Can I get an explanation of what magnetic pressure is exactly in the context of MHD? From my simple understand, it's essentially just the force that magnetic field lines exert back onto a plasma that has some incident velocity (energy) perpendicular to the field lines. An example would be the solar wind interacting with the Earth's magnetic field. The field blocks the solar wind, but there is so perpendicular pressure being exerted onto the field from the incident plasma. Is my interpretation correct?
Second question (If my interpretation is correct), is this pressure directly related to the Larmor radii trapped particles will have? Since the plasma has a Maxwell distribution, then there will be a Maxwell distribution of Larmor radii and so those would then be correlated to the pressure term? So if I wanted to know then what is the momentum threshold for this distribution of energies to break through the field entirely, how would I solve for that given the equation (Just from what I found on Wikipedia):
Say I would simplify this extremely by just looking at the 1D version of this. The $B$ term would be the 1D gradient of a dipole field whose center is aligned with the $z$-axis, (So it's center is at $x = y = 0$), while the incident plasma will be traveling along $x$ or $y$. I assume I would change the $B$-terms to $dB_x$ and do an integration of the $B$ gradient over the $x$-space of interest to find the total energy/current required by say an ion to penetrate through the whole field? That is my best guess for this.
