Hi Robertus,
Thanks for sending David's presentation. He heard about our listserve discussion and sent me the paper that goes with it. I in turn sent him the following two messages and am waiting for his reply.
Cheers, Jim
Hi David,
Yes, we've been having an e-mail discussion within the loops community, and Robertus mentioned that you had ruled out nanoflare heating. Thanks for the paper and presentation. I've only had a chance to glance at them, but they look very interesting. Do you stand by your claim? As you know, it is extremely difficult to measure event energies, especially for small events. I've had some discussions with Arnold Benz recently, and he feels strongly that we do not have accurate enough information to place reliable constraints on the problem, i.e., to determine whether nanoflares are important based on energy distributions. Clare Parnell tells me the same thing. Also, I would note that recent studies by the Max Planck group of small events observed by SUMER give power laws steeper than 2, supporting the nanoflare idea. Nanoflares of the type I believe exist are so small that they cannot be measured directly, and there is a danger in extrapolating "observed" energy distributions to lower values. The physics of large eruptive flares is probably very different from the physics of small confined flares and nanoflares. A recent study by Yashiro et al. finds that flares that are not associated with CMEs have a power law steeper than 2. I'm very interested in your feedback.
Best wishes, Jim
Hi again,
I was just looking at Section 5.1 of your paper (slide 29 in the presentation), where you discuss lower limits to the nanoflare energy based on the arguments of Markus (1999). I'm afraid I see some problems with those arguments.
First, Markus' scaling laws are P~T^3 and L~T. This gives E_th~PL~T^4, not T^6.
Second, the coronal pressure is not set by the chromospheric pressure. Rather, the chomosphere will extend to a height at which its gravitationally stratified pressure matches that of the corona, which is set by the heating. Nonetheless, I agree that there is practical lower limit to the coronal pressure produced by a nanoflare.
Third, the cross sections of the strands that are heated by nanoflares are probably very small. For example, a typical TRACE loop contains several tens of elemental flux tubes as observed in the photosphere. If energy release occurs at the interfaces of these tubes, as seems very likely, then the nanoflare-heated strands could have a diameter of 10 km or less.
The bottom line is that 10^23 erg is not a valid lower limit to the energy of nanoflares.
Cheers, Jim
-----Original Message----- From: Robert von Fay-Siebenburgen [mailto:robertus@sheffield.ac.uk] Sent: Monday, March 09, 2009 4:16 PM To: Klimchuk, James A. (GSFC-6710) Subject: Re: [Loops] summaries on nanoflare debates in "coronalloopworkshops"
jim,
see attached:), cheers, r.
On Mon, 9 Mar 2009, Klimchuk, James A. (GSFC-6710) wrote:
Valery and Robert,
Thanks for bringing up waves. I have two quick points.
- The internal plasma structure of a loop (multi-stranded or not) is
determined by the heating and cannot be decoupled from the wave dissipation (unless the wave is energetically insignificant). See Section 4.3 of the attached.
- There may be different opinions of what is meant by "nanoflare."
Some people define it to be an identifiable point-like brightening
that
probably occurs in a tiny bipole. Most loops modelers define it to be an impulsive energy release in a long and unresolved magnetic strand. It cannot be directly observed. With this definition, even resonant wave absorption produces nanoflare heating (also explained in Sections 4.3 and 4.2). I'm very curious about David Berghmans' talk and have
my
doubts about the conclusions!
Cheers,
Jim
From: loops-bounces@solar.physics.montana.edu [mailto:loops-bounces@solar.physics.montana.edu] On Behalf Of Nakariakov, Valery Sent: Saturday, March 07, 2009 9:02 AM To: A mailing list for scientists involved in the observation and modeling ofsolar loop structures; A mailing list for scientists
involved
in the observation and modelingofsolar loop structures Subject: Re: [Loops] summaries on nanoflare debates in "coronalloopworkshops"
Hi Robertus, hi all,
however, both hinode and very recent rosa observations have shown the
omnipotent presence of mhd waves ... that have the necessary poyting flux to heat the lower atmosphere or corona. so, it is not just reconnection!
There are two important aspects, in my opinion: (a) even if the Poynting flux is sufficient, there also should be sufficiently effective mechanisms for the wave energy dissipation at a reasonable height. The efficiency of both phase mixing and RA is determined by the steepness of the transverse structuring of the waveguiding plasma structures.
