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An Alternative Model of Space-Charge Limited Thermionic Current Flow Through a Plasma
Abstract
It is widely assumed that thermionic current flow through a plasma is limited by a "space-charge limited" (SCL) cathode sheath that consumes the hot cathode's negative bias and accelerates upstream ions into the cathode. Here, we formulate a fundamentally different current-limited mode. In the "inverse" mode, the sheath potentials at both electrodes are positive, trapping the ions in the plasma. The bias is consumed by the anode sheath. There is no potential gradient in the neutral plasma region from resistivity or presheath. The inverse cathode sheath potential phi_inv pulls some thermoelectrons back to the cathode, attenuating the current by a factor exp(qe*phi_inv/Temit). Thermoelectrons entering the zero-field region that undergo collisions may also be sent back to the cathode. In planar geometry, the plasma density linearly decreases across the gap and the current attenuation factor from collisions is emfp/(Lp+emfp) in terms of the mean free path and plasma length. A continuum kinetic planar plasma diode simulation model is set up to compare the properties of current modes with classical, conventional SCL, and inverse cathode sheaths. SCL modes can exist only if charge-exchange collisions are turned off in the virtual cathode region to prevent ion trapping. With the collisions, the current-limited equilibrium is inverse. Inverse operating modes should therefore be present or possible in many plasma devices that rely on hot cathodes. Evidence from past experiments is discussed. The inverse mode may offer opportunities to minimize sputtering and power consumption that were not previously explored due to the common assumption of SCL sheaths.
... secondary electron emission, thermionic emission, photoemission, etc. A local potential minimum near the emissive surface, called virtual cathode (VC), was observed in numerous previous simulations for surfaces emitting both electrons and H -. [19][20][21][22] The VC is always accompanied by a SCL sheath near the emissive surface featuring nonmonotonic sheath potential profile. Potential distribution between the potential minimum of VC and the plasma is the same as in a classic Debye sheath coupled with a Bohm presheath. ...
... The limiting condition of Equation (18), (19) clearly shows that the inverse sheath potential increases monotonically with the surface emission flux. Note that sheath potential given by Equation (18), (19) is more accurate with large surface emission fluxes such that the H + density is sufficiently low in the inverse sheath. ...
... The limiting condition of Equation (18), (19) clearly shows that the inverse sheath potential increases monotonically with the surface emission flux. Note that sheath potential given by Equation (18), (19) is more accurate with large surface emission fluxes such that the H + density is sufficiently low in the inverse sheath. A scan of the surface emission flux is performed, and the inverse sheath potential is calculated by Equation (18), Equation (16) and Equation (15) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 A c c e p t e d M a n u s c r i p t 14 Figure 6. ...
Negative hydrogen ion (H-) sources employed in neutral beam injection (NBI) system are subject to extraction efficiency issue due to the considerable volumetric losses of negative hydrogen ions. Here we propose to improve the H- extraction by activating an alternative sheath mode, the electronegative inverse sheath, in front of the H- production surface, which features zero sheath acceleration for H- with a negative sheath potential opposite to the classic sheath. With inverse sheath activated, produced H- exhibit smaller gyration, shorter transport path, less destructive collisions, and therefore higher extraction probability than the commonly believed space-charge limited sheath. Formation of the proposed electronegative inverse sheath and the space-charge limited sheath near the H--emitting surface is investigated by the continuum, kinetic simulation. Dedicated theoretical analyses are also performed to characterize the electronegative inverse sheath properties, which qualitatively agree with the simulation results. We further propose that the transition between the two sheath modes can be realized by tuning the cold ion generation near the emissive boundary. The electronegative inverse sheath is always coupled with a plasma consisting of only hydrogen ions with approximately zero electron concentration, which is reminiscent of the ion-ion plasma reported in previous NBI experiments.
... More recent 1D planar sheath theories have demonstrated the existence of an inverse sheath solution where the emitting surface is above the plasma potential and the ions are confined [5][6][7][8][9]. Time-dependent 1D simulations with chargeexchange (CX) collisions show that SCL sheaths break down due to ion trapping in the VC potential well, leading to the formation of an inverse regime [10][11][12][13]. ...
... It is noteworthy that some simulations including the case in figure 2 feature periodic instabilities that are triggered within the trapped ion cloud. The instabilities resemble the 'self-spikes' seen in planar geometry simulations [8,49] and thermionic discharge experiments [50]. It is also theoretically possible for a streaming instability [51] to occur between the passing ions and trapped ion cloud in an SCL sheath. ...
