Space Charge Limited Field Emission Research Articles

Advanced space charge limited field emission cathodes.

Several novel field emission cathodes are constructed by attaching a variety of materials to a steel substrate using multiple methods of bonding. These cathodes are tested using a pulsed relativistic (350-550kV) vircator in a space charge limited operating regime. The viability of these cathodes as advanced or alternative components in high power microwave systems is evaluated. The currents measured from the cathodes are compared to values predicted from a 3D space charge limited flow model. The performance of the cathode is determined by how the current deviates from the model, as well as the consistency and durability.

A relativistic self-consistent model for studying enhancement of space charge limited field emission due to counter-streaming ions

Recently, field emission has attracted increasing attention despite the practical limitation that field emitters operate below the Child-Langmuir space charge limit. By introducing counter-streaming ion flow to neutralize the electron charge density, the space charge limited field emission (SCLFE) current can be dramatically enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of SCLFE by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a benchmark or comparison for verification of simulation codes, as well as extension to higher dimensions.

Modeling electron flow produced by a three-dimensional spatially periodic field emitter

We study the space charge limited field emission from an emitter whose surface has a simple periodic structure with bumps. The shape of each bump is represented by a smooth function and the emission is governed by the Fowler–Nordheim–Schottky law. A mathematical scheme for modeling the potential and current structure by a set of elementary functions is developed and implemented numerically with the help of a special least square procedure. Our results show that such emitters are more efficient than emitters with long ridges only in weak electric fields. In stronger fields the latter give larger currents and they should be more durable. The emission by an individual bump in our periodic structure is compared also with that of a single emitter bump of the same shape, they appear to be quite close.

Solution for space charge limited field emission current densities with injection velocity and geometric effects corrections

When particles are injected according to the Fowler–Nordheim (FN) field emission equation, the transmitted current density will transition to the space charge limited (SCL) current density, with increasing applied diode voltage. The actual transmitted current density is the so-called SCL-FN current density. In this work, Barbour’s analytic solution for the SCL-FN current density is modified with consideration of injection velocity and also geometric effects, by solving the advanced FN equation with the effective field enhancement factor, the energy conservation equation with an initial velocity term, and Poisson’s equation simultaneously. The solution is also extended to the relativistic regime where similar transition process is found. This solution has been verified using particle-in-cell simulation with varying diode voltage, electron injection velocity, and field enhancement factor.

Field emission and field ionization in liquid 4 he

Spacecharge limited field emission and field ionization currents in liquid 4 He have been investigated for emitter potentials V s , temperatures T , and pressures p in the ranges 0 < |V s | < 3500V, 0.3 < T < 5 K, 1 < p < 25 × 105 Pa, respectively. In each case, for constant p and V s , the current i passes through a maximum at a temperature V max near 1.5 K. For T > T max it is possible to account for the characteristics on the basis of a simple theory which does not require a detailed knowledge of the current generating mechanisms, and which enables values of the ionic mobilities μ ± to be deduced from the data. The rapid decrease in i below T max is ascribed to a process in which ions become trapped on quantized vortices and subsequently escape again. A model is developed to enable values of the ionic escape probabilities to be derived from the experimental results. It was found that the current becomes temperature independent below 0.4 K. The low temperature i(V8) characteristics suggest that an effective mobility can be defined to describe ionic motion through a self generated vortex tangle. The negative ion current for T < 0.9 K showed a rapid increase with pressure for p > 10 6 Pa. This behaviour is ascribed to the presence of an increasing proportion of free ions travelling at the Landau velocity, owing to a decrease with p of the vortex nucleation probability v ; and a model is developed to enable values of v to be deduced from the experimental data. The conduction mechanism below 0.7 K is discussed, but is not understood in detail. It is inferred that Vinen’s F 2 parameter becomes temperature independent below 0.4 K.

Space charge limited field emission in a plane parallel electrode geometry

Poisson's equation in parallel geometry is solved analytically with the inclusion of the electron emission velocity spectrum predicted by quantum mechanics. The mathematical difficulty of classically defining the cathode surface is overcome, to a first approximation, by postulating a virtual cathode situated in front of the real cathode such that the majority of the emitted electrons have penetrated the potential barrier at that position. The treatment is nonrelativistic, assumes that the emission is exclusively by barrier penetration, and is expressed in parameters that enable the results to be applied to most situations of interest. It is shown that the effect of nonzero emission velocity is negligible except for the cases of cathodes of low work function operated at very high current densities. Particular attention is paid to the departure of the experimentally measured current from that predicted by the Fowler-Nordheim theory and the subsequent approach to the Langmuir-Child fully space charge limited current. It is shown that the point of departure can quantitatively be defined in terms of the fully limited current and the bearing of this on the design of field emission electron guns is considered.

Noise in space charge limited field emission devices

The noise suppression in space charge limited field emitter cathodes is calculated, and it is shown that the noise can be more strongly space charge suppressed than in thermionic cathodes. The velocity fluctuation noise of the field emitter cathode is also calculated under arbitrary space charge conditions. The results are used to evaluate the noise figure of traveling wave tubes. Low noise figures are possible if the noise suppression of the space charge limited field emitter remains intact at microwave frequencies.