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.

1 Answer

Short Answer
So the short answer is turbulent motion of the photospheric plasma on the sun.

Long Answer
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).

The purpose of going through that is to show that when the frozen-in theorem holds, it argues that the plasma and magnetic fields are effectively tied together. So if the plasma in the photosphere of the sun moves, then the magnetic field must move as well. The plasma in the photosphere is constantly churning due to pressure gradients from dynamic and thermal contributions. Thus, the magnetic fields must move to compensate.

Now the frozen-in theorem has several limitations and requires numerous assumptions. So one can imagine that it would not always hold (it actually never holds perfectly because one can (almost?) never have an infinite electrical conductivity in a plasma). In fact, plasmas are notoriously unstable because they are almost never in thermodynamic equilibrium.

If the plasma twists and turns due to differential flows causing instabilities like the Kelvin–Helmholtz instability, then this will put tremendous strain/stress on the magnetic fields (magnetic fields experience tension forces much like rubber bands). If the stress is too great, the field topology will reconfigure itself through a process called magnetic reconnection. This reconfiguration of field topology also results in the conversion of electromagnetic to particle kinetic energy. In some cases, this can result in the release of large magnetic flux ropes that are one form of coronal mass ejections.

• Thanks. MHD is very simply introduced in the course I'm taking, so your long answer was still of help. MHD is of great interest me, I must take the tie to learn it more rigorously once I've finished my degree. – rooms May 10 '15 at 10:19