ISSI Visiting Scientists Programme

__Introduction__

Solar flares emit hard X-ray radiation bursts (photon energy
ε>~10 keV) which indicate copious amounts of energy among the (mainly)
bremsstrahlung emitting electrons causing them. The process of bremsstrahlung
(and recombination) hard X-ray emission by energetic electrons is intrinsically
inefficient compared to other energy-consuming processes (such as Coulomb
heating of ambient particles in the solar atmosphere). So the observed
brightness in hard X-rays implies that electrons are accelerated at a rate of up
to 10^{37}
electrons s^{−1}
in large events. If such an electron rate were quite beamed it would correspond
to a current of some 10^{18}
Amps, spread over an observed flare area of no more than 10^{18}
cm^{2},
possibly much less. Naive application of the Ampere law implies for this a
steady-state magnetic field of order 10^{8}
Gauss, some five orders of magnitude higher than observed, and corresponding to
a magnetic energy of order 10^{42}
ergs, *ten orders of
magnitude *higher
than in the electrons themselves. Similarly, since hard X-ray fluxes are
observed to rise on a timescale ~10 s, and since the inductance of a flaring
loop of some 10^{9}
cm in length is ~10 H, application of the Faraday law implies emfs of order 10^{18}
Volts, some *fourteen *orders of magnitude higher than the energy of the
accelerated particles. While some of these difficulties can be eased by invoking
a return current, clearly, such simple “cartoon” models are inadequate to
describe the true process of electron acceleration in solar flares. In reality
these problems are “solved” by the overall electron distribution being close to
“isotropic” (very small vector flux) due to near isotropy of the beam itself and
or the oppositely directed slow plasma return current that any intense beam
automatically generates when injected in a plasma. The return current is created
very rapidly by the E fields generated by the initial rise in beam current and
charge in the system. However, the overall isotropy has to be very high and it
is essential to have observational diagnostics of the beam anisotropy to
understand properly the real solar situation. Understanding the processes of
electron acceleration and propagation in solar flares, including such large
scale electrodynamic issues, is a paramount challenge, addressing which will
lead to an increased understanding of particle acceleration in other
astrophysical sites as well as on the sun. Nearly all of space science involves
remote sensing, the interpretation of physical conditions in a source through
analysis of the radiation emitted by that source. High-energy solar physics is
no exception; we must learn about the accelerated particles through the
radiation they produce, in this case the hard X-ray bremsstrahlung. Now, the
form of the observed X-ray radiation spectrum I(ε, **r**) from a location **
r **(the “data
function”) is basically an
integral convolution of the electron spectrum
F(E, **r**) at the point **r **(the “source function”) and the
cross-section Q(ε,E) for hard X-ray production by electrons (the “kernel”):

It follows that extraction of scientifically useful
information on
F(E,**r**), and
its concomitant implications
for our understanding of electron acceleration and propagation in flares,
requires not only expertise in solar physics, but also in the solution of
integral equations such as (1).
Since 2005, a group of researchers have held a series of meetings, generously
sponsored by ISSI, to study problems related to the inference of
F(E,**r**) from hard
X-ray data. They have comprised experts in electron acceleration and propagation
in solar flares (Brown, Emslie, Kontar), data analysis (Hurford,
Kašparová) and
mathematical inversion techniques (Massone, Piana, Prato). The main source of
the data is the NASA Ramaty High Energy Solar Spectroscopic Imager (*RHESSI*)
satellite, launched in early 2002 and tasked with determining information on
I(ε,**r**) with unprecedented quality. The satellite continues to produce
data of exceptional quality and quantity. Our main previous accomplishments have
been the validation and comparison of different regularization methods in the
reconstruction of the mean electron spectrum from X-ray data, the study of the
infuence of albedo and electron-electron bremsstrahlung contribution on X-ray
solar spectroscopy and the formulation of a reconstruction method for the
differential emission measure from X-ray spectra in a thermal interpretation of
the bremsstrahlung emission process. We also focused on the integration of 2D
spatial imaging with 1D high resolution spectroscopy into an
imaging-spectroscopy approach. We developed a new method for imaging
spectroscopy that involves regularized inversion of the photon *visibility *
spectra (i.e., the twodimensional spatial Fourier transforms of the spectral
image) to obtain smoothed (regularized) forms of the corresponding electron
visibility spectra. Application of conventional visibility-based imaging
algorithms then yields images of the electron flux that vary smoothly with
energy. Both spatially-integrated spectra I_{tot}(ε)
= ∫ I(ε,**r**) d**r** and, for sufficiently intense events,
spatially-imaged spectra I(ε;x,y) have been used in our work.

**
Site created and updated by Marco Prato**

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Comments and suggestions to: marco.prato (at) unimore.it**