This paper reviews the history of multipactor discharge theory, focusing on recent models of multipactor accessibility and saturation. Two cases are treated in detail: That of a first-order, two-surface multipactor, and that of a single-surface multipactor on a dielectric. In both cases, susceptibility curves are constructed to indicate the regions of external parameter space where multipactor is likely to occur, taking into account the dependence on surface materials, and the effects of space charge and cavity loading. In the case of a dielectric, multipactor is found to deliver about 1% of the rf power to the surface. The two cases are contrasted in light of experimental observations.

Recent experiments at the University of Maryland using photoemission from a dispenser cathode have yielded some interesting results regarding the effects of the area of emission and of the ratio between the pulse length and the gap transit time on the amount of current that may be drawn from an electron gun before a virtual cathode forms. The experiments show that a much higher current density may be drawn from a short pulse or limited emitter area than is anticipated by the Child-Langmuir limiting current. There is also evidence that the current may be increased even after virtual cathode formation, which leads a distinction between a limiting current density and a current density critical for virtual cathode formation. The experiments have also yielded some interesting results on the longitudinal structure of the current pulse passed through the anode. Some empirical and theoretical scaling laws regarding the formation of virtual cathodes in an electron gun will be presented. This work was motivated by the needs of the University of Maryland Electron Ring ͑UMER͒ ͓P. G. O'Shea, M. Reiser, R. A. Kishek et al., Nucl. Instrum. Methods Phys. Res. A 464, 646 ͑2001͔͒ where the goal is to generate pulses that are well-localized in time and space.

The Child-Langmuir Law (CL), discovered a century ago, gives the maximum current that can be transported across a planar diode in the steady state. As a quintessential example of the impact of space charge shielding near a charged surface, it is central to the studies of high current diodes, such as high power microwave sources, vacuum microelectronics, electron and ion sources, and high current drivers used in high energy density physics experiments. CL remains a touchstone of fundamental sheath physics, including contemporary studies of nanoscale quantum diodes and nano gap based plasmonic devices. Its solid state analog is the Mott-Gurney law, governing the maximum charge injection in solids, such as organic materials and other dielectrics, which is important to energy devices, such as solar cells and light emitting diodes. This paper reviews the important advances in the physics of diodes since the discovery of CL, including virtual cathode formation and extension of CL to multiple dimensions, to the quantum regime, and to ultrafast processes. We review the influence of magnetic fields, multiple species in bipolar flow, electromagnetic and time dependent effects in both short pulse and high frequency THz limits, and single electron regimes. Transitions from various emission mechanisms (thermionic-, field-, and photoemission) to the space charge limited state (CL) will be addressed, especially highlighting the important simulation and experimental developments in selected contemporary areas of study. We stress the fundamental physical links between the physics of beams to limiting currents in other areas, such as low temperature plasmas, laser plasmas, and space propulsion.

We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.

This Perspective reviews the fundamental physics of space–charge interactions that are important in various media: vacuum gap, air gap, liquids, and solids including quantum materials. It outlines the critical and recent developments since a previous review paper on diode physics [Zhang et al. Appl. Phys. Rev. 4, 011304 (2017)] with particular emphasis on various theoretical aspects of the space–charge limited current (SCLC) model: physics at the nano-scale, time-dependent, and transient behaviors; higher-dimensional models; and transitions between electron emission mechanisms and material properties. While many studies focus on steady-state SCLC, the increasing importance of fast-rise time electric pulses, high frequency microwave and terahertz sources, and ultrafast lasers has motivated theoretical investigations in time-dependent SCLC. We particularly focus on recent studies in discrete particle effects, temporal phenomena, time-dependent photoemission to SCLC, and AC beam loading. Due to the reduction in the physical size and complicated geometries, we report recent studies in multi-dimensional SCLC, including finite particle effects, protrusive SCLC, novel techniques for exotic geometries, and fractional models. Due to the importance of using SCLC models in determining the mobility of organic materials, this paper shows the transition of the SCLC model between classical bulk solids and recent two-dimensional (2D) Dirac materials. Next, we describe some selected applications of SCLC in nanodiodes, including nanoscale vacuum-channel transistors, microplasma transistors, thermionic energy converters, and multipactor. Finally, we conclude by highlighting future directions in theoretical modeling and applications of SCLC.