# what is the relevance of ion cyclotron and ion collision frequency ratio

On earth, the ion cyclotron and ion collision frequency ratio is 1 at roughly 118 km, and this is used as one of the definitions of the limit to space.

What are ion cyclotron frequency and ion collision rate, and why is this relevant?

• Please add the [karman-line] tag. Thanks! Commented Aug 6, 2018 at 13:59
• Isn't the Karman Line a completely different edge-of-space definition? Commented Aug 6, 2018 at 20:46
• I've added a link, hope you don't mind. It's a good question! But I'm not sure what "What are those" means. Are you asking for explanations of what ion cyclotron frequency and ion collision frequency (rate) mean, or asking for other definitions of the "limit to space"?
– uhoh
Commented Aug 7, 2018 at 1:12
• I am asking about ion cyclotron/collision Commented Aug 7, 2018 at 4:49
• @sp2danny Thanks! Can you double check if my edit is correct? Since comments should be considered temporary, it's best to make clarifications permanent in the original post.
– uhoh
Commented Aug 7, 2018 at 7:51

Answer: Cyclotron and ion collision frequencies define the boundary between the Ionosphere and the Magnetosphere.

There is a continuum of decreasing gas density from Earth’s surface to space. So any boundary between layers of the atmosphere, or between atmosphere and space, must be arbitrary. Hopefully, these boundaries serve a useful purpose for those who defined them.

For instance, the Karman Line is useful for engineers because it sets an upper limit of altitude for aerodynamic lift. Although it is referred to as “the edge of space”, there is obviously atmosphere above it judging by the rapid decay of LEOs.

Another useful (but still arbitrary) line is the top of the Exosphere. This is the point where gas molecules are no longer gravitationally bound to Earth because the effects of solar radiation pressure exceed Earth’s gravity. Below the line, molecules follow ballistic trajectories and return to Earth. The upper Exosphere boundary is about 200,000km (half way to the moon).

Your question deals with the transition between the Ionosphere and the Magnetosphere. This is not the same as a definition of “the edge of space”. This transition is defined by the ratio of cyclotron frequency to ion collision frequency. This boundary is where these two quantities are equal, between 100 and 150km altitude.

The ion-neutral atomic oxygen collision frequency is the frequency of collisions between incoming ionic oxygen O+ and atmospheric neutral atomic oxygen. https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/93GL01699

The cyclotron frequency is the natural frequency of O+ ions spiraling around magnetic field lines in the Earth’s magnetic field.

At high altitude, incoming O+ ions have a long free path length as they spiral towards the Earth. But as they penetrate into the atmosphere, eventually the free path length shortens to the point where (on average) they make one turn of the spiral path before they collide with neutral oxygen.

So, just like the Karmen Line is useful to Engineers, the Magnetosphere/Ionosphere boundary is useful to Atmospheric Chemists.

It is interesting that all 3 of these arbitrary boundaries are defined by when totally unrelated quantities are equal:

• Karmen: aerodynamic lift = centrifugal force
• Exosphere: Solar pressure = gravitational force
• Ionosphere: Cyclotron frequency = Ion collision frequency