On the distribution function of electron spectra from hot laser plasmas

The emission of electrons from hot plasmas generated in the interaction of ultra-short (and ultra-high intensity) laser pulses with matter is often characterized by the so-called ‘hot electron temperature’. In this article it is shown that this number is not unambiguous. The reason is the following: to assign a temperature to an electron spectrum, it is necessary to describe the spectrum with a distribution function. However, different types of distribution functions are in use, e.g. the Boltzmann or Maxwell distribution, leading to different electron temperatures in spite of providing nearly the same form of the electron spectrum. For this reason, the main characteristics of all these distribution functions are presented in this article and compared. Depending on the distribution function used, the value of the hot electron temperature varies by up to 30% and in extreme cases by more than a factor of four. This fact should always be kept in mind when comparing values of hot electron temperatures. In addition, the reasons for using equilibrium distributions to describe the characteristics of laser-produced electrons—although probably no thermodynamic equilibrium is prevailing—are discussed.