Relation between space charge limited current and power loss in open drift tubes

Abstract

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 c SCL ) 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 c SCL , 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 c SCL , 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.

Efficiency Enhancement of the Axial VIRCATOR

“…However, as J IN increases further, reflection begins to occur at a value (of J IN ) smaller than J c SCL . It has recently been shown that the lowering of J SCL in open drift tubes can be predicted reasonably well within the electrostatic framework by altering the boundary conditions to account for power loss [17]. The space-charge-limited current for open drift tubes can be expressed as [17] …”

“…Its oscillations (in position and magnitude of potential) result in a high-frequency component in the output power [17]. The geometry of the open drift tube decides the frequency range in which the drift tube can be considered "open" to electromagnetic radiation.…”

“…Our strategy for improving the efficiency of the axial VIRCATOR is based on a recent result for open drift tubes [17]. A drift tube can be considered open at a given frequency if electromagnetic radiation can leak out.…”

Response to “Comment on ‘Relation between space charge limited current and power loss in open drift tubes' ” [Phys Plasmas 14, 094705 (2007)]

“…Using these inputs, an estimate of the radiated power due to space-charge forces is found to be 10% of the injected power for the system considered in Ref. 1. The figure, though not exact, 8 shows that the radiated power is far from being negligible.…”

“…Moreover, the use of the impedance in evaluating the power loss while at the same time stating that "electromagnetic effects are not expected to play a key role" is in itself contradictory. 1 Further, a frequency analysis of the radiative power loss showed 1 that when the injected current exceeds the space-charge limit, the radiation, in addition to the low-frequency component, also contains the virtual cathode oscillation frequency.…”