Measurement of transverse velocity in electron beams emitted from axisymmetric electrode systems

Some general relations are derived for the transverse momentum and angular velocity of electrons and their guiding centres in axisymmetric systems with a radial electric field. Two methods are described for measurement of the transverse velocity of electrons ejected from a coaxial electrode system. The first method uses observations of the magnetic fields at which the outermost and innermost electrons are intercepted by an anode; a modified form of the trajectory equations of Kino and Taylor is then used to estimate the behaviour of the electron beam under operating conditions. The second method deduces the transverse velocity of electrons at any axial position at which the radial electric field is small, from observation of the maximum magnetic field which permits current to reach the collector. The potential depression and axial velocity for the desired operating conditions can also be deduced.