  A novel method of using hard X-rays as a diagnostic for chromospheric density
and magnetic structures is developed to infer sub-arcsecond vertical variation
of magnetic flux tube size and neutral gas density.Using Reuven Ramaty High
Energy Solar Spectroscopic Imager (RHESSI) X-ray data and the newly developed
X-ray visibilities forward fitting technique we find the FWHM and centroid
positions of hard X-ray sources with sub-arcsecond resolution ($\sim 0.2"$) for
a solar limb flare. We show that the height variations of the chromospheric
density and the magnetic flux densities can be found with unprecedented
vertical resolution of $\sim$ 150 km by mapping 18-250 keV X-ray emission of
energetic electrons propagating in the loop at chromospheric heights of
400-1500 km. Our observations suggest that the density of the neutral gas is in
good agreement with hydrostatic models with a scale height of around $140\pm
30$ km. FWHM sizes of the X-ray sources decrease with energy suggesting the
expansion (fanning out) of magnetic flux tube in the chromosphere with height.
The magnetic scale height $B(z)(dB/dz)^{-1}$ is found to be of the order of 300
km and strong horizontal magnetic field is associated with noticeable flux tube
expansion at a height of $\sim$ 900 km.
