Abstract
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 measureξ(T)) from bremsstrahlung spectra. Inversions of simulated data show that zero-order regularisation (Tikhonov regularisation inL 2 space) is very unsatisfactory even with weighting, while first-order regularisation (Tikhonov regularisation in Sobolev space) yields reasonable results.
The method is applied to a high-resolution hard X-ray flare spectrum observed by Lin and Schwartz (1987) and yields a positive solution forξ(T) showing that a purely thermal interpretation is possible for that event. The form ofξ(T) found has two broad features: one peaking at around 107 K and falling off steeply toward 2 × 108 K; a second spread around a peak near 4.5 × 108 K. The interpretation of suchξ(T) in terms of plasma heating and conductive flux is discussed in terms of plasma heat fluxes and heating rates. For 1-D geometry, the distribution of the plasma heating rateH(T) per unit volume is inferred fromξ(T) in the limits of classical diffusive conduction and of saturated heat flux, the former being relevant atT below around 5 × 107 K and the latter at much higherT. We find there exists a maximum inH(T) around 2 × 108 K, a fact which may be important for energy release theories.
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Piana, M., Brown, J.C. & Thompson, A.M. Thermal bremsstrahlung hard X-rays and primary energy release in flares. Sol Phys 156, 315–335 (1995). https://doi.org/10.1007/BF00670230
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DOI: https://doi.org/10.1007/BF00670230