# What causes the twisting of flux loops, leading to coronal mass ejections?

I understand that the loop twisting is the ultimate originator of the CMEs but what causes this twisting? The expansion of the loops is caused by a magnetic pressure differential between the top and bottom of the loops, but the twisting itself I do not understand... Thank you.

The underlying physical mechanism is related to the concept of frozen-in magnetic flux, which is assumed in ideal MHD. This can be derived in a similar manner to how one derives the conservation of vorticity, but here it is magnetic flux. If we define the magnetic flux as: $$\Phi = \oint_{S} \mathbf{B} \cdot \hat{n} \ dA$$ where $\hat{n}$ is the outward unit normal from surface $S$ of fractional area $dA$, then we can relate $\Phi$ to the electromotive force by: $$-\frac{d \Phi}{dt} = \oint_{C} \mathbf{E} \cdot d\mathbf{l}$$ where $\mathbf{E}$ is the electric field and $d\mathbf{l}$ is the unit length along the contour $C$ path enclosing surface $S$. The frozen-in theorem argues that for an infinitely conductive plasma, then the magnetic flux should be constant in time (recall from Ohm's law that $\mathbf{j} = \sigma \mathbf{E}$, where $\sigma$ is the electrical conductivity).