Standing waves progressively transform to traveling waves.

Far away, just outgoing spherical waves remain.

DISPLAYING OUTGOING SPHERICAL WAVES.

One can easily write a software displaying outgoing waves. The wave phase is given by:

x = 2 * pi * distance / lambda

The  x  variable stands more exactly for the phase delay in radians. However, this becomes inaccurate for a smaller than pi distance because the electron is a very special emitter. It exhibits a pi / 2 phase offset at the center.

This Basic (or FreeBasic) instruction will add the  pi / 2  phase offset in the center. In addition, the amplitude there will be displayed very smoothly.

This wave generator bears the name of Mr. Jocelyn Marcotte, who discovered in March 2006, and demonstrated with his own 3-D Virtual Aether, that the well known  sin(x) / x  formula matches the electron waves. It is especially useful here because it is amazingly simple.

Adding a  t  time in radians will then produce a full rotation. Let us suppose that a full rotation needs 48 images:

t = 2 * pi * (image No.) / 48

x = 2 * pi * distance / lambda

If x < pi Then x = x + (pi / 2) * (1 – x / pi) ^ 2

y = sin (x – t) / x

Here is the program showing this:

Marcotte_Wave_Generator.bas        Marcotte_Wave_Generator.exe

The Marcotte Spherical Wave Generator.

Note the pi / 2 (or lambda / 4) additional expansion in the center, which is the rule for the electron out-waves.

Thanks to this wave generator, the computer can especially reproduce the interference pattern created between two electrons or positrons. It becomes a field of force, a powerful standing wave system because it is also amplified by aether waves. It must be evaluated with respect to the distance and also the spin because there are four possible phases at the particle center.

The electrostatic "biconvex" field of force is made of hyperbolic-ellipsoidal standing waves.

The structure is similar to that of the diffractive lens, so they should produce an Airy disk too with a focusing effect.

The wave phase in the center changes according to the distance and the particle spin.

The pi / 2 phase offset in the center expands all the spherical waves to an additional lambda / 4 position. It is of the utmost importance because those waves encounter those incoming from another electron or positron and produce the field of force shown above.

Then the field of force itself is amplified because of the same lens effect. As a result, and especially because more electrons in the vicinity truly act like stroboscopes, a very strong wave beam converges back towards electrons or positrons which caused them. I could check that such a convergent beam should produce an Airy disk, just like most convergent beams except apodized ones. One must also remember that the Airy disk is only the diffraction pattern at the focal plane. It is called the Fraunhofer diffraction whose distance is infinite for the laser, but the whole diffraction pattern anywhere else between the source and the Airy disk is called the Fresnel diffraction.

The pattern is different whether the source is plane or spherical. When two electrons come very close together, their standing waves may add constructively even in the area beyond them. Then they radiate an Airy disk exactly in their center. This transforms the whole system into a quark surrounded with a powerful gluonic field where forces involved are enormous and quite different. In addition, the phase in the center may be compatible with the positron's quadrature. So the resulting system is no longer negative: it becomes neutral. Then three quarks placed crosswise on the three Cartesian axes become a neutron, which may finally transforms into a proton if a positron is captured in the center.

The point is: the on-axis wave period explains how radiation pressure works. So this wave generator compatible with the electron will be very useful for searchers studying radiation pressure. But it should also be useful for displaying regular ripples on water in computer generated animations, and for a lot of other applications!

The program below displays outgoing waves with an artificial, really amazing 3-D effect:

Marcotte_Wave_Generator_3D.bas        Marcotte_Wave_Generator_3D.exe

DISPLAYING OUTGOING CIRCULAR WAVES.

One can apply the same reasoning to the 2-D Circular Wave Generator, which phase offset in the center is only pi / 4. Using the Huygens principle, and also the Virtual Aether, Mr. Marcotte and I already showed that the 2-D central antinode exhibits a 3 / 4 lambda diameter.

