Microwave Breakdown Calculator
In ordinary experience, air is transparent to electromagnetic waves at microwave frequencies. This is because field strengths are low in most situations. Home microwaves occasionally illustrate what happens at higher field strengths: Air breaks down into a plasma that absorbs and reflects microwaves.
In clean dry air that is far from surfaces, flames, shockwaves, radioactive decay or UV light, the free electrons that seed breakdown are generated by cosmic rays that continually shower the Earth from space. Though free electrons only last nanoseconds to microseconds in the lower atmosphere (< 36 km), cosmic rays generate them often enough to initiate breakdown almost as soon as an electromagnetic beam reaches a critical intensity. At this critical intensity and beyond it, the electric field of the beam accelerates the free electrons, enough that each collision with an air molecule results in (statistically) enough free electrons to replace those that recombine with oppositely charged ions, or attach to neutral molecules to form negative ions. The ensuing avalanche ionizes neutral air into microwave-absorbing plasma within a microsecond.
This model implements the equations of Guo-Zhi, Liu, et al. “A study of high power microwave air breakdown.” Chinese Physics 9.10 (2000): 757 to estimate the intensity at which clean dry air begins to break down into a plasma, and also the intensity at which it breaks down no further (because the plasma begins to reflect the incident beam as its ionization increases, thus limiting the incident beam’s intensity). MacDonald (1966) gives a more general account of microwave breakdown in gases.
Press ⏎ to see the model. Try your own inputs or the examples below. Refresh your browser to clear results.
Example: Breakdown over a range of altitudes and frequencies
The model can be used to generate plots of how breakdown and reflection thresholds vary with altitude and frequency.
- Plotting is started by specifying how many plots to calculate on each axis: To specify 100 points, type
plo.n = 100 «enter»
- Once calculations have finished (this may take a few seconds), press «enter» again to show the top-level variables. Plot(f,h) is the plot object, and its description should now be a hyperlink to an SVG file. Clicking this hyperlink opens a new browser window containing the plots that were just generated. If any relevant changes are made to the input values, then the plots are automatically recalculated (pressing the browser’s refresh button in the plots’ window updates the plots).
- Elements of the plots can be moved around to improve appearance. Clicking the ‘save’ button in the upper right corner of the browser’s window saves the plots as an SVG file.