проводников в магнитное поле длинной линии
Fig. 1. Symmetric and asymmetric DL (1.1, 1.3). Depositing a non-magnetic conductors in a magnetic field DL (1.2, 1.4)
If you now connect the NMP to the load, then around it will also be formed a magnetic field, but its lines are perpendicular to field lines DL. As you can see, this inclusion of the effect of perpendicular conductors to each other is minimized.
Resulting electric energy. The wave generator
Based on these findings we can now make some constructive-circuit solutions of energy extraction to the load. Figure 2.1 shows the General scheme. Here the blue color represents asymmetric DL, perpendicular to the axis of which is located a removable NWO (orange). Since the voltage across the latter will be pulsing DC, the decoupling circuit is necessary on the one hand the NWO to turn on the diodes (VD1-VDn), and on the other to connect all of the NWO with one wire.
Circuit of the generator Gw and loads Rn must be electrically isolated, otherwise the electric field FOR probing the induced charges on the NPM, will also go through the load. Despite this, still may need a periodic reset of the load circuit accumulated relative to the ground of the charge, for example, by means of the discharger. If the voltage on the NWO to get this small, order At 1-4, it makes sense in series with the load to enable the source voltage (about one volt).
Конструктивно-схемотехнические решения съёма электрической энергии с длинной линии
Fig. 2. Structural-electrical circuitry removing electrical energy from the DL.
* Drawing can be opened in full scale by clicking on it.
The scheme on Fig. 2.1 will be large enough and not constructive in execution. Figure 2.2 shows a more compact version of the same device. Here DL is wound on the coil bobbin (grey), and NMP, together with the diodes placed inside of her. The disadvantage of this execution can be considered a larger number of harmonics in the generator Gw for wave formation. Advantage — capture including longitudinal waves, which in fact is formed in an asymmetric DL is made in the form of the coil [5].
Calculation of output power
From the first part we already know how is PSV. For the number of harmonics \(N \le 12\) formula for PSV will be like this: \[S \approx 8 a^2 \sum_{i=1}^{N} { i^2 (i-1)^2 \over (2i-1)^2} \qquad (2.1) \] and for \(N \ge 12\): \[S \approx 2 a^2 \left({N^3 \over 3} + {N^2 \over 2} + {N \over 6}\right) \qquad (2.2)\]: \(a^2\) is the square of the amplitude of the harmonics, or its energy, and \(S\) — PSV, or the total energy displacement in DL. Recall that these formulas are calculated for the half-wave case, when the amplitude of all harmonics is the same. Considering that the load is consistent with the NMP system, can be represented the formula for the power received at the load: \[P = k \, f \, S \qquad (2.3) \] Here \(k \) — factor, which includes the absolute and relative magnetic permeability, velocity of wave, wave and load resistance design of the actual device: the length of the NWO, their number and location; \(f\) is the frequency of the oscillator. Formula (2.3) shows the linear dependence of the output power from the square of the displacement waves and frequencies. From it in particular implies that at the same total power of the generator Gw (input power), more output power will have a device with a large number of harmonics. When this number is large enough, then the specific \(P\) will be approximately proportional to \(N\). The value of \(S\) for quasiparabolic pulses can be rented here.
Now, knowing the General principles of construction of devices based on the displacement of the center of the standing wave, our readers can come up with your own design and circuit solutions. We will be glad if some of them you send us — we have to publish it.
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The materials used

Vyacheslav Gorchilin, 2016
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