Two-dimensional limiting current in crossed-field gap

摘要

The classical space-charge-limited (SCL) current or the Child-Langmuir (CL) law [1] continues to be an active area of research in the field of sheath physics, high-power vacuum microelectronics and accelerator physics. The 1D classical CL law is only extended to the multi-dimensional models, which is valid in the classical, weakly-relativistic and quantum regime, recently [2]. For crossed-field devices, where a transverse magnetic field is applied across the vacuum gap, the 1D CL law [J{sub}(cf)(1D)] for both the laminar flow (magnetic field B < B{sub}H Hull cut-off magnetic field) [3] and turbulent flow (B > B{sub}H) region [4] were reported more than a decade ago. However, as crossed-field microelectronic devices such as crossed-field amplifiers and magnetrons decrease in size, the gap spacing and the width (or radius) of emission becomes comparable and 2D effects cannot be ignored. Therefore, it would be important to take into account the 2D effect and obtain an analytical formulation to calculate the maximum CL current density that can be emitted from a finite 2D emission area, such as a 2D infinite strip, for a crossed-field gap.