<h3>Disclaimer</h3>
<p>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.</p>
<h3>Dielectric constant of the corona</h3>
<p>The <a href="https://en.wikipedia.org/wiki/Stellar_corona" rel="nofollow noreferrer">Sun's corona</a></p>
<blockquote>
<p>... 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 <span class="math-container">$1\,000\,000 {\rm K}$</span> much hotter than the surface of the Sun.</p>
</blockquote>
<p>So let's dig a bit into plasma physics.</p>
<p>According to I. M. Podgornyi's article <em><a href="https://link.springer.com/chapter/10.1007/978-1-4684-0724-2_7" rel="nofollow noreferrer">Determination of the Dielectric Constant of a Plasma</a></em>, in the absence of a magnetic field,  the dielectric constant <span class="math-container">$\varepsilon$</span> of a plasma can be written</p>
<p><span class="math-container">$$ \varepsilon(\omega) = 1 - {{4\pi {e^2}n} \over {{m_e}{\omega ^2}}} \cdot {1 \over {1 - i{{{v_{col}}} \over \omega }}}$$</span></p>
<p>where <span class="math-container">$\omega$</span> is the angular frequency of the electromagnetic wave, <span class="math-container">$e =  1.60217662 \cdot 10^{-19} {\rm C}$</span> is the charge of an electron, <span class="math-container">$m_e = 511 {\rm keV} = 9.10938356 \cdot 10^{-31} {\rm kg}$</span> is the mass of an electron, <span class="math-container">$i$</span> the <a href="https://en.wikipedia.org/wiki/Complex_number" rel="nofollow noreferrer">imaginary unit</a>.</p>
<p>The frequency of collisions <span class="math-container">$ν_{col}$</span> with charged particles is given by</p>
<p><span class="math-container">$${v_{col}} = {{{{2.10}^{ - 5}}{n_i}Z} \over {T_e^{3/2}\left( {\rm eV} \right)}}.$$</span></p>
<p>Here, we have <span class="math-container">$T_e \approx 80\ldots90 {\rm eV} = 10^6 {\rm K}$</span> the temperature of a plasma given in <a href="https://www.britannica.com/science/electron-volt" rel="nofollow noreferrer">electron volt</a>, and (average?) <span class="math-container">$Z$</span> the charge number.</p>
<p>The next step towards an answer would be to figure out <em>all</em> parameters in this equation, in particular the <em>average</em> composition of the plasma (in terms <span class="math-container">$n$</span> and <span class="math-container">$Z$</span>).</p>
<p>I did not yet manage that (yet), see also my question <a href="https://astronomy.stackexchange.com/questions/43429/typical-properties-of-the-corona-of-a-star?noredirect=1&amp;lq=1">Physical properties of the stellar corona?</a></p>
<h3>References</h3>
<p>The following publications might be helpful for determining <span class="math-container">$n_i$</span> and <span class="math-container">$Z$</span> for some or all consitutents of the coronal plasma:</p>
<ul>
<li><p>Mercier, Chambe: <em><a href="http://dx.doi.org/10.1051/0004-6361/201425540" rel="nofollow noreferrer">Electron density and temperature in the solar corona from multifrequency radio imaging</a></em> could help us with <span class="math-container">$n_e$</span>.</p>
</li>
<li><p>Bo Thidé: <em><a href="http://dx.doi.org/10.13140/RG.2.2.16990.54084" rel="nofollow noreferrer">Radio Studies of Solar-Terrestrial Relationships</a></em> shows a graph with the radially dependent plasma frequency of the solar corona at a given temperature.</p>
</li>
<li><p>V. G. Ledenev, V. V. Tirsky, V. M. Tomozov: <em><a href="https://www.researchgate.net/publication/252439478_High-frequency_waves_in_the_solar_coronal_plasma" rel="nofollow noreferrer">High-frequency waves in the solar coronal plasma</a></em> looks like saying something about <span class="math-container">$\omega$</span>.</p>
</li>
</ul>
<h3>Related</h3>
<ul>
<li><a href="https://astronomy.stackexchange.com/questions/16674/what-is-the-temperature-of-the-solar-atmosphere-the-corona-and-how-is-it-measu/">What is the temperature of the solar atmosphere (the corona) and how is it measured?</a></li>
</ul>

CC BY-SA 4.0
2021-04-20T21:35:09.087Z
The solar corona is practically a collisionless plasma, so you can safely neglect the collision term here (even in the photosphere it should be negligible unless $\omega$ corresponds to radio waves).
Thomas
CC BY-SA 4.0
2021-04-16T09:44:07.337Z
2021-04-20T11:55:52.523Z
2021-04-20T11:55:52.523Z
B--rian
<ol>
<li><p>What is the dielectric constant of a star, especially its corona? Is it of order 1 or is it quite large?</p>
</li>
<li><p>How much do &quot;impurities&quot; (elements other than H and He) affect the dielectric constant?</p>
</li>
</ol>

