Multipaction is an effect that occurs with RF fields, usually in a vacuum or low pressure condition. Essentially it results from an ion moving back and forth (in response to an RF field) and knocking other electrons off the sides when it hits. If the transit time of the electron is nicely synchronized with the RF field, then just as it hits, the field is right to pull the new electrons towards the other side, and a cascading avalanche can result (if the electron emission coefficient (greek lower case delta) is >1). The table below gives values for clean, outgassed surfaces. Bear in mind that without special cleaning, surfaces can have a delta as high as 4.
|
Secondary Electron Coefficient
|
|||
|---|---|---|---|
|
Metal
|
d (electrons per incident electron)
|
Electron Energy at deltamax
(eV) |
Electron Energy for delta=1
(eV) |
| Al | 1.9 | 220 | 35 |
| Au | 1.1 | 330 | 160 |
| Cu | 1.3 | 240 | 100 |
| Fe | 1.3 | 350 | 120 |
| Mo | 1.3 | 360 | 120 |
| Ni | 1.3 | 460 | 160 |
| W | 1.45 | 700 | 200 |
As the number of electrons bouncing back and forth grows, the current can increase to the point where a hot spot forms on the cavity wall, increasing outgassing, melting the wall, evaporating material, and all manner of "bad things."
A bunch of math will result in a handy equation, often referred to as the multipactoring threshold:
Vo = (2*pi*d/lambda)^2 * (me*c^2)/(pi*e)
where:
Vo is the voltage between the sides of the cavity
me= mass of electron
lambda = wavelength
d = spacing between walls
c = speed of light (3E8 m/sec)
e = charge on an electron
The secondary electron emission actually goes down as the electron energy rises over the peak, so breakdown can sometimes be avoided by rapidly raising the RF power (as in a pulsed radar system, for instance).
If the pressure is high, then the electron will likely hit another gas molecule or atom before hitting the other side, so multipaction is less likely. Therefore, the mean free path would need to be on the order of the spacing for multipaction to occur.
Interestingly, aluminum seems to have a really high secondary emission coefficient, a good reason for plating it with something else in a waveguide intended for use in vacuum.