2021 SOLUTIONS
2021 LOOK BACK
2020 SOLUTIONS
RIEMANN HYPOTHESIS
NSE & 0-POINT ENERGY
YME & 0-POINT ENERGY
ENTROPY & 0-P. ENERGY
PLASMA HEATING
MHD
WHO I AM
LITERATURE


In fluid description of plasmas (MHD) one does not consider velocity distributions. It is about number density, flow velocity and pressure. This is about moment or fluid equations (as NSE and Boltzmann/Landau equations).

The “mother" of all hydrodynamic models is the continuity equation treating observations with macroscopic character, where fluids and gases are considered as continua. The corresponding infinitesimal volume “element” is a volume, which is small compared to the considered overall (volume) space, and large compared to the distances of the molecules. The displacement of such a volume (a fluid particle) then is a not a displacement of a molecule, but the whole volume element containing multiple molecules, whereby in hydrodynamics this fluid is interpreted as a mathematical point.

One of the key differentiator between plasma to neutral gas of neutral fluid is the fact that its electrically positively and negatively charged particles are strongly influenced by electric and magnetic fields, while neutral gas is not.

An ideal plasma is a non-dissipative flow of the incompressible charged particles (CaF).

The MHD equations are derived from continuum theory of non-polar fluids with three kinds of balance laws:

(1) conservation of mass

(2) balance of linear momentum

(3) balance of angular momentum (Ampere law and Faraday law).

The MHD equations consists of 10 equations with 10 parameters accompanied with appropriate boundary conditions from the underlying Maxwell equations (CaF).

In (EyG) it is proven that smooth solutions of non-ideal (viscous and resistive) incompressible magneto-hydrodynamic (plasma fluid) equations satisfy a stochastic (conservation) law of flux. It is shown that the magnetic flux through the fixed Plasma is an ionized gas consisting of approximately equal numbers of positively charged ions and negatively charged electrons.


References

(BrK) Braun K., 3D-NSE, YME, GUT solution, 2019

(CaF) Cap F., Lehrbuch der Plasmaphysik und Magnetohydrodynamik, Springer-Verlag, Wien, New York, 1994

(EyG) Eyink G. L., Stochastic Line-Motion and Stochastic Conservation Laws for Non-Ideal Hydrodynamic Models. I. Incompressible Fluids and Isotropic Transport Coefficients, arXiv:0812.0153v1, 30 Nov 2008

(HaW) Hayes W. D., An alternative proof of the circulation, Quart. Appl. Math. 7 (1949), 235-236

(SeW) Sears W. R., Resler E. L., Theory of thin airfoils in fluids of high electrical conductivity, Journal of Fluid Mechanics, Vol. 5, Issue 2 (1959), 257-273