  We build a single vertical straight magnetic fluxtube spanning the solar
photosphere and the transition region which does not expand with height. We
assume that the fluxtube containing twisted magnetic fields is in
magnetohydrostatic equilibrium within a realistic stratified atmosphere subject
to solar gravity. Incorporating specific forms of current density and gas
pressure in the Grad--Shafranov equation, we solve the magnetic flux function,
and find it to be separable with a Coulomb wave function in radial direction
while the vertical part of the solution decreases exponentially. We employ
improved fluxtube boundary conditions and take a realistic ambient external
pressure for the photosphere to transition region, to derive a family of
solutions for reasonable values of the fluxtube radius and magnetic field
strength at the base of the axis that are the free parameters in our model. We
find that our model estimates are consistent with the magnetic field strength
and the radii of Magnetic bright points (MBPs) as estimated from observations.
We also derive thermodynamic quantities inside the fluxtube.