... The bias potential is mostly consumed by the sheath at the outer boundary anode, see figure 4(p). The fluctuations in the shot 4 data are a result of self-spike instabilities that were also seen in past 1D planar inverse modes, cf figure 12 of reference [8]. Self-spikes create significant fluctuations in the currents of both electrons and ions. ...
Recent one-dimensional simulations of planar sheaths with strong electron emission have shown that trapping of charge-exchange ions causes transitions from space-charge limited (SCL) to inverse sheaths. However, multidimensional emitting sheath phenomena with collisions remained unexplored, due in part to high computational cost. We developed a novel continuum kinetic code to study the sheath physics, current flow and potential distributions in two-dimensional unmagnetized configurations with emitting surfaces. For small negatively biased thermionic cathodes in a plasma, the cathode sheath can exist in an equilibrium SCL state. The SCL sheath carries an immense density of trapped ions, neutralized by thermoelectrons, within the potential well of the virtual cathode. For further increases of emitted flux, the trapped ion cloud expands in space. The trapped ion space charge causes an increase of thermionic current far beyond the saturation limit predicted by conventional collisionless SCL sheath models without ion trapping. For sufficiently strong emission, the trapped ion cloud consumes the entire 2D plasma domain, forming a mode with globally confined ions and an inverse sheath at the cathode. In situations where the emitted flux is fixed and the bias is swept (e.g. emissive probe), the trapped ions cause a large thermionic current to escape for all biases below the plasma potential. Strong suppression of the thermionic emission, required for the probe to float, only occurs when the probe is above the plasma potential.
... In this case, a normal Childlaw sheath still exists between plasma and the local potential minimum called a virtual cathode (VC), so plasma dynamics are not essentially modified [39]. Recent works reported that a floating SCL sheath cannot remain stable due to cold ion accumulation in a VC [40,41]. But no one to our knowledge has studied a RF plasma with intense boundary emission. ...
... The charge exchange collision frequency is proportional to ion velocity. The validity of the above two collision terms has been justified in previous works [40,47,48]. Surface emission is characterized by the EVDF boundary condition in the following way (taking the left boundary as an example): ...
... To sustain an IRP in practice, one can capitalize on boundary emission though SEE [63][64][65], thermionic emission [40,45,46], and photoemission [66][67][68]. In boundaries of many RF-heated plasma systems, ion flux is damaging, e.g., in a plasma thruster [69], tokamak edge region [70][71][72], etc. Ion flux induces wall erosion and impurity influx [73,74],which may be eradicated by invoking IRP. ...
The plasma sheath is the non-neutral space charge region that isolates bulk plasma from a boundary. Radiofrequency (RF) sheaths are formed when applying RF voltage to electrodes. Generally, applied bias is mainly consumed by a RF sheath, which shields an external field. Here we report evidence that an intense boundary emission destroys a normal RF sheath and establishes a type of RF plasma where external bias is consumed by bulk plasma instead of a sheath. Ions are naturally confined while plasma electrons are unobstructed, generating a strong RF current in the entire plasma, combined with a unique particle and energy balance. The proposed model offers the possibility for ion erosion mitigation of a plasma-facing component. It also inspires techniques for reaction rate control in plasma processing and wave mode conversion.
... Only a few years later, Campanell penetrated with his arguments that, at a very high electron emission, the floating potential of the electrode could become positive with respect to the plasma potential. [14][15][16][17][18][19][20][21][22][23] He named such a potential structure an inverted sheath. At a first glance, such a potential structure might be primarily of academic interest. ...
... This is in good agreement with the scenario of inverted sheath formation proposed by Campanell and co-workers in a series of papers. [14][15][16][17][18][19][20][21][22][23] According to these papers, positive ions created by various ionization mechanisms get trapped in the potential well caused by strong electron emission. In this way, they neutralize negative space charge of the emitted electrons and lead to the formation of an inverted sheath. ...
Formation of an “inverted sheath” is studied by particle-in-cell (PIC) simulation using the code XPDP1 [Verboncoeur et al., J. Comp. Phys. 104, 321–328 (1993)]. Examples of current carrying and floating sheaths are presented. It is shown that the results of the PIC simulation are in excellent agreement with the model developed recently [Gyergyek et al., Phys Plasmas 27, 023520 (2020)]. In this work, it is shown how to normalize the results from the simulations, which are given in SI units, to the dimensionless variables of the model. The procedure can also be reversed. From a given solution of the model, the input parameters of the simulation can be determined. Excellent matching between the results of the model and of the simulations is obtained in both cases. The length of the system is an eigenvalue of the model, while for the simulations, it has to be selected in advance and it is fixed. The appropriate selection of the length of the system is briefly discussed, and so it is the role of the external circuit in the XPDP1 code. Injection of particles into the system is such that monotonically decreasing potential profiles are enforced. A monotonic space charge density profile with surplus of negative charge at the left (collector) electrode and surplus of positive charge at the right (source) electrode must be created. As a consequence, a neutrality point must exist somewhere between the electrodes. The “inverted sheath” is the region between the neutrality point and the collector. By appropriate injection of the particles, the location of the neutrality point can be enforced to any position between the electrodes including the electrodes themselves.
