What is the dielectric constant of a star? What is the dielectric constant of a star, especially its corona? Is it of order 1 or is it quite large?

How much do &quot;impurities&quot; (elements other than H and He) affect the dielectric constant?
Disclaimer
This not (yet) a full answer, since I only  focus on approaching part 1 of the question, namely the calculation of the dielectric constant of the corona.
Dielectric constant of the corona
The Sun's corona

... extends millions of kilometres into outer space and is most easily seen during a total solar eclipse [...]  measurements indicate strong ionization in the corona and a plasma temperature in excess of $1\,000\,000 {\rm K}$ much hotter than the surface of the Sun.

So let's dig a bit into plasma physics.
According to I. M. Podgornyi's article Determination of the Dielectric Constant of a Plasma, in the absence of a magnetic field,  the dielectric constant $\varepsilon$ of a plasma can be written
$$ \varepsilon(\omega) = 1 - {{4\pi {e^2}n} \over {{m_e}{\omega ^2}}} \cdot {1 \over {1 - i{{{v_{col}}} \over \omega }}}$$
where $\omega$ is the angular frequency of the electromagnetic wave, $e =  1.60217662 \cdot 10^{-19} {\rm C}$ is the charge of an electron, $m_e = 511 {\rm keV} = 9.10938356 \cdot 10^{-31} {\rm kg}$ is the mass of an electron, $i$ the imaginary unit.
The frequency of collisions $ν_{col}$ with charged particles is given by
$${v_{col}} = {{{{2.10}^{ - 5}}{n_i}Z} \over {T_e^{3/2}\left( {\rm eV} \right)}}.$$
Here, we have $T_e \approx 80\ldots90 {\rm eV} = 10^6 {\rm K}$ the temperature of a plasma given in electron volt, and (average?) $Z$ the charge number.
The next step towards an answer would be to figure out all parameters in this equation, in particular the average composition of the plasma (in terms $n$ and $Z$).
I did not yet manage that (yet), see also my question Physical properties of the stellar corona?
References
The following publications might be helpful for determining $n_i$ and $Z$ for some or all consitutents of the coronal plasma:

Mercier, Chambe: Electron density and temperature in the solar corona from multifrequency radio imaging could help us with $n_e$.

Bo Thidé: Radio Studies of Solar-Terrestrial Relationships shows a graph with the radially dependent plasma frequency of the solar corona at a given temperature.

V. G. Ledenev, V. V. Tirsky, V. M. Tomozov: High-frequency waves in the solar coronal plasma looks like saying something about $\omega$.


Related

What is the temperature of the solar atmosphere (the corona) and how is it measured?