Thermo-field Electron Emission Research Articles

Thermal effects in field electron emission from idealized arrangements of independent and interacting micro-protrusions

Modelling studies of thermo-field electron emission (TFE) from protrusions at a cathode surface usually use simulations in 2D axial symmetry. Indeed, time-dependent simulations in 3D are very demanding in computation time. Often, 3D simulations have been restricted to stationary pure field electron emission to account for the drastic current decrease caused by electric field screening when the emitters are close. Little interest has therefore been granted to the heat exchanges occurring between nearby emitters. Although the temperature is a second-order parameter in TFE compared to the electric field, thermal effects become non-negligible in high current density regimes, where self-heating is well established. The present study focuses on the thermal effects occurring during the TFE from micro-protrusions. Our model considers a DC voltage but solves in time the temperature evolution coupling the heat equation and the current continuity equation. The protrusions are modelled as hemiellipsoids with 2D axial symmetry. Emission enhancement due to the increase of the temperature in the thermo-field regime compared to the pure field regime is detailed as a test case for isolated protrusions. Then, full 3D simulations are used to investigate the thermal coupling between multiple neighbouring protrusions via their outwards heat fluxes inside the cathode. The results show a higher current increase due to thermal coupling for dome-like protrusions with a low field enhancement factor. The current increases up to 13% of the total current for aspect ratios of 1, but this value is reached for an extreme applied electric field, hardly reachable in experiments. For sharper protrusions with higher field enhancement, the interaction range through the cathode being shorter, the thermal coupling is suppressed by electrostatic screening. Nevertheless, in arrangements of densely distributed field emitter, when the screening is compensated by a higher voltage, our model predicts the possibility of a moderate but noticeable thermal coupling even for sharp protrusions: a parametric study indicates up to 14.5% of the emitted current being caused by a thermal coupling through the cathode bulk, for protrusions with an aspect ratio of 10 under a fixed applied electric field of 0.4 GV m−1 in DC mode.

Kinetic analysis of direct-current driven microdischarges with thermo-field electron emission at atmospheric pressure

Recent studies have shown that thermo-field emission is a dominating electron source of microdischarges at cathode temperatures far above room temperature. However, little research has focused on the post-breakdown nature of microdischarges. In order to explore the post-breakdown characteristics of thermo-field emission-driven microplasms, a one-dimensional implicit particle-in-cell with Monte Carlo collision method is adopted and updated by using thermo-field electron emission to investigate the kinetic characteristics of direct-current argon microdischarges at atmospheric pressure. The fundamental properties of microplasmas, such as electric field, particle number density, averaged particle temperature and current density are analyzed in the post-breakdown regime. In addition, sheath behavior is investigated to further observe how the space charge affects the thermo-field emission. The results indicate that thermo-field emission-driven micro-scale discharges can produce high current density and high-energy particles with a low applied voltage of 20 V. The impact of cathode temperature on enhancing the thermo-field emission is more pronounced, compared to the applied voltage and the electrode spacing. The electron energy probability function shows a multi-peak distribution.

Об электронной эмиссии из фокальной области симметрично сходящейся поверхностной плазмонной волны на свободной поверхности металлической пленки

Based on the theory of reflection of a plane electromagnetic wave from a plane-layered structure, the excitation and focusing of a radially converging surface plasmon wave on the free surface of a gold film in the Kretschmann scheme are considered. The distribution of the electric field in the vicinity of the focus on the free surface of the film is quantitatively studied. Based on this distribution and the theory of thermofield electron emission from a metal, the time averaged current of electron emission is estimated depending on the amplitude of the normal component of the electric field of the wave at the center of the focal distribution. It was shown that the main part of the emission current comes from a region around the focus center with a diameter of the order of a tenth of the working wavelength in vacuum, and a negligible part of the emission current comes from surrounding the central maximum of the diffraction rings.

Two-dimensional particle simulation on the behavior of multi-charged copper ions in the cathode spot of a pulsed vacuum arc discharge

The behavior of multicharged ions in the cathode spot of pulsed copper vacuum arc is studied by the 2D3V electrostatic Particle-In-Cell Direct Simulation Monte Carlo method. This method tracks the position and velocity of electrons, neutrals, and copper ions charged from +1 to +4 simultaneously, which couples with external circuit physics as well as heat conduction at the cathode. The general thermofield electron emission developed in recent years is used in the vacuum arc simulation. The simulation starts from complete vacuum until the arc current reaches the steady state at about 3 A limited by the external circuit, and the arc voltage is between 20 and 30 V. During the discharge, the cathode temperature increases from room temperature to around 8000 K. The breakdown process is visualized by the distribution of ion density at different stages of arc discharge: from a small volume of cathode spot to a conductive current path between electrode gaps. The vacuum arc plasma is found to be highly ionized, with an average charge state slightly above two and electron density on the order of 1020 cm−3. The positively charged ions move in the direction from the cathode to anode, which is opposite to the direction of the applied external field. Ion energies at the steady state increase from 20 to 200 eV when charge states increase from +1 to +4. This indicates that the electrostatic acceleration of ions is caused by a dynamic space-charge field in the breakdown process of pulsed vacuum arc discharge.

