Solitonic Model of the Electron, Proton and Neutron

In present article alternative (to Standard Model) hypothesis of structure of electron, proton and neutron is suggested. The others elementary particles (except photon and neutrino) are not stable and they are considered as unsteady soliton-similar formations. In series of experiments indirect confirmations of existence of quarks were obtained, for instance in experiments by scattering of electrons at nuclei, performed at Stanford linear accelerator by R. Hofshtadter, look for instance [1]. At that, experiments by elastic and deeply inelastic scattering gave quite different results: in first case take place pattern of scattering at lengthy object, in second case is pattern of scattering at "point" centers, that is interpreted as confirmations of existence of quarks. However what "point" formations appear only in deeply inelastic scattering don’t may be an evidence of quarks existence, because to above-mentioned fact may be given and another explanations: in moment of birth of new particles, which take place in deeply inelastic scattering, structure of nucleon change, it sharply diminish in volume, but after appearance of new particles nucleon return to initial state. Or process of birth of new particles occur in "point" volume inside nucleon and these energy "point" centers disappear after completion of process particles birth. And fact that experiments by elastic scattering gave pattern of scattering at lengthy object prove inexistence of quarks in nucleus. In theory of Standard (quarkual) Model come into at least 20 parameters artificially introduced from outside, such as "colour" of particles, "aroma" etc., that is its fundamental demerit. Theoretical work, which is present here, has no demerits of Standard Model, it completely describe structure of elementary particles therefore it can help in discovery new ways of making energy, elaboration perfectly new devices for its production and to achieve progress in such fields as nuclear power engineering, nanotechnology, high-powerful lasers, clean energy and others.


Introduction
In present article alternative (to Standard Model) hypothesis of structure of electron, proton and neutron is suggested. The others elementary particles (except photon and neutrino) are not stable and they are considered as unsteady soliton-similar formations. In series of experiments indirect confirmations of existence of quarks were obtained, for instance in experiments by scattering of electrons at nuclei, performed at Stanford linear accelerator by R. Hofshtadter, look for instance [1]. At that, experiments by elastic and deeply inelastic scattering gave quite different results: in first case take place pattern of scattering at lengthy object, in second case is pattern of scattering at "point" centers, that is interpreted as confirmations of existence of quarks. However what "point" formations appear only in deeply inelastic scattering don't may be an evidence of quarks existence, because to above-mentioned fact may be given and another explanations: in moment of birth of new particles, which take place in deeply inelastic scattering, structure of nucleon change, it sharply diminish in volume, but after appearance of new particles nucleon return to initial state. Or process of birth of new particles occur in "point" volume inside nucleon and these energy "point" centers disappear after completion of process particles birth. And fact that experiments by elastic scattering gave pattern of scattering at lengthy object prove inexistence of quarks in nucleus. In theory of Standard (quarkual) Model come into at least 20 parameters artificially introduced from outside, such as "colour" of particles, "aroma" etc., that is its fundamental demerit. Theoretical work, which is present here, has no demerits of Standard Model, it completely describe structure of elementary particles therefore it can help in discovery new ways of making energy, elaboration perfectly new devices for its production and to achieve progress in such fields as nuclear power engineering, nanotechnology, high-powerful lasers, clean energy and others.

Rotating Monochromatic Electromagnetic Wave
Let us write down Maxwell's equations in spherical coordinates supposing that: 1) There are no losses; Here r,θ, ϕ spherical coordinates of the observation point; r E  и H θ  -components of the electromagnetic field, j φ  -density of electric current, ρ  -volume charge density; ω-circular frequency of field alteration i -imaginary unit ε-dielectric permittivity -magnetic permeability Figure 1.
Substituting the expression for H θ  from (2) in (4), we obtain: Wave number -General solution of Helmholtz equation: .
This situation can be interpreted as rotation of spherical coordinate system around axis z in positive direction ϕ with angular velocity . d dt φ Let us find it from the condition: Having differentiated this expression on t, we receive, This expression describes two waves, moving to meet one another by circular trajectories, along the parallels. Pointing's vector in each point is directed at tangent to the corresponding parallel [2,3].
Let us consider a wave, moving in positive direction ϕ. The wave phase will be written down as Arc length along the corresponding parallel. In the considered case the wave number is a function of coordinates and frequency. Thus, the wave, which is described, can exist only at availability of spatial and frequency dispersion [4][5][6]. Dispersion equations will be obtained below, apart from the already found expression (7′′).
Let us suppose that This equation can be satisfied, if Thus, initial Helmholtz equation has split into the system of two equations. We substitute in these equations instead of ( , ) ( ) ( ) , we are searching the solution as the product of two functions) and divide the first equation byf(r), and the secondby g(ϕ). We receive Equations (16) and (18) are equivalent to equations (7) и (7′), which were received earlier from Maxwell's equations, and The solution of equation (18) was found earlier, look (13).
Let us copy (19) as: Where v r -phase velocity of electromagnetic wave in radial direction. As in the central symmetric equation angular dependence is absent, it is logical to assume that v r= v=2ωrsinθ Instead of (19′), we are having This is Euler equation, it has the solution Let us converse expression (22).

