Characteristic Radiation - $K_{\alpha}$, ... ; but no $K_{\gamma}$ While studying the characteristic spectra of x-rays I came across one question that lets me doubt that I have fully understood what is going on. 
The $K_{\alpha}$ line is due to inner orbital electrons being ejected from the K-shell of the atoms by the x-ray source. The place is then filled by an electron from the L-shell. Since the energy in the L-shell is higher than in the K-shell, a photon is emitted with the energy $\Delta E=\hbar\omega$. This process corresponds to the $K_{\alpha}$ line.
Analogously for the $K_{\beta}$ line. 
So from my understanding a $K_{\gamma}$ (and so on) should also exist, but I couldn't find anything about this.
Is this simply due to the low probability of this transition so one cannot observe it, because its intensity is lower than the Bremsstrahlungs spectrum?  
 A: Here is a spectrum from a tungsten x-ray tube:

One sees the strong W K$_{\alpha 1}$ and K$_{\alpha 2}$ lines. The W K$_{\beta}$ line is also labeled. The K$_{\gamma}$ line is not labeled but visible. Its energy is about 2 keV higher than K$_{\beta}.$ These transitions involve the N shell.
One sees why K$_{\gamma}$ is not usually mentioned. In electron-induced x-ray spectra, it is weaker than the Bremsstrahlung background. If one wants to study the spectrum (for example to study the $4p$ bands of iron or copper), one uses x-ray excitation.
A: In addition to the probability of a gamma transition being much lower, there is also a factor of practicality. For a K-gamma transition to occur an electron must be ejected from the K-shell (principle quantum number = 1), then an electron from the N-shell (principle quantum number = 4) must drop down to fill the vacancy. This means the element must have electrons in the N-shell. For elements which have electrons in the N-shell, the energy required to eject an electron from the K-shell is very high. For these elements, it is often more pragmatic to characterize them by their L or M series lines since lower energy X-rays are needed.