... Recent studies [10][11][12][13] argue that inverse sheaths, instead of virtual cathodes, form near strongly emitting surfaces, allowing them to float above the plasma potential. Indeed, previous studies showed that strongly emitting probes can float higher than the plasma potential measured by cold probes [14]. ...
... It is found that at moderate neutral pressure (>0.1 Pa argon) and very strong emission (I emit >50 I es ), the results of previous emissive sheath studies by Ye et al and Sheehan et al [5,9] would fail to describe both the variation of the I-V trace and that of the inflection points as the emitted current increases. Experimental results suggest that the effects described by Campenall et al's study on inverse sheath formation [10][11][12][13]30] can influence the I-V characteristics of a strongly emitting probe in a voltage region near the plasma potential, causing the strongly emitting inflection point and the floating potential to increase beyond the conventionally predicted V p -kT e /e. To our knowledge, this is the first experimental evidence of inverse sheath effects not only affecting the floating potential but also a proportion of the I-V trace of an emissive probe. ...
I–V traces of strongly emitting emissive probes are investigated in a multidiople filament discharge. It is found that at sufficiently high neutral pressure and emitting current, the variation of the I–V traces and their associated inflection points no longer follow the previous predictions of space charge limited (SCL) models. A new, steep slope region of the I–V trace appears near the plasma potential when the probe is strongly emitting, causing the inflection point and the floating potential to increase towards the plasma potential as emission current increases, rather than staying constant. This is, to our knowledge, the first experimental evidence that the effects predicted by Campanell et al’s
inverse sheath theory (2017 Physics of Plasmas 24 057101) not only affect the floating potential but also a region in the I–V trace of an emissive probe. It is also found that the double inflection point structure when the probe is biased below the ionization energy of the working gas is highly likely to be an emission retardation effect from enhanced virtual cathode formation due to the increased local electron density. The implications of these findings on hot cathode sources are briefly discussed.
... Only a few years later, Campanell penetrated with his arguments that at a very high electron emission, the floating potential of the electrode could become positive with respect to the plasma potential. [9][10][11][12][13][14][15][16][17] He named such a potential structure an inverted sheath. At a first glance, such a potential structure might be primarily of academic interest. ...
... Some qualitative models of inverted sheath presented together with computer simulations, of course, already exist in the literature. 10,14,16 According to these models, an inverted sheath can be formed when very slow positive ions are accumulated at the virtual cathode so that they neutralize excess of negative space charge and cause the transformation of the potential profile into the inverted sheath form. Such slow ions could be created by charge exchange collisions of ions with very slow neutrals. ...
A one-dimensional, kinetic model of inverted sheath formation in a plasma system bounded by two infinitely large planar electrodes (the source and the collector) has been developed for the first time. It is assumed that ions and electrons are injected into the system from the source with half-Maxwellian distributions, and emitted electrons are also injected from the collector with a half-Maxwellian distribution. It is assumed that the potential increases monotonically from the source to the collector. Consequently, the distribution functions of ions, electrons, and emitted electrons anywhere in the system can be written as functions of the potential. Zero and first moments of the distribution functions give particle densities and fluxes. From these, the floating condition for the collector is derived and the Poisson equation is written. The first integrals of the Poisson equation give the conditions for the electric field at the source and at the collector. The model consists of five basic equations: (1) collector floating condition, (2) neutrality condition at the inflection point of the potential, (3) source electric field condition, (4) collector electric field condition, and (5) Poisson equation. The model contains nine parameters. Five of them are plasma parameters: (1) ion mass μ, (2) ion temperature τ, (3) ion source strength α, (4) temperature of emitted electrons σ, and (5) emission coefficient ε. Then there are two potentials, (1) floating potential of the collector ΨC and potential at the inflection point ΨP and (2) electric fields, (1) electric field at the collector ηC and (2) electric field at the source ηS. If five of them are selected, the other four can be found from the system of equations (1)–(4). Numerical solutions of the Poisson equation give axial profiles of the potential, electric field, and space charge density. The model can be used for parametric analysis of the inverted sheath formation. Usually μ, τ, α, ε, and σ are selected and then ΨC, ΨP, ηC, and ηS are found from the system of equations (1)–(4). This means that the particle densities are selected independently, but the potentials and electric fields are then calculated in a self-consistent way with the selected parameters.