Structuring is definitely an unknown parameter, as you've pointed out:
if (IF) we want to get closer to loop fine structure
(multi-thread vs whatever) or uncover the operating heating function,
a
very promising and currently already available way is of the one by magneto-seismology.
I agree. As I have mentioned in this forum before, there are several coronal seismological indications of the subresolution structuring of the corona. But, what is important is not only the spatial scale of structuring, but also the gradients of the plasma parameters.
(b) The amplitudes of the observed transverse waves are sufficiently high to produce a significant change of the magnetic field in the vicinity of the potential reconnection sites. Hence, the waves can effectively contribute to reconnection,
and
then the separation of "wave-based" and "reconnection-based"
mechanisms
for heating seems to be a bit too artificial.
All the best,
Valery
Hi Jim, Robertus and others,
I left the nanoflare business some time ago. I will thus reply more at the philosophical level rather than on the technical details.
The one thing that I remember from my own work is that nanoflare heating is an absolutely hopeless business. It is based on the assumption that we can extrapolate (!) the slope of the distribution over many order of magnitude (!) into unobserved territory (!). It only works if you take as extrapolating slope the few outlier studies (!) that find a slope steep enough. And you must believe (!) that sufficiently small events can actually really exist.
There was a time when I was ready to take all these hurdles. What really killed my faith however is the realization that, when analyzing data and identifying members of the flare distribution, one needs to identify flares one by one. At small scales (where most events are) you essentially see a bunch of brightening pixels and one needs to group these pixels in events. The 'grouping criterium' can be strict ('touching' pixels belong to the same event) or somewhat more relaxed ('close-by' pixels can belong to the same event). In the first case you get many small events, in the last case you get fewer & bigger events. Comparing the two cases, will give you widely different slopes.
My conclusion: determining the slope for gradually smaller flares is gradually more subjective. We are not proving anything by measuring & extrapolating slopes of small event distributions.
I do not mean to say that nanoflares (whatever small energy releases at unobserved scales) are not interesting or not relevant for coronal heating. At the contrary, I am personally looking forward to see their appearance in the so-called hot channel of the high-res EUV imager foreseen on Solar Orbiter! I am just saying that extrapolating ill- defined power laws is, in my humble opinion, not proving anything.
David
On 11 Mar 2009, at 14:55, Klimchuk, James A. (GSFC-6710) wrote:
Hi Robertus,
Thanks for sending David's presentation. He heard about our listserve discussion and sent me the paper that goes with it. I in turn sent him the following two messages and am waiting for his reply.
Cheers, Jim
Hi David,
Yes, we've been having an e-mail discussion within the loops community, and Robertus mentioned that you had ruled out nanoflare heating. Thanks for the paper and presentation. I've only had a chance to glance at them, but they look very interesting. Do you stand by your claim? As you know, it is extremely difficult to measure event energies, especially for small events. I've had some discussions with Arnold Benz recently, and he feels strongly that we do not have accurate enough information to place reliable constraints on the problem, i.e., to determine whether nanoflares are important based on energy distributions. Clare Parnell tells me the same thing. Also, I would note that recent studies by the Max Planck group of small events observed by SUMER give power laws steeper than 2, supporting the nanoflare idea. Nanoflares of the type I believe exist are so small that they cannot be measured directly, and there is a danger in extrapolating "observed" energy distributions to lower values. The physics of large eruptive flares is probably very different from the physics of small confined flares and nanoflares. A recent study by Yashiro et al. finds that flares that are not associated with CMEs have a power law steeper than 2. I'm very interested in your feedback.
Best wishes, Jim
Hi again,
I was just looking at Section 5.1 of your paper (slide 29 in the presentation), where you discuss lower limits to the nanoflare energy based on the arguments of Markus (1999). I'm afraid I see some problems with those arguments.
First, Markus' scaling laws are P~T^3 and L~T. This gives E_th~PL~T^4, not T^6.
Second, the coronal pressure is not set by the chromospheric pressure. Rather, the chomosphere will extend to a height at which its gravitationally stratified pressure matches that of the corona, which is set by the heating. Nonetheless, I agree that there is practical lower limit to the coronal pressure produced by a nanoflare.
Third, the cross sections of the strands that are heated by nanoflares are probably very small. For example, a typical TRACE loop contains several tens of elemental flux tubes as observed in the photosphere. If energy release occurs at the interfaces of these tubes, as seems very likely, then the nanoflare-heated strands could have a diameter of 10 km or less.
