Bremsstrahung radiation?

Yep, the background is bremsstrahlung (the "spikes" in that image are characteristic radiation).

The reason it has a maximum is this: as you know, bremsstrahlung is produced by the decceleration of charged particles as they interact with electric fields. There is a certain range of energies that are most likely under a given set of conditions. In general, most incoming particles will lose most, but not quite all, of their energy in the first collision or two (hence the maximum at short wavelengths) before undergoing some other interaction.

A very small percentage will lose all of it, and likewise a small number will lose only a small fraction before moving on- there's no upper limit on the wavelength that can be emitted (an incident electron can lose an arbitrarily small amount of energy), hence the tail extending to infinity. There is a sharp cutoff at shorter wavelengths, as the electron can never lose more energy than it had to begin with.