... This saturation value is considered an approximation of the plasma potential [10,29]. Some authors have shown that this saturation value is caused by the formation of the virtual cathode [8,11,[22][23][24] and is on the order of k B T e /e below the plasma potential [16,23,30] Others have found that the floating potential can not only reach the plasma potential, but it can even exceed it [31][32][33][34][35][36][37][38]. ...
This paper analyses and characterizes a thermionic emissive probe operating in both the temperature-limited current regime (T-region) and the space-charge-limited current regime (S-region) characterized by the formation of a virtual cathode.
For this last case, we obtain the potential profile, the emitted current that overcomes the virtual cathode, as well as the thickness and depth of the potential well in front of the probe for different probe temperatures, plasma electron temperatures and neutral gas pressures.
From these results, we obtain the I-V curves and the floating potential.
Depending on the probe radius,
when the floating potential is reached in the S-region, its value saturates, becoming almost independent of the probe temperature and the electron temperature.
... Although some experiments initially seemed to confirm this saturation value of the floating potential beyond the SCL transition [18,31], Yip et al recently showed that for moderate pressures (0.01-0.4 Pa), the floating potential not only exceeds this saturation value but can even reach values higher than the plasma potential [32]. This is possible due to the formation of inverse sheaths instead of a virtual cathode, as indicated by Campanell et al [33][34][35][36][37]. ...
This article studies the interaction of an argon plasma with an emissive probe considering the effect of both ionization and ion-neutral collisions. The floating potential is determined from the I-V characteristic curves as a function of the probe temperature, neutral gas pressure and plasma electron temperature. This potential increases with increasing probe temperature until reaching the plasma potential, exceeding the saturation value previously indicated by other authors. Finally, a relationship between the plasma electron temperature and the probe temperature at which the floating potential reaches the plasma potential is shown, demonstrating that these probes can be used for diagnosis of the plasma electron temperature.
... In recent years, there have been numerous studies on lowering the work functions of candidate electrode materials [11] and mitigating the adverse impact of the negative space-charge [12][13][14]. One of the practical approaches to suppress the space-charge effect is shown to be lowering the vacuum gap distance separating the two electrodes. ...
We present a comprehensive model to fully characterize the behavior of thermionic energy conversion devices subject to constant heat flux inputs. Thermionic energy converters (TECs) have recently gained enormous attention mainly due to technological advances enabling the fabrication of converters with micro/nanometer interelectrode gaps. The reduced gap appeared to solve the long-lasting issue of negative space-charge build-up within TECs. However, the decrease in gap distance leads to the appearance of new physics in the energy interactions between the two electrodes, such as the image-charge effect and near-field thermal radiation. The intertwined energy exchange mechanisms require a deeper look and a systematic approach for accurately modeling the performance of TECs in the micro/nanoscales, especially in practical applications where the device is exposed to external energy sources such as concentrated solar power. We conducted a steady-state energy balance analysis to calculate the operating temperatures of the electrodes by considering constant heat flux inputs (such as concentrated solar energy) to the emitter and various cooling rates of the collector. The potential barrier profile within the interelectrode gap, the net current density, and the power output are subsequently calculated for a TEC with electrodes made of tungsten with and without electron reflection. The optimal values of the gap distance are also reported for various input scenarios revealing considerable deviation from the previously reported ones. An overall efficiency of
with a power output of 19.2 kW/m2 can be reached for a TEC with perfectly absorbing electrodes at the gap distance of
m operating under a heat flux input of 50 kW/m2 and convective heat transfer coefficient of 500 W/m2K. We believe that the present work provides an unabridged framework for the rigorous analysis of thermionic power generation with (sub) micrometer interelectrode distances and offers substantial insight into the design and characterization of TECs.
... In this case, normal Child-law sheath still presents between plasma and the potential dip called virtual cathode (VC) near boundary, so dynamics of plasma are not essentially modified 25 . Recent works reported that a floating SCL sheath can become unstable due to cold ion trapping 26,27 . But no one has studied a RF plasma with intense boundary emission. ...
Current models of capacitively coupled plasma indicate that external bias is mainly consumed by oscillating sheathes which shield external field. We report first evidence that strong boundary emission destroys normal radio-frequency (RF) sheath and establishes a new RF plasma where external bias is consumed by bulk plasma instead of sheathes. This produces ion confinement and intense RF current in bulk plasma, combined with unique particle and energy balance. Proposed model offers new method for wave mode conversion and a reaction rate control technic in low pressure plasma processing.
