X-ray studies of various shapes of electron-velocity distribution functions and of electron confinement affected by kilovolt-range electrostatic potentials

Several types of x-ray diagnostics, such as x-ray energy spectrum analyses, x-ray absorption methods, and x-ray tomographic reconstructions using various types of x-ray detectors (i.e., a Si(Li), a pure Ge, a NaI(Tl), Si surface-barrier detectors, as well as microchannel plates) have been employed for obtaining various shapes of electron-velocity distribution functions as well as their spatial profiles: (i) a plateau-shaped electron-velocity distribution function in the plug region, supporting a scaling theory between thermal-barrier potentials and ion-confining potentials (Cohen's strong electron-cyclotron heating theory); (ii) mirror-trapped 60-keV relativistic Maxwellian electrons in the thermal-barrier region; and (iii) two-component Maxwellian electrons in the central cell have been observed in the tandem-mirror GAMMA 10. During experiments with thermal barriers, it has been observed that the bulk-electron temperature and its evolution with time in the central cell are quite different from the electron energy and its temporal evolution in the plug region. These differences as well as the different shape of the electron-velocity distribution function in each region have clearly demonstrated the existence of a thermal-isolation effect due to the thermal barriers between the central cell and the plug region. X-ray tomography data in these three regions have shown good axisymmetric radial profiles peaked on the magnetic axis; this axisymmetric shape is useful for reducing nonambipolar radial particle losses. Furthermore, the validity of the Pastukhov theory for electron-energy confinement that is enhanced due to the formation of thermal-barrier potentials has been demonstrated using the electron-energy balance analyses. These data have represented a good electron-energy confinement capability due to the formation of thermal barriers.