Curl, twist and helicity are all having to do with rotation.
Gyromotion is the particle rotating about the axis, and curl is the magnetic field rotating about the axis. If there are electrons with a parallel velocity I would expect a curl component.
Curl is the mathematical description of the rotation of the magnetic field using vectors.
It is the vector rotation of the magnetic field, following the right hand rule, that causes the helicity(twist) of flux tubes.
I am sorry, but this is really complicating stuff if you start using words differently from how they are defined.
Twist is just the "rolling up of the field lines" into a rope like structure, but curl is mathematical operator and helicity is a physical quantity, and both may or may not have something to do with the field lines being twisted.
The curl of the magnetic field is defined as:
[latex]
[\nabla \times {\bf B}]_{k} = dB_{j}/dx_{i} - dB_{i}/dx_{j}
[/latex]
which applies to ANY magnetic field, not just twisted field lines.
And then the helicity of the magnetic field is defined as the volume integral:
[latex]
H = \int_{V} {\bf A} \cdot {\bf B} dr^3
[/latex]
Wher
A is the vector potential and
[latex]
{\bf B} = \nabla \times {\bf A}
[/latex]
which works for ANY magnetic field.
tusenfem said:
And again I have no idea what exactly you mean here. Do you mean a flux rope (like the figure MM keeps on presenting)? Or do you mean a plasmoid? Or ... And what do you mean with "wrapped with a curl >0 shell?" Curl of WHAT?
CLUSTER has observed a plasma filled flux tube rope that has a inner core that has field aligned currents with an outer sheath that has a curl component. The outer sheath has a helical twist to it where as the inner core has no twist. This has been anecdotally(visually but no instrument stuck into the flux tube) observed on the solar surface as well..
Now it is getting a bit clearer, you mean to say that cluster observed a flux rope and that the in the centre there is a "straight" field line and if you move away from the centre there is wound up or twisted magnetic field lines, of which the "winding" will change the further you move away from the centre.
Here are two papers by Jim Slavin one of the experts on flux ropes.
However, whether curl(B) > 0 or < 0 depends wholly on the field itself.
So my question to those that want to weigh in on this:
Does reconnection only happen in flux ropes?
If not what is the configuration that you think is required?
No, reconnection does not happen
in flux ropes, it happens
between flux ropes. As a flux rope only has field in the same direction there is nothing to facilitate reconnection.
What is needed is
oppositely directed magnetic field, or at least field lines with a significant angle between them (the so called component reconnection in 3D).
Is reconnection a pinch like process?
No, a pinch is when the current in the flux rope gets so strong that it will "squeeze together' because the magnetic pressure becomes stronger than the plasma pressure (see e.g. Bennett pinch). However, when you pinch a flux you do not get appropriate conditions for reconnection.
Are there electric fields involved in the particle acceleration?
As there is a strongly varying magnetic field there are electric fields, especially along the separatrices (see this recent paper
by Parnell et al. (2010).
However, the bulk acceleration of the plasma is provided by the magnetic tension of the field lines, which shoot the
whole plasma away from the reconnection point/line in the reconnection exhaust. Observations in the tail show that the main plasma velocity is
perpendicular to the magnetic field direction in these flows (with the plasma "glued" to the magnetic field).
