Corrigendum: Model for how an accretion disk drives astrophysical jets and sheds angular momentum (2018 Plasma Phys. Control. Fusion 60 014006)

Clumps of ions and neutrals in the weakly ionized plasma in an accretion disk are shown to follow trajectories analogous to those of ﬁ ctitious ‘ metaparticles ’ having a charge to mass ratio reduced from that of an ion by the ionization fraction. A certain class of meta-particles have zero-canonical angular momentum and so spiral in towards the star. Accumulation of these meta-particles establishes a radial electric ﬁ eld that drives the electric current that ﬂ ows in bidirectional astrophysical jets lying along the disk axis and provides forces that drive the jets. The entire process converts gravitational potential energy into jet energy while absorbing angular momentum from accreting material and shedding this angular momentum at near in ﬁ nite radius.

The terms containing r 2 y   -· ( ) in equations (9a) and (9c) had the wrong sign in the paper 'Model for how an accretion disk drives astrophysical jets and sheds angular momentum Because the magnitude of the terms with the wrong sign was shown to be negligible in the discussion of equation (12) this incorrect sign has no impact on the discussion of the jet velocity as presented in section 4.1. However, the incorrect sign does have an impact on the jet collimation discussion presented in section 4.2. The ultimate result remains the same but the logical argument leading to this result needs to be corrected and in particular the argument given in equations provides a retarding force for sufficiently large z k ¶ ¶ and this retarding force will overcome the accelerating force given in equation (27) if Thus retardation occurs if there is a sudden increase in κ which corresponds to a sharp turning of the poloidal field direction at the jet tip. Specifically, the poloidal field near the z axis is nearly in the z direction in the jet main body but at the jet tip turns abruptly to be in the r direction.
The second equivalent way is to note that there is a bunching up and hence greater density of poloidal flux surfaces at the jet tip. This occurs because the bundle of poloidal magnetic field lines that had been in the main jet body and aligned nearly parallel to the z axis turns to go in the positive Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. r direction and then at larger r turns again to go in the negative z direction. This bunching up of poloidal field lines at the tip occurs because the jet distends what were initially dipole-like poloidal flux surfaces and stretches these flux surfaces out to the length of the jet. Thus, for a given r the poloidal flux is a slightly decreasing plateau going from z=0 to the instantaneous length of the jet, while at the tip of the jet there is a cliff-like sudden fall-off of the poloidal flux from its plateau value to a much lower value in the vacuum-like region above the tip (i.e., region where z exceeds the jet length). The sudden fall-off region is where the distended poloidal field lines are bunched up. The greatly enhanced poloidal flux density in the cliff-like region implies that at the tip B 2 has a sharp local maximum with respect to z. The curvature term B R R 2 0 m -ˆin equation (24) is large and points in the z direction at the hair-pin-like 180°turnaround of the bundle of poloidal field lines near the tip. For z slightly less than the location of maximum B 2 the gradient term B 2 2 0 m -^( ) is similarly large and also points in the z direction so the two terms on the right-hand side of equation (24) are additive and give a net retardation force at the tip. However, for z slightly larger than the location of maximum B 2 , i.e., just above the tip, the B 2 2 0 m -^( )now points in the positive z direction whereas the curvature term B R R 2 0 m -ĉ ontinues to point in the negative z direction so above the tip the curvature and gradient terms cancel rather than add. This is essentially a statement that the region above the tip has no current so the left-hand side of equation (24) vanishes, i.e., the curvature and gradient terms on the right-hand side of equation (24) are equal in magnitude and have opposite signs.
The third equivalent, but less precise way is to note that the squeezing together of the poloidal field lines in the main body near the z axis implies there is a positive J f while the turning of these field lines at the jet tip to go in the positive r direction implies that at the jet tip there is a positive B .
r The axial magnetic forcecomponent J B r f is thus negative and, if sufficiently large, will overcome the positive J B r f magnetic force component and result in a retardation.
These arguments indicate that near the tip the jet slows down as was assumed in the remainder of section 4.2 which showed that such slowing down leads to a collimation of the jet.