One is able to formulate in a very general way the mathematical problem of turbulence in the following form.

One has a system of second-order nonlinear partial differential equations with three space variables and one time variable. One looks for solutions sufficiently complex and nonstationary to represent irregular oscillations.

In a perfectly conducting body the lines of magnetic force move with the material; the total number crossing the surface in either direction is therefore constant, and cannot be changed by motions of the material forming the body. Both in terrestrial magnetism and in sunspots, large changes in the external field are observed which do involve a change in the total number of lines and cannot be explained by a mere crowding together of lines of force that already cross the surface. In these phenomena loops of field must emerge through the surface, and the theory must involve the finite conductivity of the material.

The spectral theory of isotropic magnetogasodynamic turbulence proposed by the author some years ago gives the following expression for the spectral functions of kinetic and magnetic energies.

A technique has been developed whereby ionized gas (plasma) can be projected, by magnetic forces, at speeds of 3X107 cm/sec through a vacuum region free from a magnetic field. The plasma has also been projected across magnetic fields in vacuum at speeds of 107 cm/sec. It is further possible to have present in the magnetic field a background electrically conducting medium in the form of a low-pressure (about one micron) ionized gas. This gas is photoionized by the ultraviolet light from the plasma gun. With the background conducting medium we can calculate, following Spitzer, the electric resistivity η transverse to a strong magnetic field to be η = 1.29X1013(Z lnΛ)T−3/2 emu = 106 emu for T=105 °K (electron temperature), Z=1, lnΛ = 2.3. The magnetic Reynolds number Rm for L =10 cm and V = 107 cm/sec is thus Rm=4πLV/η = 103. Consequently, there is no doubt that with this technique we are producing magnetohydrodynamic phenomena in the laboratory.