In this numerical group project, we worked on the 1958 paper by Parker. 

Here we examine the physics of interplanetary gas and magnetic fields by analyzing Eugene Parker’s model of solar coronal dynamics. By evaluating the force balance and radial heat conduction in a static coronal model, the study shows that hydrostatic equilibrium requires an unphysical, finite pressure at infinity that exceeds the interstellar medium pressure by several orders of magnitude. This pressure mismatch proves that a static coronal equilibrium is impossible, making the continuous outward expansion of the corona into the solar wind physically inevitable. Hydrodynamic modeling demonstrates that global pressure gradients accelerate coronal plasma to supersonic speeds of 500 to 1500 km/s, even when thermal speeds remain well below the solar escape velocity. Furthermore, we prove that a 1-D expansion restricts flow speeds below thermal limits (approximately 129 km/s), establishing three-dimensional spherical expansion as a strict physical requirement for generating steady, high-speed solar winds. Incorporating mechanical wave heating at base temperatures of 2 to 3 million Kelvin accounts for observed solar mass loss rates of roughly 10^14 g/s and terminal wind speeds around 500 km/s.

Extending the fluid framework to magnetohydrodynamics via Alfvén’s flux-freezing theorem, the presentation demonstrates that the highly conducting solar plasma drags dipole magnetic field lines outward, winding them into the characteristic Parker Spiral in the Sun’s rotating reference frame. To resolve local angular momentum non-conservation in Parker’s original equations, the authors introduce a modified variant model that satisfies ideal magnetohydrodynamic momentum conservation while maintaining nearly identical spiral path lengths. Order-of-magnitude energy density calculations reveal that magnetic energy density falls off rapidly and does not dominate plasma kinetic energy beyond the corona. Integrating the Maxwell stress tensor yields a solar rotational deceleration torque of approximately 5.8 x 10^30 dyne cm, corresponding to a characteristic spin-down timescale of 30 billion years—confirming that interplanetary magnetic torque cannot significantly slow solar rotation over the Sun’s lifetime. Finally, expansion-driven pressure anisotropy triggers the firehose instability, driving plasma turbulence and forming a disorganized magnetic shell beyond 1 AU, as confirmed by solar flare cosmic ray measurements.

This was done as a part of the coursework of Fluid and Magnetohydrodynamics at IISER Kolkata.