Leonid Benkevitch, Divya Oberoi
The electron number density N_e distributions in solar chromosphere and
corona are usually described with models of different nature: exponential for
the former and inverse power law for the latter. Moreover, the model functions
often have different dimensionality, e.g. the chromospheric distribution may
depend solely on solar altitude, while the coronal number density may be a
function of both altitude and latitude. For applications which need to consider
both chromospheric and coronal models, the chromosphere-corona boundary, where
these functions have different values as well as gradients, can lead to
numerical problems. We encountered this problem in context of ray tracing
through the corona at low radio frequencies, as a part of effort to prepare for
the analysis of solar images from new generation radio arrays like the
Murchison Widefield Array (MWA), Low Frequency Array (LOFAR) and Long
Wavelength Array (LWA). We have developed a solution to this problem by using a
{\em patch} function, a thin layer between the chromosphere and the corona
which matches the values and gradients of the two regions at their respective
interfaces. We describe the method we have developed for defining this patch
function to seamlessly "stitch" chromospheric and coronal electron density
distributions, and generalize the approach to work for any arbitrary
distributions of different dimensionality. We show that the complexity of the
patch function is independent of the stitched functions dimensionalities. It
always has eight parameters (even four for univariate functions) and they may
be found without linear system solution for every point. The developed method
can potentially be useful for other applications.
View original:
http://arxiv.org/abs/1110.2516
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