CC BY-SA 4.0
2020-03-18T01:19:57.910Z
Thanks for the edit, I've adjusted the wording a bit to better fit the site. Just fyi the answer will be different at radio frequencies and optical frequencies (visible light).
uhoh
CC BY-SA 4.0
2020-03-18T17:43:47.320Z
I'm not sure that there is a simple answer.  Plasma is a conductor, not a dielectric. The dielectric constant of a perfect conductor is infinite, but the highly rarified plasma in the corona isn't a perfect conductor. However this link http://farside.ph.utexas.edu/teaching/em/lectures/node100.html may interest you.
James K
CC BY-SA 4.0
2020-03-18T19:28:45.583Z
Trying for the world's biggest capacitor here?  :-)  .   Now, as pointed out, plasmas conduct, but depending on the frequency band you're interested in, you may find some ranges where the plasma does hold energy rather than conduct it.
Carl Witthoft
CC BY-SA 4.0
2020-03-19T09:24:54.970Z
@JamesK there's nothing wrong with talking about the dielectric constant of conductors or other lossy materials; they are simply complex valued rather than real: https://en.m.wikipedia.org/wiki/Permittivity#Complex_permittivity
uhoh
CC BY-SA 4.0
2020-03-19T09:25:33.667Z
@CarlWitthoft ditto.
uhoh
CC BY-SA 4.0
2021-04-15T08:14:13.230Z
@JamesK I found [Determination of the Dielectric Constant of a Plasma](https://link.springer.com/chapter/10.1007/978-1-4684-0724-2_7) which gives a formula and might be helpful for the corona - I have to think of it. Do you think we could estimate all the parameters?
B--rian
<star><the-sun>
What is the dielectric constant of a star?
user1937362
# What is the dielectric constant of a star?

(Asked by: username_0 on 2020-03-17)

1. What is the dielectric constant of a star, especially its corona? Is it of order 1 or is it quite large?
2. How much do "impurities" (elements other than H and He) affect the dielectric constant?

**Tags:** star, the-sun
> **Comments:**
> **username_1**: Thanks for the edit, I've adjusted the wording a bit to better fit the site. Just fyi the answer will be different at radio frequencies and optical frequencies (visible light).  
> **username_2**: I'm not sure that there is a simple answer.  Plasma is a conductor, not a dielectric. The dielectric constant of a perfect conductor is infinite, but the highly rarified plasma in the corona isn't a perfect conductor. However this link http://farside.ph.utexas.edu/teaching/em/lectures/node100.html may interest you.  
> **username_3**: Trying for the world's biggest capacitor here?  :-)  .   Now, as pointed out, plasmas conduct, but depending on the frequency band you're interested in, you may find some ranges where the plasma does hold energy rather than conduct it.  
> **username_1**: @JamesK there's nothing wrong with talking about the dielectric constant of conductors or other lossy materials; they are simply complex valued rather than real: https://en.m.wikipedia.org/wiki/Permittivity#Complex_permittivity  
> **username_1**: @CarlWitthoft ditto.  
> **username_4**: @JamesK I found [Determination of the Dielectric Constant of a Plasma](https://link.springer.com/chapter/10.1007/978-1-4684-0724-2_7) which gives a formula and might be helpful for the corona - I have to think of it. Do you think we could estimate all the parameters?  

---

## 1 answers

### Answer by username_4 on 2021-04-16. Score: 1

### 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](https://en.wikipedia.org/wiki/Stellar_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](https://link.springer.com/chapter/10.1007/978-1-4684-0724-2_7)*, 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](https://en.wikipedia.org/wiki/Complex_number).

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](https://www.britannica.com/science/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?](https://astronomy.stackexchange.com/questions/43429/typical-properties-of-the-corona-of-a-star?noredirect=1&lq=1)

### 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](http://dx.doi.org/10.1051/0004-6361/201425540)* could help us with $n\_e$.
* Bo Thidé: *[Radio Studies of Solar-Terrestrial Relationships](http://dx.doi.org/10.13140/RG.2.2.16990.54084)* 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](https://www.researchgate.net/publication/252439478_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?](https://astronomy.stackexchange.com/questions/16674/what-is-the-temperature-of-the-solar-atmosphere-the-corona-and-how-is-it-measu/)

> **Comments:**
> **username_5**: The solar corona is practically a collisionless plasma, so you can safely neglect the collision term here (even in the photosphere it should be negligible unless $\omega$ corresponds to radio waves).  

---