The surface temperature of a tungsten surface facing hot hydrogen plasma is evaluated, thanks to 1d/3v particle-in-cell simulations in floating wall conditions. At each iteration, the plasma heat flux to the cathode is equalized with the outgoing one, which is due to thermionic emission, surface radiation, and heat conduction through the wall. The thermal conductivity is chosen within the range 35–160 W m−1 K−1 in the different simulations in order to take into account the surface condition. A transition from a cold temperature surface to a hot one arises for a critical thermal conductivity, whose value depends on the plasma parameters. This transition is very abrupt and leads to a space charge limited regime where the thermionic current penetrating the plasma has reached its maximal value and is about three times the Bohm current. Changing the initial conditions in the code, more particularly, the timing of electron emission, can lead to a very different final surface temperature. This history effect and the associated hysteresis are evidenced by means of fluid calculations, which are in a good agreement with the simulation results as well as with previous experimental measurements.
The dynamics of an argon plasma in the gap of a thermionic diode is investigated using particle-in-cell (PIC) simulations. The time-averaged diode current, as a function of the relative electrical potential between the electrodes, is studied while the plasma density depletes due to recombination on the electrode surfaces. Simulations were performed in both one and two dimensions, and significant differences were observed in the plasma decay between the two cases. Specifically, in two dimensions it was found that the electrostatic potential gradually changes as the plasma decays, while in one dimension fluctuations in the plasma led to large potential fluctuations which changed the plasma decay characteristics relative to the two-dimensional case. This creates significant differences in the time-averaged diode current. Furthermore, it was found that the maximum time-averaged current is collected when the diode voltage is set to the flat-band condition, where the cathode and anode vacuum biases are equal. This suggests a novel technique of measuring the difference in work functions between the cathode and anode in a thermionic converter.
An experiment is performed on a large plasma device operated by the Basic Plasma Science Facility at the University of California, Los Angeles, in which an electrically floating structure is placed near the end of the 18-m magnetized plasma column. The structure consists of a flat carbon plate that acts as a mask for a smaller, ring-shaped LaB6 emissive surface whose temperature can be externally controlled. This configuration has been previously used to study electron heat transport and pressure-driven avalanches [B. Van Compernolle and G. J. Morales, Phys. Plasmas 24, 112302 (2017)] by biasing the LaB6 ring-cathode with respect to a distant anode in a cold afterglow plasma. In contrast, the present study is performed during the active portion of the steady-state discharge in which the nominal plasma parameters are determined by the injection of an electron beam from a BaO cathode at the opposite end. It is found that, even without an applied bias on the LaB6 cathode, the self-consistent potential and current profiles are modified near the end plate as the LaB6 temperature is increased, resulting in density increases on the field lines in contact with the ring-cathode. In the absence of enhanced ionization, at the largest cathode temperatures, the ambient density can be doubled. A theoretical model is presented that provides a quantitative explanation for the experimental observations.
Space-charge-limited (SCL) current density for time-invariant injection (under long-pulse condition) via the diode cathode is the maximum transportable density, while it can be leveraged higher when the injection pulselength becomes shorter than the transmit time for electrons (i.e., under short-pulse condition). However, both limits mentioned above apply for the time-invariant injection condition and the role of time-varying current density for injection remains elusive. In this paper, we numerically investigate the SCL electron flow with time-variant injection. Using particle-in-cell simulation, four different time-variant profiles for electron injection are enforced, and the maximum current densities are determined resulting from the space charge effect for various pulse lengths. We speculate that the time-variant density of injection via the diode cathode will contribute to transport enhancement in the short-pulse condition.
Accumulation of cold ions trapped within a space-charge-limited sheath collapses the sheath, causing a transition to the inverse sheath mode. A driving mechanism creating trapped ions is charge-exchange collisions which occur between fast ions and cold neutrals. Due to the complex nature of the temporally evolving sheath, it is difficult to predict how long the transition takes. Depending on the properties of the plasma, emitted electrons, and neutrals, the time scale can range from microseconds to hours. For experimental situations, it is important to understand whether the sheath will transition to an inverse mode within the observation time allotted. In this paper, we establish a theoretical basis for defining transition time of the sheath in terms of plasma properties. Calculations include an analytical approximation for the length of the virtual cathode, the amount of charged particles in each layer of the space-charge-limited sheath, and a time for its transition to the inverse sheath. The theoretical model is then compared to 1D kinetic simulations of a space-charge-limited sheath with charge-exchange collisions present. The results are applied to estimate transition time scales for applications in laboratory plasma experiments, the lunar sheath, and tokamaks.
