Steady states of solar coronal loops as nonaxisymmetric toroidal flux ropes

Consistent MHD steady states for coronal loops on the surface of the sun, modeled as magnetic flux ropes, are derived for the first time, based on the equilibrium and stability of toroidal magnetically confined fusion plasmas. Coronal loops, like magnetic tori, are unstable to expansion in major radius. The solar gravity and plasma beta, previously ignored, are crucual parameters in the steady state. For loops with a predominantly axisymmetric magnetic axis, three analytical steady states exist in terms of beta and the normalized solar gravity parameter $\hat{G}=ga/v_A^2$, where $g$ is the acceleration due to gravity, ordered in inverse aspect ratio: high beta ($\beta\sim\epsilon$) and small gravity $\hat{G}\sim\epsilon^3$, which resembles a nearly axisymmetric high-beta tokamak, and high beta with larger $\hat{G}\sim\epsilon^2$, and low beta ($\beta\sim\epsilon^2$) with $\hat{G}\sim\epsilon^3$, which are more strongly nonaxisymmetric. Comparison with observations shows that the two high beta states bracket the range of thin coronal loops in solar active regions $\epsilon\sim 0.02$ and $\hat{G}$ orders the loops by height. The low beta solution may describe certain thicker loops $\epsilon\sim 0.1$ that grow to solar flares or Coronal Mass Ejections.