The bottom line is that 10^23 erg is not a valid lower limit to the energy of nanoflares.
Cheers, Jim
-----Original Message----- From: Robert von Fay-Siebenburgen [mailto:robertus@sheffield.ac.uk] Sent: Monday, March 09, 2009 4:16 PM To: Klimchuk, James A. (GSFC-6710) Subject: Re: [Loops] summaries on nanoflare debates in "coronalloopworkshops"
jim,
see attached:), cheers, r.
On Mon, 9 Mar 2009, Klimchuk, James A. (GSFC-6710) wrote:
Valery and Robert,
Thanks for bringing up waves. I have two quick points.
- The internal plasma structure of a loop (multi-stranded or not)
is determined by the heating and cannot be decoupled from the wave dissipation (unless the wave is energetically insignificant). See Section 4.3 of the attached.
- There may be different opinions of what is meant by "nanoflare."
Some people define it to be an identifiable point-like brightening
that
probably occurs in a tiny bipole. Most loops modelers define it to be an impulsive energy release in a long and unresolved magnetic strand. It cannot be directly observed. With this definition, even resonant wave absorption produces nanoflare heating (also explained in Sections 4.3 and 4.2). I'm very curious about David Berghmans' talk and have
my
doubts about the conclusions!
Cheers,
Jim
From: loops-bounces@solar.physics.montana.edu [mailto:loops-bounces@solar.physics.montana.edu] On Behalf Of Nakariakov, Valery Sent: Saturday, March 07, 2009 9:02 AM To: A mailing list for scientists involved in the observation and modeling ofsolar loop structures; A mailing list for scientists
involved
in the observation and modelingofsolar loop structures Subject: Re: [Loops] summaries on nanoflare debates in "coronalloopworkshops"
Hi Robertus, hi all,
however, both hinode and very recent rosa observations have shown the
omnipotent presence of mhd waves ... that have the necessary poyting flux to heat the lower atmosphere or corona. so, it is not just reconnection!
There are two important aspects, in my opinion: (a) even if the Poynting flux is sufficient, there also should be sufficiently effective mechanisms for the wave energy dissipation at a reasonable height. The efficiency of both phase mixing and RA is determined by the steepness of the transverse structuring of the waveguiding plasma structures.
Structuring is definitely an unknown parameter, as you've pointed out:
if (IF) we want to get closer to loop fine structure
(multi-thread vs whatever) or uncover the operating heating function,
a
very promising and currently already available way is of the one by magneto-seismology.
I agree. As I have mentioned in this forum before, there are several coronal seismological indications of the subresolution structuring of the corona. But, what is important is not only the spatial scale of structuring, but also the gradients of the plasma parameters.
(b) The amplitudes of the observed transverse waves are sufficiently high to produce a significant change of the magnetic field in the vicinity of the potential reconnection sites. Hence, the waves can effectively contribute to reconnection,
and
then the separation of "wave-based" and "reconnection-based"
mechanisms
for heating seems to be a bit too artificial.
All the best,
Valery
<Prague.pdf>_______________________________________________ Loops mailing list Loops@solar.physics.montana.edu https://mithra.physics.montana.edu/mailman/listinfo/loops
--- David Berghmans Royal Observatory of Belgium
Dear David,
Welcome back! Indeed you did leave the nanoflare business some time ago, when we realized that we will never agree on power-law exponents because as you described there is a subjective element in the definition of a nanoflare. I fully agree with you, David, that power-law indices are useless and that we must not extrapolate them. However, power-laws are not the only way to evaluate nanoflares. In the mean time we have tried to estimate the energy input by the observed events. For this estimate, the distribution is not needed, just sum over all events and pixels. The observed energy in the soft X-rays and EUV events at peak flux is about 12% of the radiated output in the quiet sun (Benz & Krucker 2002). This includes only observed events above 5 10^24 erg. What we measure, however, is the thermal energy at one instant of the event. This thermal energy is not the flare energy, but the result of precipitating particles heating the chromosphere. The particle acceleration is not the flare either, but arguably the result of waves that have been excited by the reconnection process (e.g. transit-time damping). Thus the real difficulty is to estimate the total energy input into the corona from the observed nanoflares.
