On why discs generate magnetic towers and collimate jets

We show that accretion discs with magnetic fields in them ought to make jets provided that their electrical conductivity prevents slippage and there is an ambient pressure in their surroundings. We study equilibria of highly wound magnetic structures. General Energy theorems demonstrate that they form tall magnetic towers, the height of which grows with every turn at a velocity related to the circular velocity in the accretion disc. The pinch effect amplifies the magnetic pressures toward the axis of the towers, the stability of which is briefly considered. We give solutions for all twist profiles Phi(P ) =Omega(P )t and for any external pressure distribution p (z ). The force-free currents are given by and we show that the constant pressure case gives which leads to analytic solutions for the fields.