Relation between space charge limited current and power loss in open   drift tubes
  Drift space is a region free from externally applied fields. It is an important part of many devices involving charged particle beams. The space charge effect imposes a limit on the current that can be transported through a drift space. A reasonable estimate of the space charge limited current density (J_{SCL}^{c}) in 'closed' drift tubes can be obtained from electrostatic considerations despite the fact that charge particle transport results in electromagnetic radiation. We deal here with the situation where the drift tube is 'open' to electromagnetic radiation, for instance due to the presence of a dielectric window. In such cases, electromagnetic radiation leaks out of the window which results in a decrease in the average kinetic energy of electrons. If the injected current density is much lower than J_{SCL}^{c}, power loss does not result in a change in the transmitted current. As the injected current density is increased, power loss increases and at a critical value lower than J_{SCL}^{c}, reflection of electrons begins to occur. We also show that the lowering of the space charge limited current on account of power loss can be incorporated in the standard electrostatic picture by introducing an effective voltage for the collection plate. 
Debabrata Biswas and Raghwendra Kumar