Aetheric vortex
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Fundamental chapters: Vortex and Ring
The magnetized aether may support the helical vortex rings, including a very stable and self-contained. They are called the “vacuum domains”, “leptons” etc.
Any area of the magnetized aether is under a static pressure of the surrounding space (see "Gravity"), which is an inexhaustible energy source for the vortex. The symmetrical pressure is shaping a magnetic field as close as possible to the spherical shape. The pressure value is determined by the law of Bernoulli: \[P=-\frac{\rho v^2}{2}-U-const\tag{1}\]
The similarity of the magnetic and velocity fields allows to use the condition \(\rho\sim B^2\sim v^2\), with which the vortex continuum can be considered quadratic barotropic, to which the known theory of vortices is applicable. The quadratic dependence doubles the pressure gradient force, therefore, the total electromagnetic energy of a vortex is the doubled kinetic energy of its beams: \[E=\int\rho v^2\mathrm{d}V\tag{2}\]
The atheric vortices kinematics is the same as the kinematics of vortices within any other medium.
The known spherical Hill’s vortex does not exist without the boundary conditions on a sphere of the limited volume. For an aetheric vortex in a vacuum it is not practical.
The Hicks's vortex, unlike the Hill’s vortex, is propagated over the infinite volume, and therefore it can exist in the vacuum. The Gromeka-Lamb equation ("Vortex", 4) for this vortex is: \[\frac{1}{2}grad\;v^2+2\;grad\frac{P+U}{\rho}=\mathbf{\overrightarrow{f}}\tag{3}\]
The fictional force acceleration, which exists due to the mutual compensation of the electromagnetic forces ("Magnetism", 4) within a continuous vortical flow \((grad\;\rho=0)\): \[\mathbf{\overrightarrow{f}}=-\frac{1}{2}grad\;v^2=grad\frac{P+U}{\rho}\tag{4}\]
Thus the magnetic ("Magnetism", 7) and electrostatic ("Electricity", 5) forces are equal: \[\rho\mathbf{\overrightarrow{f}}=q\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}=\frac{v^2}{c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{5 - SI}\] \[\rho\mathbf{\overrightarrow{f}}=q\frac{\mathbf{\overrightarrow{v}}}{c}\times\mathbf{\overrightarrow{B}}=\frac{v^2}{4\pi c^2}(curl\mathbf{\overrightarrow{H}})\times\mathbf{\overrightarrow{B}}\tag{5 - CGS}\] \[\varepsilon\rho\mathbf{\overrightarrow{f}}=q\mathbf{\overrightarrow{v}}\times\mathbf{\overrightarrow{B}}=v^2(curl\mathbf{\overrightarrow{B}})\times\mathbf{\overrightarrow{B}}\tag{5 - Sim.}\] The well-known Maxwell's form of law of the magnetic effect of an electric current in a material domain follows from (5): \[q\mathbf{\overrightarrow{v}}=curl\mathbf{\overrightarrow{H}}\tag{6 - SI}\] \[q\mathbf{\overrightarrow{v}}=\frac{c}{4\pi}curl\mathbf{\overrightarrow{H}}\tag{6 - CGS}\] \[q\mathbf{\overrightarrow{v}}=c^2curl\mathbf{\overrightarrow{H}}\tag{6 - Sim.}\] The charged aetheric vortex can be represented as an eddy current, which produces a magnetic vortical field.
The stable aetheric vortices are electrically charged.
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