Regards, Arnold
________________________________________________________________________ Arnold Benz Institute of Astronomy email benz@astro.phys.ethz.ch ETH Zurich, HIT J 23.1 voice ++41-44-632 42 23 CH-8093 Zurich fax ++41-44-862 68 25 Switzerland web http://www.astro.phys.ethz.ch/staff/benz/benz.html _________________________________________________________________________
Dear All, The debate about the reality of nano-flares reminds me an attempt we did in 1995 to understand the origin of the fast wind in CHs as a result of discrete events (jetlets). Sorry, this is not exactly loop physics. We looked at the faintest Yohkoh SXR transient brightenings (TBs) inside the North CH at time of solar minimum and before the SoHO works appear. The threshold was typically 10^24 ergs in term of radiative output in SXR, as events were short in time (less than 3 min), over a background of virtually zero value, even when using long exposure times (up to 55 s), times significantly larger than what Shimizu-san used in his classical PhD analysis of TBs. We thought that this is a way to avoid overlapping effects (events were single or 2 pixels events) and we avoided measurements done during the passage through the radiation belts to limit the influence of cosmic rays. Events were considered as real (solar) when at least 3 consecutive images show a definite signature. We got a lot of events in this 2 MK range (this was reported in an Astron. Astrophys. L. paper of the late Yohkoh epoch which is left un-noticed by almost all nano-flare afinados, but I attached it for your record- Thank you).
The lesson we got is that 2 MK small events (2 or more orders of magnitude fainter than what Shimizu-san analyzed) do exist and proliferate in CHs, and not just at the very surface of the Sun. The question “how much flux ?” seems indeed open. An individual event is associated with several consequences, not just a radiative signature at 2 MK.
Is not correct to think that nano-flares can as well accelerate energetic particles (electrons…) in bi-directional flows and produce a signature (chromospheric “evaporation”) well outside the reconnection site? Looking at the faintest events seen in 304 inside a CH, with a partial frame sequence, gives even more “individual” events. The less is the energy range (temperature), the bigger is the number of events you see and probably the deeper you look at. And it is also true that the shaking of field lines (transverse waves, spicules, etc.) is starting well down the low corona and this should also affect loops but, in CHs, it is more obvious, although making reconnections in a dominant polarity open field could be a challenge.
This is a naïve interpretation of what is observed and I humbly and respectfully will read/evaluate with great interest all interpretations that you would propose in term of the network, quiet Sun, and or active regions coronal (transient) magnetic field that we cannot measure, including the case of multi-stranded loops.
Sorry for my broken English. Serge
*
*
Arnold Benz a écrit :
Dear David,
Welcome back! Indeed you did leave the nanoflare business some time ago, when we realized that we will never agree on power-law exponents because as you described there is a subjective element in the definition of a nanoflare. I fully agree with you, David, that power-law indices are useless and that we must not extrapolate them. However, power-laws are not the only way to evaluate nanoflares. In the mean time we have tried to estimate the energy input by the observed events. For this estimate, the distribution is not needed, just sum over all events and pixels. The observed energy in the soft X-rays and EUV events at peak flux is about 12% of the radiated output in the quiet sun (Benz & Krucker 2002). This includes only observed events above 5 10^24 erg. What we measure, however, is the thermal energy at one instant of the event. This thermal energy is not the flare energy, but the result of precipitating particles heating the chromosphere. The particle acceleration is not the flare either, but arguably the result of waves that have been excited by the reconnection process (e.g. transit-time damping). Thus the real difficulty is to estimate the total energy input into the corona from the observed nanoflares.
Regards, Arnold
Arnold Benz Institute of Astronomy email benz@astro.phys.ethz.ch ETH Zurich, HIT J 23.1 voice ++41-44-632 42 23 CH-8093 Zurich fax ++41-44-862 68 25 Switzerland web http://www.astro.phys.ethz.ch/staff/benz/benz.html _________________________________________________________________________
Loops mailing list Loops@solar.physics.montana.edu https://mithra.physics.montana.edu/mailman/listinfo/loops
Arnold,
Thanks to both you and David for your valuable input. I have a quick comment, just to make sure no one misinterprets what you wrote. The events that you and Sam detected account for about 12% of the radiated output in the quiet Sun. The remainder of the radiated output could be produced by smaller events that cannot be individually detected. Here's an interesting tidbit: If nanoflares have an energy of 10^24 erg (it could be smaller), they must occur at a rate of about one per second in each coronal loop to satisfy the energy requirements. That's awfully tough to detect, especially when you consider that the cooling timescale is of order 100+ seconds!