Influence of the Thermo-Field Electron Emission from the Cathode with a Thin Insulating Film on the Film Emission Efficiency and Ignition Voltage of the Townsend Gas Discharge

A model of the thermo-field electron emission from the metal cathode with a thin insulating surface film at temperatures of 200–400 K is developed. An expression for the film emission efficiency in the gas discharge is obtained. The efficiency is equal to the fraction of electrons emitted into the film from the metal substrate, which enter the discharge volume and increase the effective secondary-electron emission yield of the cathode. It is shown that the thermo-field mechanism of electron emission influences noticeably the ignition voltage of the low-current discharge with such cathode at rather low temperatures exceeding the room temperature by less than 100 K.

Kinetic Model of Short Vacuum Arc With Hot Evaporating Anode

A kinetic 1-D model of an ultrashort (10 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> ) vacuum arc was developed to research the vacuum arc near-anode region and the influence of anode plasma on the cathode attachment self-consistently. The kinetic model is a model of 1D3V particle-in-cell and direct simulation Monte Carlo type. The model takes into account the main types of elastic and inelastic collisions of particles in the plasma as well as evaporation and thermofield electron emission from both of the electrodes. The model has three task parameters: cathode temperature, anode temperature, and voltage drop applied to the gap. The plasma state in the gap, current density, and energy flux density to the electrodes are the outcome of the model. The calculations have shown that the anode temperature variation strongly influences both the plasma column parameters and the cathode attachment. It was shown that, at the ratio <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{a}/T_{c} \sim 1$</tex> </formula> (with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$T_{a}$</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> $T_{c}$</tex></formula> being the anode and cathode temperatures, respectively), the plasma in the gap changes the direction of motion.

Kinetic Modeling of Initiation of Explosion Center on Cathode Under Dense Plasma

A kinetic 1-D spherically symmetric model of heating of microprotrusion (with a curvature radius of 1 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> ) on the cathode under dense plasma is developed. The kinetic model is a model of 1D3V PIC/DSMC type. The model takes into account the main types of elastic and inelastic collisions of particles in the plasma as well as evaporation and thermofield electron emission from the cathode. The surrounding plasma parameters in the model are fixed on the boundary placed at a certain distance from the microprotrusion. The applied voltage drop is also fixed on the same boundary. The further evolutions of the plasma, current, and cathode temperature are calculated self-consistently taking into account the influence of the plasma generated during the process. The calculations have shown that, under the certain condition, thermal runaway is developed and the cathode surface temperature reaches the critical one. However, this instability is not caused by microprotrusion Joule heating because the current density is comparatively small <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$(&lt;10^{8}\ \hbox{A}/\hbox{cm}^{2})$</tex></formula> at that moment.

Modeling of Cathode Plasma Flare Expansion

A kinetic 1-D model of cathode plasma flare expansion to the interelectrode vacuum gap was developed. The kinetic model is a model of 1D3V particle-in-cell and direct simulation Monte Carlo type. The model takes into account the main types of elastic and inelastic collisions of particles in the plasma as well as evaporation and thermofield electron emission from the cathode. The model treats the plasma flare expansion and the electron emission from the outer plasma boundary of the flare self-consistently. The plasma characteristics of the cathode flare obtained with the model are in a reasonable agreement with known experimental results.

Kinetic Modeling of Heating of Metal Microdroplet by Surrounding Plasma

A kinetic 1-D spherically symmetric model of heating of metal microdroplet (with a radius of 1–2 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu \hbox{m}$</tex></formula> ) by surrounding plasma was developed. The kinetic model is a model of 1D3V particle-in-cell/direct simulation Monte Carlo type. The model describes thermo-field electron emission and evaporation from the droplet surface and correspondent plasma creation. The droplet heating is self-consistently modeled, taking into account the influence of the plasma generated during the process. The calculations have shown that, beginning from the certain surface temperature, the droplet is heated mostly by electron flux from the plasma. A certain kind of thermal instability takes place in the developed model. Beginning from the certain value, the droplet surface temperature hyperbolically grows and reaches the critical temperature; after that, the calculation is stopped because of model restrictions.

On thermofield electron emission from metal microtips

The electric field in the vicinity of a cone apex has an integrable singularity. Therefore, in order to calculate the thermofield emission current from a conical tip, it is necessary to find the emission current density at extremely high electric fields at the cone apex. In this paper, an original method for correctly calculating the electric field near a perfect conical tip and a tip with a rounded apex is proposed. A universal numerical approach to calculating thermionic, field, and thermofield electron emission from metal in a wide range of surface electric fields is offered. It is shown that, at high electric fields, the thermofield current density tends to a certain limiting (saturated) value, and the reason for this saturation is revealed. It is found that, for moderate fields, the total electron emission current from a conical tip is determined by the current from the immediate vicinity of the apex and depends substantially on the curvature radius of its rounding.