So formulas are different. Firstly, the core correction threshold is pi / 2 instead of pi:

If x < pi / 2 Then x = x + (pi / 4) * (1 – (2 * x / pi)) ^ 2

Secondly, waves are expanded to an additional lambda / 8 position, not lambda / 4, and amplitude fades according to the square root of the distance. So Mr. Marcotte's formula must be modified this way:

y = sin(x + pi / 4 – t) / sqr(x)

I elaborated those formulas on Oct. 2, 2007. This program shows that they produce very smooth outgoing waves:

Circular_Wave_Generator.bas        Circular_Wave_Generator.exe

According to the diagram below, the core amplitude is higher for 2-D circular standing waves, as it was also the case for spherical waves.

2-D circular standing waves, according to Huygens' Principle and the Virtual Aether.

The dotted line shows the approximate Gaussian distribution curve given by :  y = pi ^ (–x ^ 2)

This bell-shaped curve is not really relevant here, but the comparison is interesting.

Spherical standing waves will be very useful in the future for a lot of applications. Up to now, scientists are definitely not aware that they can especially build up enormous pressures inside the central core. 

In addition, microwaves emitted from the inner surface or a sphere produce a similar pattern. They can build up huge quantities of energy focused inside a very small spherical core. And this energy may be recycled if the sphere internal surface is metallic.

THE ACOUSTIC THERMONUCLEAR PLANT

The point is: this small core is the perfect place for thermonuclear fusion, because both heat and pressure are needed to transform hydrogen, deuterium and tritium into helium. Moreover, this little sphere stands far away from any solid matter, which otherwise would melt. The microwaves will produce heat, and also very strong magnetic and electric fields inside the compressed plasma. Magnetic fields correctly applied facilitate fusion because hydrogen unpaired electron and proton behave like small magnets. For example, such fields are present on the sun surface, especially around sunspots. 

This central sphere will simply become a little sun, constantly producing heat, hence electricity. It will work! 

Both the acoustic and electronic (microwave) systems can coexist and achieve the very high pressure and heat requirements. Russia experimented in 1961 a 57 megaton hydrogen bomb which detonator was a plutonium bomb. This is unthinkable for producing electricity. The goal is to safely obtain the fusion temperature and pressure point. Tritium for example is a dangerous substance which must be severely controlled. In addition, the fusion process produces neutrons which make matter in the vicinity become radioactive.

The moon surface contains huge quantities of helium-3, whose fusion produces safer protons, but needs higher temperature. It also may directly transform energy into electricity because protons are positive.

The most recent project in Cadarache, France, uses very strong magnetic fields in order to facilitate the fusion process and to isolate the plasma from any solid matter. But it still needs very high pressure and temperature, and so adding the standing wave method to the process appears quite relevant and reasonable.

The magic formula.

The pressure diagram is the same as that of the electron. The whole reactor would look like artificial electron, and so Mr. Marcotte's formula is still relevant. The larger the sphere, the higher the pressure. Additionally, the shorter the wavelength, the higher the pressure too:

y = sin(x) / x

x = 2 * pi * distance / lambda

The  x  variable is given by: 2 * pi * distance / lambda, and so the wavelength is important. On the other hand, a bigger core should produce more heat and energy. The core pressure is normalized to 1, but the goal is to obtain the required pressure for the fusion to become possible. The equation indicates which pressure should be applied on the inner side of the sphere.

Obviously, the amplitude is always positive for a compressed medium because vacuum is the lower limit. An asymmetry appears for very high amplitude levels. So, before proceeding, the hydrogen overall pressure should already be very high. The device also needs a chimney for collecting heat, and a system for recycling the hydrogen. The sphere can be replaced by an ellipsoid with two focus cores, producing a sort of "artificial quark" with high amplitude plane standing waves in-between. Then those standing waves may participate to the fusion process and greatly improve the device efficiency.

I presume that engineers will find a practical way to produce Huygens wavelets on the inner surface of the sphere. Technically, most of the energy produced by at least one thousand loudspeakers regularly spaced should be transferred to the central core. I could check this with my own computerized medium without any surprise, because it is simply the Huygens Principle.

A chain reaction.

It should be emphasized that a chain reaction and self-amplification occurs. The resulting heat causes additional reactions to take place, allowing the standing wave system to oscillate permanently.