Matter Desynchronization, page 2 of 4
The plasma frequency is proportional to the number—density of electrons in the metal: (Wp)^2 = N (e)^2 / M Ko Where N is the number—density of electrons, (e) is the electron charge, M is the mass of the electron, and Ko is the permittivity constant. To find N requires knowledge of the metal’s density (g/cmA3) and atomic weight (g/mole) and the value of Avogadro’s number (per mole). The following assumes there is one free electron per atom: N = density * Avogadro’s number / atomic weight N = N * 10^6 cm^3 / m^3 (electrons per cubic meter)
N is directly proportional to the mass density. For constant mass, a decrease in density requires an increase in volume. A large increase in volume would significantly lower the plasma frequency, greatly increasing the transparency of the metal.
Achieving the Volume Increase
“The physical properties of a metal crystal are a function of the crystal structure,” observed engineer Frank H. Rockett. [3] An acoustic wave heats the crystal by compressing it. [4] And, “at certain temperatures,” wrote R.A. Burton, head of mechanical engineering at Northwestern, “crystalline substances may change in lattice arrangement, and a sudden change of volume occurs at constant temperature, making the coefficient of expansion momentarily infinity.” [5] If the volume were infinite, the iron would become transparent to all electromagnetic frequencies. For the iron to be transparent from radar to optical frequencies the volume would be finite. Since the volume change is at the level of the crystal lattice, no macrophysical change in volume is expected. “The chief acoustooptic effect is the change of the optical index of refraction of the material under the influence of strain caused by the acoustic wave. As the pressure on a material changes, so does its density and thus its index of refraction,” according to Dr. Michael Brienza of United Technologies Corporation. [6] Frederic Keffer, professor of physics at the University of Pittsburgh, explains how ferromagnetic resonance at high signal power can lead to large precessions of interacting spins and that these can yield acoustic waves in the sample under ~resonance [7]: “[The nonlinear equations of motion for the interacting spins are] important for the large—amplitude precessions induced by the intense microwave fields...Large—amplitude precessions can...break up into acoustic vibrations.. .This is called magneto—acoustic resonance.” The foregoing suggests the liklihood that ferromagnetic resonance, via the acoustical pathway, could render metallic iron transparent to frequencies of light in the radar to optical range. This conductor has seemingly become an insulator, since the conductivity also depends on the number—density. What follows assumes that the iron now has measurable dielectric properties and that a high electric field can induce a very large nonlinear polarization in it. 2B) Nonlinear Electric Polarization The purpose of this section is to show how a large relative permittivity can arise and to apply the approximation that the index of refraction is the squareroot of the relative permittivity. [8] The electric field that binds electrons to an atom is greater than 10^l0 V/m. Ordinarily, a linear operation connects the field and the polarization. In strong fields, i.e., 10^9 V/m, the polarization becomes nonlinearly related to the field [9,10]: P = Ko (xE + yE^3) Where Ko is the permittivity constant, the linear coefficient x is close to unity and the nonlinear coefficient y is of the order l0^-l0 m/V. Only odd powers of the series are relevant. Since the cubed term is the most significant, P = Ko(10^17) The linear relation (alone) for the same field is: P = Ko (10^9) The nonlinear increase in P is equivalent to a (10^17 / 10^9) = = 10^8 increase in the susceptibility (relative permittivity). This yields a refractive index of 10^4. Because of the quadratic Stark effect the characteristic spectra for iron are shifted toward the red end of the spectrum. [11] The energy levels of many-electron atoms are split and the shift is to lower energies by an amount depending on the square of the electric field. 2C) Homopolar Generator This section describes how to develop the kind of electric field that will produce a very large susceptibility. According to Faraday, a change in magnetic flux will induce a voltage in a nearby conductor. Lenz determined that any change in flux is opposed by the flux of the induced magnetic field. [12] Faraday realized there were exceptions to the rules he and Lenz had formulated. The homopolar generator cuts no magnetic flux, yet produces a voltage; no back e.m.f. is generated. [12] The homopolar generator develops a motional electric field. The electric field is produced either by the rotation of a medium whose plane is perpendicular to the lines of a static B field or the medium is stationary and the lines of the B field rotate through the medium. Consider the former case. A circular disk, an insulator, is rotated on an axle about the magnetic field. An electric field extends radially outward from the center of the disk. This field revolves around the disk like light sweeps around a lighthouse. For the generator thus described to perform work, a conducting band is affixed to the rim of the disk and brushes are attached to the axle and edge of the disk; a voltage develops across these contacts. The rotation of the disk satisfies the expression for the motional electric field, v X B, giving rise to an electric field which cannot be identified with a change of flux. [12] The magnitude of the E field is: E = Wr sin theta B Where W is the angular frequency of the disk, r is the radius of the disk, theta is the angle between the tangential velocity, Wr, and B; B is the magnetic flux density in Teslas. [13] The voltage across the contacts is: V = B W r^2 / 2 (B _|_ Wr) 2D) Ferromagnetic Resonance This section exploits the fact that the experimental setup for ferromagnetic resonance satisfies the conditions for a hornopolar generator. Recall that the purpose of a homopolar generator is to obtain an electric field sufficient to produce a large relative permittivity and thus attain an index of refraction great enough to yield a significant temporal desynchronization. An introduction to this subject is available by Vonsovskii, S.V. , Ferromagnetic Resonance (1966). In uniform resonance (low power) the magnetization vector, M, precesses at an angle about the vertical. This angle is usually small and most authorities regard M as parallel to H. The vector M rotates at the precession (resonant) frequency of the elementary moments. This frequency is in the microwave range for an H that produces saturation (H > = 7.95 x 10^4 A/rn). In the preceding, ferromagnetic resonance (magneto-acoustic resonance) led to the transformation of iron from a conductor to an insulator. This occured during nonlinear interaction of the spins. The magnetization vector is then a magnetic field rotating through an insulating medium; a homopolar generator is present. The magnitude of the E field is: E = rW sin theta M Uo Assuming the sample is a disk or a short upright cylinder, r is the radius of the circular surface, W is the resonant microwave frequency, theta is the angle between rW and H (they cease to be _|_at high signal power), M is the magnetization in A/rn and Uo is the permeability constant, Take the following values: H Uo = 2.0 T (slightly less than saturation magnetization for iron) r = 1 meter W = 1. 75 x lO^lO radians / sec f = W / 2pi = 2.8GHz |