A mechanism that triggers double arcing during plasma arc cutting

Double arcing (DA) is a phenomenon when a transferred arc, flowing inside an electrically insulated nozzle, breaks into two separate arcs: one that connects the cathode and the nozzle and another that connects the nozzle and a work-piece. It is a commonly accepted opinion that the reason for DA is high voltage drop in the plasma inside the nozzle. However, the specific mechanism that triggers the DA development is not clear. In this paper, we propose such a mechanism. Dielectric films deposited inside the nozzle's orifice play the key role in this mechanism. These films are charged by ion current from plasma. A strong electric field is created inside the film and at the boundary of the film and clean metal of the nozzle. This gives rise to a thermo-field electron emission from the clean metal that borders the film. Emitted electrons are accelerated at the voltage drop between the nozzle and plasma. These electrons produce extra ions, which in turn move back to the film and additionally charge it. This sequence of events leads to explosive instability if the voltage drop inside the nozzle is high enough. Experiments to check the proposed mechanism are suggested.

Erosion of carbon arc cathodes operating in the thermo-field electron emission mode

Steady-state modelling and experimental results are given on the electric arc attachment on cold carbon cathodes working at low pressure. The modelling results are compared with the case of copper cathodes and with experimental data on vacuum arc erosion characteristics for graphite materials. A region of existence of a physically meaningful solution for self-sustained operation of the steady-state cathode spot is given in the electron temperature–cathode spot plasma pressure space. A solution domain comprised between Te ≈ 1.2–1.5 eV and p≈ 2–45 atm corresponding to carbon surface temperatures in the range 4200–4900 K is found. Values of the local heat flux to the cathode surface are evaluated in the range 1–20 × 1010 W m−2, and ratios of the various contributions to this flux and current density are given. Also given are the cathode spot radii and upper/lower limits for the erosion rate through vapourization, these being compared with experimental data. It is shown that the cathode spot pressure conditions can provide a mechanism for the control of macroparticle emission on carbon. This effect is used experimentally through cathode spot plasma confinement for the reduction of the microdroplet emission in arc sources used for diamondlike film deposition. Experimental data obtained on graphite materials are in agreement with the model-based design guidelines.

Numerical modeling of thermal response of thermofield electron emission leading to explosive electron emission

This paper gives a numerical model to deal with the thermal effect of field-induced thermal-assisted current passing through the microprotrusion on the cathode surface of a planar high-voltage vacuum diode. The model of protrusion is based on a one-dimensional truncated cone, whose physical and thermal properties have been assumed temperature dependent. The influences of space charge effect and Nottingham effect are included. According to the simulations, the delay times of explosive electron emission of cathodes made of different materials are given and compared with the experimental results, which seems to be in agreement.

Simple algorithm to calculate T-F electron emission current density

The Gauss-Chebyshev quadrature formula is suggested to calculate the transparency of the potential barrier at the metal-vacuum boundary. It is shown that in the most interesting cases ONE node is enough to obtain accuracy of a few percent when calculating thermo-field electron emission current density.

Calculation of calorimetric effect of thermo-field electron emission

The aim of the calculation presented in this report is to get more data about the specific calorimetric effect, e.g. the cathode cooling or heating per electron, of thermo-field electron emission from metals over wide ranges of work functions, e/spl phi/=2.0 to 4.5 eV, electron temperatures T/sub c/=2000 to 4500 K, and electric field strengths F=10/sup 6/ to 10/sup 8/ Vcm/sup -1/. For metals such as Cu, Nb, Mo, and W, most commonly used in vacuum electron discharge devices, the temperature range has been further expanded up to 500 to 10000 K.

Arc spot ignition caused by sheath instability

The transition from the stationary and homogeneous state of the collision-free space charge sheath between plasma and wall to a strongly inhomogeneous and instationary state with are spots is initiated by local enhancement of power supply from the plasma, connected with increasing electron emission. The general relations between surface emissivity, net current density, sheath potential, and power density in such "active" boundary layers are derived, taking the feedback of emitted electrons on the plasma parameters into account, as far as necessary. Joule heat generation is taken into account. The decisive effect of the transition is the rapidly increasing yield of thermo-field electron emission. Conditions and possible paths to sheath instability and arc spot formation are discussed.

Current-voltage characteristic of quantum-well heterostructures

The current-voltage characteristic (CVC) of a system of quantum wells separated by wide barriers is investigated theoretically. The current normal to the heterolayers is determined by thermo-field electron emission which is specific in some respects due to the specific character of the density of states inside the quantum well in the electric field. The CVC is shown to have a number of sections with different activation energies. The theory is compared with experiment.