System of Equations for Electron
Basing on results of the previous section, let us write down expressions for electromagnetic field inside the electron, assuming that it is concentrated inside the orb of radius a 0 (1 ln ) sin ; 2 Here a is electron radius, E 0 amplitude of electric field intensity at r=a; z=const characteristic impedance inside the electron, P-unknown coefficient and P≤0 At that the internal electron medium possesses frequent and spatial dispersion, as well as anisotropy. Dispersion equations have the following appearance [7][8][9][10][11] Here v r ,v θ ,v ϕ -phase velocity of rotating monochromatic electromagnetic wave in corresponding direction. In viewed case, the electromagnetic wave is being spread only in the direction ϕ, and we shall need expressions v r and v θ for searching the formulas of dielectric and magnetic permeability, as well as wave numbers of corresponding directions; z r , z θ, z ϕ, z characteristic impedances inside the electron; ε φ , и, µ φ were found before, see (12′) (12′′) In view of (24)(24′)(24′′), let us write down expressions for ε r , ε θ ,µ r ,µ θ  Let us find dimensionless wave numbers. .
Despite of this, all basic electrons' parameters -charge q rest energy W, magnetic moment M-expressed through integrals by volume from the functions specified above, prove to be finite quantities [12][13][14][15]. Look further.
From (5), we find volume charge density inside electron Integrating ρ on electron's volume, we shall receive this expression for its charge q.  . (27) From expressions (25), (27) it is visible that in the interval of change of r from 0 to a,ρ and j ϕ once change the sign. It can be explained by the fact that in the viewed structure, the substantial role is played by the rotating monochromatic electromagnetic wave, and the space charge density and electric current density -are auxiliary or even fictitious quantities in the sense that inside the particle there is neither any charged substance nor its motion [16]. Inside the electron, it is not the charge that is the source of electric field, but electric field is the source of the charge. In its turn, it is not the electric current that is the source of magnetic field, but magnetic field is the source of the electric current [17][18][19][20][21][22]. Thus, a deduction about vector nature of elementary charge can be made. Now we shall determine electron's rest energy as electromagnetic wave energy inside a particle. .
Here w-is volume density of electromagnetic wave energy, Where M m -is magnetic moment, created by volumetric current; M L -magnetic moment, attributed to impulse moment, i.e. to rotation.
Basing on Barnett effect, we are making a supposition, that the impulse moment, attributed to rotation, creates additional magnetic moment [21,23].
Being aware of the fact that electron's impulse moment is equal 2  , from (28′) we find expression for L.
Thus, we have received the system of algebraic equations for electron. ; Here e -charge of electron, m-it's mass.
Three equations contain five unknown quantities: E 0 , a, z, p, γ Let us add this system with equations, which we shall receive from boundary conditions.
At r=a, R=a In the exterior area, the same as and in the interior area, electric field intensity possesses only radial component. Here R -distance from electron's center to the observation point in the exterior area, ε 0vacuum dielectric permeability [24].
In the exterior area, the same as and in the interior area, magnetic field intensity possesses only meridional component.

It is obvious that
then from (33) follows: On the other hand it is known that the electric field, having passed through dielectric layer, cannot increase, therefore In other words, correlations (33′) (33′′) (33′′′) will be simultaneously executed only in one case, if ε r= ε 0 ; . 0 .
Now under Biot-Savart's law, we are finding magnetic field in the exterior area.
At r=a R=a 0 . .
We substitute (30′) in (32′). "Dimensions" of electron for the present are not discovered by experimental way, though precision of measuring is led to 10 -18 m. Within the framework of the model considered it may be explained by the next way: electron is not hard particle with this quantity of vector E, which exist inside it, unlike from proton and neutron, quantity of vector E inside which approximately 10 7 times as much [26][27][28][29][30][31].
For positron, the system of equations will take a somewhat different view.
Boundary conditions are the same as for electron. Hence  The last system with exactness to a sign has the same solutions, as system (56)(55′)(57)

Conclusion
Within the framework of the model, which is considered, electron, proton and neutron represent a monochromatic electromagnetic wave of corresponding frequency spread along parallels inside the spherical area, i.e. a wave, rotating around some axis. At that along each parallel, exactly half of wave length for electron and proton and exactly one wave length for neutron, is kept within, thus this is rotating soliton. This is caused by presence of spatial dispersion and anisotropy of a strictly defined type inside the particles. In electron vector E is directed to center of particle, that correspond to negative charge, and in proton vector E is directed from center of particle, that correspond to positive charge. Thus, by natural way, all basic parameters of particles are obtained: charge, rest energy, mass, radius, magnetic moment and spin, that is confirmed by mathematical expressions, which are discovered.