Thanks again, Jim
-----Original Message----- From: loops-bounces@solar.physics.montana.edu [mailto:loops- bounces@solar.physics.montana.edu] On Behalf Of Arnold Benz Sent: Thursday, March 12, 2009 4:52 PM To: A mailing list for scientists involved in the observation and
modeling ofsolar
loop structures Subject: Re: [Loops] FW: summaries on nanoflare debatesin "coronalloopworkshops"
Dear David,
Welcome back! Indeed you did leave the nanoflare business some time
ago,
when we realized that we will never agree on power-law exponents
because
as you described there is a subjective element in the definition of a nanoflare. I fully agree with you, David, that power-law indices are useless and that we must not extrapolate them. However, power-laws are not the only way to evaluate nanoflares. In
the
mean time we have tried to estimate the energy input by the observed events. For this estimate, the distribution is not needed, just sum
over
all events and pixels. The observed energy in the soft X-rays and EUV events at peak flux is about 12% of the radiated output in the quiet
sun
(Benz & Krucker 2002). This includes only observed events above 5
10^24
erg. What we measure, however, is the thermal energy at one instant of the event. This thermal energy is not the flare energy, but the result of precipitating particles heating the chromosphere. The particle acceleration is not the flare either, but arguably the result of waves that have been excited by the reconnection process (e.g. transit-time damping). Thus the real difficulty is to estimate the total energy
input
into the corona from the observed nanoflares.
Regards, Arnold
Arnold Benz Institute of Astronomy email benz@astro.phys.ethz.ch ETH Zurich, HIT J 23.1 voice ++41-44-632 42 23 CH-8093 Zurich fax ++41-44-862 68 25 Switzerland web http://www.astro.phys.ethz.ch/staff/benz/benz.html __________________________________________________________________ _______
Loops mailing list Loops@solar.physics.montana.edu https://mithra.physics.montana.edu/mailman/listinfo/loops
Dear all, please find on Astro-PH at the following link:
http://arxiv.org/abs/0904.0878
a new paper that supports the detection of widespread hot plasma in non-flaring active regions from Hinode/XRT observations (see the abstract below). The paper has just been accepted for publication on ApJ. We have devoted an Appendix to the issue of filter calibration. Thank you for your attention Best regards Fabio Reale
Evidence of widespread hot plasma in a non-flaring coronal active region from Hinode/XRT Authors: Fabio Reale, Paola Testa, James A. Klimchuk, Susanna Parenti
Abstract: Nanoflares, short and intense heat pulses within spatially unresolved magnetic strands, are now considered a leading candidate to solve the coronal heating problem. However, the frequent occurrence of nanoflares requires that flare-hot plasma be present in the corona at all times. Its detection has proved elusive until now, in part because the intensities are predicted to be very faint. Here we report on the analysis of an active region observed with five filters by Hinode/XRT in November 2006. We have used the filter ratio method to derive maps of temperature and emission measure both in soft and hard ratios. These maps are approximate in that the plasma is assumed to be isothermal along each line-of-sight. Nonetheless, the hardest available ratio reveals the clear presence of plasma around 10 MK. To obtain more detailed information about the plasma properties, we have performed Monte Carlo simulations assuming a variety of non-isothermal emission measure distributions along the lines-of-sight. We find that the observed filter ratios imply bi-modal distributions consisting of a strong cool (log T ~ 6.3-6.5) component and a weaker (few percent) and hotter (6.6 < log T < 7.2) component. The data are consistent with bi-modal distributions along all lines of sight, i.e., throughout the active region. We also find that the isothermal temperature inferred from a filter ratio depends sensitively on the precise temperature of the cool component. A slight shift of this component can cause the hot component to be obscured in a hard ratio measurement. Consequently, temperature maps made in hard and soft ratios tend to be anti-correlated. We conclude that this observation supports the presence of widespread nanoflaring activity in the active region.
