In suitable conditions on the radiation source the synchrotron process can be described by a Fredholm integral equation whose integral kernel is expressed in terms of a modified Bessel function of the second kind. We present a completely general solution of this equation. We point out that the linear inverse problem of determining the electron...
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1998 (v1)PublicationUploaded on: December 5, 2022
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1998 (v1)Publication
The instability properties of bremsstrahlung spectrum inversion to yield source electron spectra in flares are examined in terms of singular value decomposition (SVD) for the cases of thin- and thick-target models for different bremsstrahlung cross-sections. It is shown that, for the Kramers and Bethe-Heitler cross-sections, analytic...
Uploaded on: March 27, 2023 -
1995 (v1)Publication
Transient stellar mass loss has already been studied as an inverse problem by Brown and Wood (1994) and by Calvini, Bertero and Brown (1995), in the hypothesis of a uniform flow speed nu (r)= nu 0. Here we consider a generalization of this inverse problem to an accelerated wind profile based on an empirical form for nu (r) with an adjustable...
Uploaded on: March 27, 2023 -
2008 (v1)Publication
Context. Hard X-Ray bremsstrahlung continuum spectra, such as from solar flares, are commonly described in terms of power-law fits, either to the photon spectra themselves or to the electron spectra responsible for them. In applications various approximate relations between electron and photon spectral indices are often used for energies both...
Uploaded on: March 31, 2023 -
1995 (v1)Publication
Various methods are explored for obtaining regularized solutions of the severely ill-posed Laplace inversion problem involved in deriving plasma temperature (T) structure (differential emission measure xi(T)) from bremsstrahlung spectra. Inversions of simulated data show that zero-order regularization (Tikhonov regularization in L2 space) is...
Uploaded on: April 14, 2023 -
1999 (v1)Publication
We consider the hard x-ray emission process by interaction between the electrons and the ions in the solar atmosphere. We provide the integral equations describing this process as an inverse problem in the case of uniform ionization of the plasma and of a simple but rather realistic approximation of non-uniform conditions. The singular system...
Uploaded on: April 14, 2023 -
2004 (v1)Publication
Hard X-ray spectra in solar flares provide knowledge of the electron spectrum that results from acceleration and propagation in the solar atmosphere. However, the inference of the electron spectra from solar X-ray spectra is an ill-posed inverse problem. Here we develop and apply an enhanced regularization algorithm for this process making use...
Uploaded on: March 25, 2023 -
2005 (v1)Publication
Kontar et al. (2004) have shown how to recover mean source electron spectra F(E) in solar flares through a physical constraint regularization analysis of the bremsstrahlung photon spectra I(ε) that they produce. They emphasize the use of non-square inversion techniques, and preconditioning combined with physical properties of the spectra to...
Uploaded on: March 25, 2023 -
2011 (v1)Publication
Because hard X-rays represent prompt, optically-thin, radiation from energetic electrons, they are a relatively straightforward, and hence valuable, tool in the diagnostic study of °are-accelerated electrons. The observed X-ray °ux (and polarization state) is fundamentally a convolution of the cross-section for the hard X-ray emission...
Uploaded on: March 31, 2023 -
2004 (v1)Publication
The cross-section for bremsstrahlung photon emission in solar flares is in general a function of the angle θ between the incoming electron and the outgoing photon directions. Thus the electron spectrum required to produce a given pho- ton spectrum is a function of this angle, which is related to the position of the flare on the solar disk and...
Uploaded on: April 14, 2023 -
2003 (v1)Publication
By inverting the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) hard X-ray photon spectrum with the Tikhonov regularization algorithm, we infer the effective mean electron source spectrum for a time interval near the peak of the 2002 July 23 event. This inverse approach yields the smoothest electron flux spectrum consistent with...
Uploaded on: April 14, 2023