Coherent Transition Radiation (CTR)
Transition radiation (TR) generated by electron beams is a common tool for transverse and longitudinal beam diagnostics. The simple treatment of TR is possible by method of virtual quanta. As the beam passes through the media interface, the field of the beam is reflected, in the form of transition radiation. For a single electron crossing a perfect conductor boundary at 45 deg angle, the TR spectral angular fluence at small angle is given by:
The radiation is peaked at the 1/gamma openning angle, to reflect the difference in velocity between the virtual photons of electric field and the real photons. The single electron TR spectrum depends on the media dispersive properties; and for a metal, the spectrum is flat, until deep UV.
The macro-field of an electron beam also gets reflected from a perfect
conductor surface as a Coherent Transition Radiation (CTR). CTR
properties are quite different from the incoherent TR. For an
ultrarelativistic electron beam one can find:
,
where I(w) is a Fourier transform of the electron beam current. The term with the Bessel function is a spatial coherence factor which significantly differes from unity only for the small wavelengths (i.e. in the case of microbunching measurements). The current term reflects the beam longitudinal profile information, and is responsible for the CTR spectral distribution cut-off at the wavelengths of the order of bunch length. Hence, from the direct spectral or temporal measurement of the CTR signal one can extract electron beam bunch length information.
Follow the menu on the left; for information on the CTR spectral measurments, temporal measurements with the CTR interferometer; and, also, electron beam microbunching diagnostics based on the CTR.