= Magnetic-pressure equality radius under Keplerian winding
{title2=$R_{\rm eq}\propto t^{2/3}$}
For <Keplerian rotation>, initial $B_R\propto R^{-1}$ and thermal pressure $p\propto R^{-2}$, <axisymmetric magnetic winding> gives $B_\phi=-(3/2)\Omega tB_R$. If the initial <plasma beta> is $\beta_p>1$, the formal equality of <magnetic pressure> and gas pressure occurs at
$$
R_{\rm eq}^3=\frac{9GMt^2}{4(\beta_p-1)}.
$$
The magnetic-to-thermal pressure ratio decreases with radius, so magnetic pressure dominates inside this radius. In a disk with a finite radial range, an equality radius exists in the disk only when this formal radius lies within that range.
Back to article page
