Helicity and Magnetic Helicity

SOURCE FOR CONTENT: Davidson, P.A., 2001, An Introduction to Magnetohydrodynamics. 3.  The purpose of this post is to introduce the concepts of helicity as an integral invariant and its magnetic analog. More specifically, I will be showing that is invariant and thus correlates to the conservation of vortex line topology using the approach given in […]

“Proof” of Alfven’s Theorem of Flux Freezing

SOURCE FOR CONTENT: Choudhuri, A.R., 2010. Astrophysics for Physicists. Ch. 8.  In the previous post we saw the consequences of different regimes of the magnetic Reynolds’ number under which either diffusion or advection of the magnetic field dominates. In this post, I shall be doing a “proof” of Alven’s Theorem of Flux Freezing. (I hesitate to call […]

Consequences and some Elementary Theorems of the Ideal One-Fluid Magnetohydrodynamic Equations

SOURCE FOR CONTENT: Priest, E. Magnetohydrodynamics of the Sun, 2014. Cambridge University Press. Ch.2.; Davidson, P.A., 2001. An Introduction to Magnetohydrodynamics. Ch.4.  We have seen how to derive the induction equation from Maxwell’s equations assuming no charge and assuming that the plasma velocity is non-relativistic. Thus, we have the induction equation as being Many texts […]

Basic Equations of Ideal One-Fluid Magnetohydrodynamics: (Part V) The Energy Equations and Summary

SOURCE FOR CONTENT: Priest E., Magnetohydrodynamics of the Sun, 2014. Ch. 2. Cambridge University Press.   The final subset of equations deals with the energy equations. My undergraduate research did not take into account the thermodynamics of conducting fluid in order to keep the math relatively simple. However, in order to understand MHD one must […]

Monte Carlo Simulations of Radiative Transfer: Basics of Radiative Transfer Theory (Part IIa)

SOURCES FOR CONTENT: Chandrasekhar, S., 1960. “Radiative Transfer”. Dover. 1. Choudhuri, A.R., 2010. “Astrophysics for Physicists”. Cambridge University Press. 2. Boyce, W.E., and DiPrima, R.C., 2005. “Elementary Differential Equations”. John Wiley & Sons. 2.1.   Recall from last time , the radiative transfer equation where and are the emission and absorption coefficients, respectively. We can further define […]