[Loops] summaries on nanoflare debates in "coronalloopworkshops"

Fri Mar 6 09:12:14 MST 2009

Mitch,

> 
> Dear All,
> I have been away from coronal heating for a number of years, so I am
> asking for some guidance.
> 
> Here is my problem:
> The Parker model for heating relied heavily on energy storage
> throughout a coronal loop. In the absence of reconnection the field
> lines within
> a loop would become increasingly tangled: the free energy within a
> loop then increases as time squared, giving a power input increasing
> linearly with time. Throw in reconnection,
> and the system reaches a steady state at some saturation time t_sat.
> Here the heating power is linear in t_sat. Physically, t_sat tells you
> the time needed to stress the field up to levels where reconnection
> takes off, as in the secondary instabilities of Dahlburg, Linton and
> Antiochos. The curious thing is that the heating rate goes down if
> reconnection is more easy to trigger, because the saturation time is
> smaller for easy reconnection.

Yes, this has always been a fascinating result.  If the energy release
process were highly efficient, the corona would be much cooler.  The
process must have a "switch-on" property whereby it remains dormant
while magnetic stresses build to substantial levels and then turns on.
The nice thing about the secondary instability is that it occurs at the
right level of stress to produce the observed temperatures and loss
rates.  (By the way, the secondary instability work is Dahlburg,
KLIMCHUK, and Antiochos!!!)  Note that this switch-on property is
generic.  It must apply to flares, CMEs, and any magnetically driven
process.

> 
> Having grown up with these ideas, it is difficult to reconcile myself
> with the newer observations suggesting the location of heating mostly
> at the base of loops. This causes two problems: first, is there enough
> volume of stressed field in the chromosphere/transition region to
> store the saturation level energy (yes, I know B is stronger down
> there, but still...). Secondly, reconnection may be too easy down
> there because of lower magnetic Reynolds numbers. Can someone convince
> me that you can still get 10^7 ergs/cm^2-sec active region heating
> rates?

You raise a valid concern.  The integral of B^2 over the transition
region volume is small.  Note that B is the shear component of the
field, since we are interested in the free energy available to heat the
plasma.  One might be even more concerned about the chromosphere, which
is also not very thick and which has much greater heating requirements.
The situation there is helped by the fact that the field may be more
highly concentrated in discrete flux tubes (at least in the low
chromosphere).  For a given magnetic flux, the volume integral of
magnetic energy goes as one over the filling factor.  Say we take a
magnetic flux density of 100 G, a chromospheric thickness of 2x10^8 cm,
and a filling factor of 10%.  The energy per unit area is then 10^12
erg/cm^2.  For the transition region (h ~ 2x10^7 cm, f ~ 1), the number
is more like 10^10 erg/cm^2.  To satisfy the coronal energy budget of
10^7 erg/cm^2/s^1 in active regions, the field must be "recharged" every
1000 s.  Maybe this isn't so bad, since stresses can propagate down from
the corona (ultimately they come from the photosphere motions).

Cheers,
Jim

> 
> Best Wishes
> Mitchell Berger
> 
> On Fri, Mar 6, 2009 at 2:13 AM, Brooks, David (Forn Natl)
> <dhbrooks at ssd5.nrl.navy.mil> wrote:
> >
> > Dear All,
> >
> > A good example (I would say that...) of hot loops in locally
unipolar
> > regions
> > as seen by SOT (that Harry mentioned) is video 4 in our paper:
> > http://www.iop.org/EJ/article/1538-4357/689/1/L77/23039.html
> >
> > It also shows that dynamic events in the chromosphere/transition
region
> > cluster
> > around the active region neutral line in mixed flux regions. These
are the
> > resolvable events that Jim referred to that don't reach high
temperatures.
> >
> > Best wishes,
> > David Brooks
> >
> >
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