# Blandford-Znajek process: Why/how does the current flow along the magnetic field lines?

I have put a bit of commentary enumerating my confusions in parentheses

I read in Black Holes and Time Warps (Kip Thorne), that quasars can generate their jets from four different processes. These all involved the accretion disk, but there was one which doesn't make quite as much sense. It was called the Blandford-Znajek process, and it involved magnetic field lines carrying current.

The process was visualized in two ways. A black hole, with magnetic field lines, is spinning. In the first visualisation (viewpoint actually), the magnetic field lines 'spin' along with the black hole, and nearby plasma is anchored onto the field lines by electrical forces (where did the electrical fields come from?). The plasma can slide along the field lines but not across them (why?). Since the field lines are spinning, centrifugal forces will fling them up and down the field lines, forming jets.

The other viewpoint is this, and it makes even less sense (to me that is, I haven't had a formal education in GR): The magnetic fields and the swirl of space generate a voltage difference across the field lines (Why? How?). The voltage carries current across the magnetic field lines (why are the field lines behaving like wires?). This current travels across plasma, which accelerates it, creating the jets.

Now the main thing that doesn't make sense, is that magnetic field lines are behaving like wires. Why would they? I suspect the answer lies hidden somewhere in the equivalence of EM waves in different frames, but I can't think up any convincing argument from that side.

If the answer involves GR equations, you don't need to solve it here (wouldn't make sense to me), but if you have to, just refer to the equation and what you did to it, along with the final result. Thanks!

Thinking of magnetic field lines as rigid wires with tension (and also pressure, more on that later) is a great way to form intuition when dealing with fluids that have negligible resistivity - the behavior of such a system falls under the heading of ideal magnetohydrodynamics (ideal MHD), and I would definitely recommend consulting references on that.

You might already be familiar with the phenomenon of synchrotron radiation from electrons interacting with a magnetic field. As an electron moves in the field, it experiences an acceleration in the plane perpendicular to the magnetic field (flux) that can produce cyclical motion in that plane. If you consider a situation where the radius of the cyclical motion is small compared to other relevant length scales in the problem, then you can see how the electron might appear as though is "trapped" on the field line, as it continues to move freely in the direction parallel to the field line.

In addition to trapping particles on field lines, magnetic fields in highly conductive fluids have two other significant effects on the fluid dynamics: magnetic tension and magnetic pressure. Magnetic tension accounts for the restoring force that the magnetic field exerts when curvature is induced in the field lines. Magnetic pressure accounts for the restoring force to bunching lines together. Magnetic pressure is not hard to understand, since the magnetic energy density goes as the amplitude of the field squared, and bunching field lines together is equivalent to increasing the amplitude of the field. All of these statements can be handled rigorously by writing down equations for conservation of mass, momentum and energy for the fluid, and combining them with Maxwell's equations for the magnetic field and neglecting resistivity in the fluid (this is ideal MHD).