Hot cathodes are crucial components in a variety of plasma sources and applications, but they induce mode transitions and oscillations that are not fully understood. It is often assumed that negatively biased hot cathodes have a space-charge limited (SCL) sheath whenever the current is limited. Here, we show on theoretical grounds that a SCL sheath cannot persist. First, charge-exchange ions born within the virtual cathode (VC) region get trapped and build up. After the ion density reaches the electron density at a point in the VC, a new neutral region is formed and begins growing in space. In planar geometry, this 'new plasma' containing cold trapped ions and cold thermoelectrons grows towards the anode and fills the gap, leaving behind an inverse cathode sheath. This explains how transitions from temperature-limited mode to anode glow mode occur in thermionic discharge experiments with magnetic fields. If the hot cathode is a small filament in an unmagnetized plasma, the trapped ion region is predicted to grow radially in both directions, get expelled if it reaches the cathode, and reform periodically. Filament-induced current oscillations consistent with this prediction have been reported in experiments. Here, we set up planar geometry simulations of thermionic discharges and demonstrate several mode transition phenomena for the first time. Our continuum kinetic code lacks the noise of particle simulations, enabling a closer study of the temporal dynamics.
Electrons emitted from a solid surface can noticeably affect characteristics of plasma
sheath surrounding that surface by modifying current balance at wall, charge separation in
sheath region and Bohm criterion at sheath edge. We establish a static sheath model with
kinetic electrons and cold ions to emphasize the effect of different total emitted
electron velocity distribution functions (EEVDFs) on classic sheath solution and its
structure transition. Four total EEVDFs with same average energy are considered
separately. It is found that total EEVDFs influence the sheath solution and the threshold
of total electron emission coefficient (EEC) for classic sheath dramatically, and can
cause no solution for critical space-charge limited (SCL) sheath. These results indicate
that, as EEC increases from zero gradually, the sheath will not transit from classic
sheath to SCL sheath structure for some special total EEVDFs.
Atmospheric pressure arcs have recently found application in the production of nanoparticles. Distinguishing features of such arcs are small length and hot ablating anode characterized by intensive electron emission and radiation from its surface. We performed one-dimensional modeling of argon arc, which shows that near-electrode effects of thermal and ionization non-equilibrium play important role in operation of a short arc, because the non-equilibrium regions are up to several millimeters long and are comparable with the arc length. The near-anode region is typically longer than the near-cathode region and its length depends more strongly on the current density. The model was extensively verified and validated against previous simulation results and experimental data. Volt-Ampere characteristic (VAC) of the near-anode region depends on the anode cooling mechanism. In case of strong anode cooling when anode is cold, the anode voltage decreases with current density, therefore suggesting the arc constriction near the anode. Without anode cooling, the anode temperature increases significantly with current density, leading to drastic increase in the thermionic emission current from anode. Correspondingly, the anode voltage increases with current density - and the opposite trend in the VAC is observed. The results of simulations were found to be independent of sheath model used: collisional (fluid) or collisionless model gave the same plasma profiles for both near-anode and near-cathode regions.
This paper presents a new relativistic solution for the space-charge-limited current for coaxial
vacuum diodes. The solution is deduced using a methodology that combines exact partial solutions
and numerical fitting. The expression obtained presents a maximum error of 2% in the verified
voltage range from 0 V to 846 MV and the radius ratio from 0.05 to 0.95.
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.
A two-dimensional axisymmetric quasi-neutral fluid model of an emissive hollow cathode that includes neutral xenon, single charge ions and electrons has been developed. The gas discharge is coupled with a thermal model of the cathode into a self-consistent generic model applicable to any hollow cathode design. An exhaustive description of the model assumptions and governing equations is given. Boundary conditions for both the gas discharge and thermal model are clearly specified as well. A new emissive sheath model that is valid for any emissive material and in both space charge and thermionic emission limited regimes is introduced. Then, setting the emitter temperature to an experimentally measured profile, we compare simulation results of the plasma model to measurements available in the literature for NASA NSTAR barium oxide cathode. Qualitative discrepancies between simulation results and measurements are noted in the cathode plume regarding the simulated plasma potential. Motivated by experimental evidence supporting the occurrence of ion acoustic instabilities in the cathode plume, an enhanced model of electron transport in the plume is presented and its consequences analyzed. Using the obtained plasma model, simulated quantities in the plume are qualitatively comparable with measurements. Inside the cathode, the simulated plasma density agrees well with measurements and is within the ±50% experimental uncertainty associated with these measurements. A comparison of simulation results of the full coupled cathode model for the NASA NSTAR cathode with experimental measurements is presented in a companion paper, as well as a physical analysis of the cathode behavior and a parametric study of the influence of the operating point and key design choices.