Fabio Many thanks for that - peter cargillhad told me about it and so I have been looking out for it - -super - well done Eric
On Tue, Apr 7, 2009 at 10:21 AM, Reale Fabio reale@astropa.unipa.it wrote:
Dear all, please find on Astro-PH at the following link:
http://arxiv.org/abs/0904.0878
a new paper that supports the detection of widespread hot plasma in non-flaring active regions from Hinode/XRT observations (see the abstract below). The paper has just been accepted for publication on ApJ. We have devoted an Appendix to the issue of filter calibration. Thank you for your attention Best regards Fabio Reale
Evidence of widespread hot plasma in a non-flaring coronal active region from Hinode/XRT Authors: Fabio Reale, Paola Testa, James A. Klimchuk, Susanna Parenti
Abstract: Nanoflares, short and intense heat pulses within spatially unresolved magnetic strands, are now considered a leading candidate to solve the coronal heating problem. However, the frequent occurrence of nanoflares requires that flare-hot plasma be present in the corona at all times. Its detection has proved elusive until now, in part because the intensities are predicted to be very faint. Here we report on the analysis of an active region observed with five filters by Hinode/XRT in November 2006. We have used the filter ratio method to derive maps of temperature and emission measure both in soft and hard ratios. These maps are approximate in that the plasma is assumed to be isothermal along each line-of-sight. Nonetheless, the hardest available ratio reveals the clear presence of plasma around 10 MK. To obtain more detailed information about the plasma properties, we have performed Monte Carlo simulations assuming a variety of non-isothermal emission measure distributions along the lines-of-sight. We find that the observed filter ratios imply bi-modal distributions consisting of a strong cool (log T ~ 6.3-6.5) component and a weaker (few percent) and hotter (6.6 < log T < 7.2) component. The data are consistent with bi-modal distributions along all lines of sight, i.e., throughout the active region. We also find that the isothermal temperature inferred from a filter ratio depends sensitively on the precise temperature of the cool component. A slight shift of this component can cause the hot component to be obscured in a hard ratio measurement. Consequently, temperature maps made in hard and soft ratios tend to be anti-correlated. We conclude that this observation supports the presence of widespread nanoflaring activity in the active region.
Loops mailing list Loops@solar.physics.montana.edu https://mithra.physics.montana.edu/mailman/listinfo/loops
Dear loop group,
here a few new studies on coronal loops. The nice thing about oscillating loops is that they can easier be separated from the background due to their dynamic motion, and thus lend themselves to less ambiguous hydrodynamic modeling.
Share & enjoy, Markus
Aschwanden,M.J. and Terradas,J. 2008, The Astrophysical Journal, 686, L127-L130 URL1="http://www.lmsal.com/~aschwand/eprints/2008_cooling.pdf" The effect of radiative cooling on coronal loop oscillations
Aschwanden,M.J. 2008, The Astrophysical Journal Letters, 672, L135-L138 URL1="http://www.lmsal.com/~aschwand/eprints/2007_nanotest.pdf" An observational test that disproves coronal nanoflare heating models
Aschwanden,M.J. 2009, Astronomical Society of the Pacific Conference Series, "Beyond Discovery - Toward Understanding", Second Hinode Science Meeting, 29 Sept - 3 Oct 2008, Boulder, Colorado, USA, (eds. M.Cheung, B.Lites, T.Magara, J.Mariska, and K.Reeves), Vol ..., (in pess) URL1="http://www.lmsal.com/~aschwand/eprints/2009_hinode.pdf" Hydrodynamic Modeling of Coronal Loops wth Hinode and STEREO
Aschwanden,M.J. 2009, Space Science Reviews, ... (Topical Issue on Coronal Seismology), in press URL1="http://www.lmsal.com/~aschwand/eprints/2009_ISSI.pdf" - _movies/" The 3D geometry, motion, and hydrodynamic aspects of oscillating coronal loops
Aschwanden,M.J., Wuelser,J.P., Nitta,N., and Lemen,J. 2009, Solar Physics, ... (Topical Issue on STEREO; in press) URL1="http://www.lmsal.com/~aschwand/eprints/2008_euvi.pdf" Solar flare and CME observations with STEREO/EUVI
Sandman,A., Aschwanden,M.J., DeRosa,M., Wuelser,J.P. Alexander,D. 2009, Solar Physics, ... Topical Issue on STEREO (subm.) URL1="http://www.lmsal.com/~aschwand/eprints/2009_sandman.pdf" Comparison of STEREO/EUVI Loops with Portential and Force-Free Magnetic Field Models
______________________________________ Dr. Markus J. Aschwanden Solar & Astrophysics Laboratory Lockheed Martin Advanced Techology Center Org. ADBS, Bldg. 252 3251 Hanover St., Palo Alto, CA 94304, USA Phone: 650-424-4001, FAX: 650-424-3994 URL: http://www.lmsal.com/~aschwand/ e-mail: aschwanden@lmsal.com ______________________________________
loops@solar.physics.montana.edu