Radiation Emission Involving Free Electrons

The emission of radiation is one of the most important tools for diagnosing conditions in plasmas and can play a significant role in moving energy. For plasmas at all but the highest densities, we can assume that electrons are either in bound quantum states with energies dominated by the central potential of ionic nuclei, or they are unbound, occupying a continuum of free-electron states. We have seen that free electrons do not really occupy a true energy continuum (see Section 1.3), but a free electron means that the density per unit energy of quantum states is high, so that we can often consider the free-electron energies as continuous. Radiation arising from free electrons dominates in low atomic number plasmas. Radiation transition probabilities scale rapidly with increasing atomic number: for example, as Z 4 for hydrogen-like ions, while radiation for free-electron transitions scales at a lesser rate proportional to Z 2 (see Section 5.2). In complete thermal equilibrium with the radiation field in equilibrium with particle temperatures, the emission of radiation is given by the Planck black-body formulas derived in Chapter 4. However, complete thermal equilibrium is rare in laboratory plasmas and the more tenuous astrophysical plasmas as radiation absorption within the dimensions of the plasmas is small. We consider the radiation processes involving free electrons in this chapter. A full quantum mechanics understanding is generally not required to model emission from free electrons, so we discuss the emission of radiation in this chapter using largely classical non-quantum treatments. The Bohr model for bound energy states is utilised in considering emission from an electron making a transition from a free to bound state. Cyclotron Radiation Astrophysical plasmas such as those near a neutron star have strong embedded magnetic fields and even in interstellar space there is a weak magnetic field (≈ 10−10 Tesla). The plasmas studied in magnetic fusion research have magnetic fields in the range 0.1 –10 Tesla confining the plasma. Confinement works as charged particles orbit with helical-shaped trajectories around an imposed magnetic field B0 .