The paper gives an overview of the most common non-equilibrium approaches for modeling of tungsten-inert gas arc plasma, which have been developed up to date, in particular two-temperature and fully non-equilibrium approaches. The first group implies thermal non-equilibrium but chemical equilibrium whereas the second group describes the arc plasma avoiding assumptions of both thermal and chemical equilibrium. The common and specific features of the physical description are discussed. Results of the most recent fully non-equilibrium model, which is applied for the first time to tungsten-inert gas arc arrangement with a truncated conical tip of a doped tungsten cathode, are compared with those of previously published non-equilibrium models and experimental data. The general diffusion representation and more accurate boundary conditions incorporating the properties of the space-charge sheaths adjacent to the electrodes enable a novel description of the arc core, the near-electrode regions and the arc fringes in a self-consistent manner and provides a deeper insight into the arc properties.
A Thermionic Bare Tether (TBT) is a long conductor coated with a low work-function material. In drag mode, a tether segment extending from anodic end A to a zero-bias point B, with standard Orbital-motion-limited current collection, is followed by a complex cathodic segment. In general, as bias becomes more negative in moving from B to cathodic end C, one first finds Space-Charge-Limited (SCL) emission covering up to some intermediate point B*, then full Richardson-Dushman (RD) emission reaching from B* to end C. An approximate analytical study, which combines current and voltage profile equations with results from asymptotic studies of the Vlasov-Poisson system for emissive probes, is carried out to determine the parameter domain covering two limit regimes, which are effectively controlled by just two dimensionless parameters involving ambient plasma and TBT material properties. In one such limit regime no point B* is reached and thus no full RD emission develops. In an opposite regime, SCL segment BB* is too short to contribute significantly to current balance.
A quasi-static theoretical 1D model is developed to describe the sheath structure of a strongly emissive plasma-facing material and is subsequently applied to emissive probes' experimental data - which are usually supposed to be an efficient tool to directly measure plasma potential fluctuations. The model is derived following the space-charge limited emission current model developed in Takamura et al., [Contrib. Plasma Phys. 44(1-3), 126-137 (2004)], adding the contribution of secondary emission due to back-diffusion of plasma electrons at the emitting surface. From this theory, current-voltage characteristics of emissive probes are derived. A theoretical relation between the floating potential of an emissive probe and plasma parameters is obtained and a criterion is derived to determine the threshold between the thermoemission limited current regime and space-charge limited current regime. In the space-charge limited regime, a first order expansion is then applied to the quasi-static relation to study the effect of plasma fluctuations on emissive probe measurements. Both the mean values and the fluctuations of the floating potential of an emissive probe predicted by the model, as well as the potential value at which the transition between emission current regimes occurs, are compared to three sets of experimental data obtained in two different plasma devices.
The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities. The plasma sheath also provides a boundary condition and can often have a significant global impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the continuum kinetic code, Gkeyll, which directly solves the Vlasov-Maxwell equations. The code uses a novel version of the finite-element discontinuous Galerkin scheme that conserves energy in the continuous-time limit. The fields are computed using Maxwell equations. Ionization and scattering collisions are included; however, surface effects are neglected. The aim of this work is to introduce the continuum kinetic method and compare its results with those obtained from an already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and fields adjust self-consistently at the wall. The work presented here demonstrates that the kinetic and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multi-fluid model can be a useful approximation for simulating the plasma boundary. There are differences in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions of the distribution function presented here highlight the non-Maxwellian distribution of electrons in the sheath, emphasizing the need for a kinetic model. The densities, velocities, and the potential show a good agreement between the kinetic and fluid results. However, kinetic physics is highlighted through higher moments such as parallel and perpendicular temperatures which provide significant differences from the fluid results in which the temperature is assumed to be isotropic. Besides decompression cooling, the heat flux is shown to play a role in the temperature differences that are observed, especially inside the collisionless sheath.
The instability of a monoenergetic electron beam in a collisional one-dimensional plasma bounded between grounded walls is considered both analytically and numerically. Collisions between electrons and neutrals are accounted for the plasma electrons only. Solution of a dispersion equation shows that the temporal growth rate of the instability is a decreasing linear function of the collision frequency which becomes zero when the collision frequency is two times the collisionless growth rate. This result is confirmed by fluid simulations. Practical formulas are given for the estimate of the threshold beam current which is required for the two-stream instability to develop for a given system length, neutral gas pressure, plasma density, and beam energy. Particle-in-cell simulations carried out with different neutral densities and beam currents demonstrate good agreement with the fluid theory predictions for both the growth rate and the threshold beam current.
