In this research we examine how electron heat moves along magnetic field lines and how this affects temperature variations in plasmas. Specifically we wrote FORTRAN code to solve the electron temperature equation numerically. We also solved the steady state electron temperature equation analytically using an integrating factor. We verified that the numerical and analytical solutions obtained the same result. Finally we calculated the standard deviation of temperature in our domain for the steady state. Gaussian legendre quadrature was used to integrate various functions. We represented our magnetic field and heat source with Fourier series. The sin and cosine coefficients for the heat source and the inhomogeneous magnetic field strength were given in an input file along with other initial conditions which our code read prior to each run. This allowed different numerical experiments to be run without the need to recompile the code for each one. The primary result that was found was that an increase in the initial background temperatures led to smaller variations in temperature. That is, as plasma collisionality decreases with increasing mean temperature, diffusive electron heat flow is capable of smoothing out temperature perturbations more effectively.
Kushlan, Michael, "Diffusive Electron Heat Flow and Temperature Variance Along Magnetic Field Lines" (2014). Physics Capstone Project. Paper 4.