Course : P464 - Plasma Physics and Magnetohydrodynamics Spring Semester 2023-24

Submitted by : @Abhinav Roy - Int. M.Sc. Physics, NISER (2020-25) - Email, Personal Webpage

Supervised by : Dr. Luke R. Chamandy, Reader, School of Physical Sciences, NISER - Email, NISER IRNIS

Github Repo :

https://github.com/AbhinavRoy99/P464-NISER

Task 1

Problem Statement

To solve numerically the mean-field galactic dynamo equations (in the z-direction) derived using the first order smoothing approximation, $\displaystyle \varepsilon \ =\ \alpha \overline{\boldsymbol{B}} \ -\ \eta _{t}\boldsymbol{\nabla } \times \overline{\boldsymbol{B}}$, in the kinematic regime.

• Explore the evolution of the magnetic field magnitude and of the exponential decay rate.
• Explore the evolution of the spatial solution for $B_{r}$ and $B_{\phi}$, and of the pitch angle of the mean magnetic field $p_B$.
• Explore how different boundary conditions affect the results.
• Explore how different seed fields affect the results.

Theory

Methods of Numerical Solutions

Results

Defining Seed Fields

I’ve used 3 different cases of seed fields to check the efficiency of my code.

• Case 1 :