Thermionic energy converter (TEC) is a heat engine that generates electricity directly using heat as its source of energy and electron as its working fluid. Despite having a huge potential as an efficient direct energy conversion device, the progress in vacuum-based thermionic energy converter development has always been hindered by the space charge problem and the unavailability of materials with low work function. It is only recently that researchers have started to look back into this technology as recent advances in manufacturing technology techniques have made it possible to solve these problems, making TECs a viable option in replacing current energy production systems. The focus of this paper is to review the challenges of producing efficient and practical TECs, along with recent findings and developments in mitigating these challenges. Furthermore, this paper looked into potential applications of TECs, based on recent works and technologies, and found that, with certain improvements, it can be applied in many sectors.
A stability theory is developed for a plasma diode in which an electron beam supplied from the emitter propagates without collisions in the self-consistent electric field against the immobile ion background. An integral equation for the amplitude of the perturbed field is deduced using the Q,G method for the regime without electron reflection from a potential barrier. Analytic solutions to this equation are obtained for a number of important particular cases, and the plasma dispersion properties are examined.
When an unmagnetized plasma comes in contact with a material surface, the
difference in mobility between the electrons and the ions creates a nonneutral
layer known as the Debye sheath (DS). However, in magnetic fusion devices, the
open magnetic field lines intersect the structural elements of the device with
near grazing incidence angles. The magnetic field tends to align the particle
flow along its own field lines, thus counteracting the mechanism that leads to
the formation of the DS. Recent work using a fluid model [P. Stangeby, Nucl.
Fusion {\bf 52}, 083012 (2012)] showed that the DS disappears when the
incidence angle is smaller than a critical value (around $5^\circ$ for
ITER-like parameters). Here, we study this transition by means of numerical
simulations of a kinetic model both in the collisionless and weakly collisional
regimes. We show that the main features observed in the fluid model are
preserved: for grazing incidence, the space charge density near the wall is
reduced, the ion flow is subsonic, and the electric field and plasma density
profiles are spread out over several ion Larmor radii instead of a few Debye
lengths as in the unmagnetized case. As there is no singularity at the DS
entrance in the kinetic model, this phenomenon depends smoothly on the magnetic
field incidence angle and no particular critical angle arises. The simulation
results and the predictions of the fluid model are in good agreement, although
some discrepancies subsist, mainly due to the assumptions of isothermal closure
and diagonality of the pressure tensor in the fluid model.
The influence of electron reflection and secondary electron emission due to electron impact from the anode on discharges driven by thermionic emission is studied by the self-consistent one-dimensional particle-in-cell Monte Carlo collisions model. Two regimes are considered. In the first regime, the two-stream instability is excited and large anode sheath potential is obtained. It is found that in this regime, the reflected electrons play a significant role. In the second regime, the instability is not excited and the anode sheath potential is small. The dominant anode process in this regime is the secondary electron emission. It is shown that in both regimes, the anode processes significantly influence the plasma parameters.
Hot cathode and hollow anode argon DC glow discharge plasma at different pressures of (0.04, 0.05, 0.06, 0.07, 0.09, 0.2, 0.4, and 0.8 mbar) has been investigated. The experiments were carried out under the influence of pressure and filament cathode current on voltage – current characteristics of glow discharge and its breakdown voltage. Plasma parameters have been measured and obtained using single probe method at fixed discharge current (Id=1.88 mA) and hollow anode diameter. A computer MATLAB program is performed for this purpose. It was shown that the discharge voltage – current characteristics curve has a positive resistance and represents an abnormal glow region at pressure (0.04 and 0.06) mbar for different filament current. The breakdown voltage increases as the filament current is increased. In different pressure, electron temperature shows different behavior with increasing filament current. Electron density varies nearly inversely with the filament current, but it is increase due to increase of pressure from (1 to 3 mbar), then tends to decrease for the higher pressure. There are two groups of electrons according to the two peaks of (EEDFs), and the peaks amplitude decrease, with the increases of both filament current and gas pressure.
In this paper we propose new boundary conditions at the hot walls with
thermionic electron emission for two-temperature thermal arc models. In the
derived boundary conditions the walls are assumed to be made from refractory
metals and that the erosion of the wall is small and, therefore, is not taken
into account in the model. In these boundary conditions the plasma sheath
formed at the electrode is considered as the interface between the plasma and
the wall. The derived boundary conditions allow the calculation of the heat
flux to the walls from the plasma and consequently the thermionic electron
current that makes the two temperature thermal model self consistent.
The heating of plasma electrons during discharges driven by thermionic emission is studied using one-dimensional particle-in-cell Monte Carlo collisions modeling that self-consistently takes the dependence of the thermionic current on the plasma parameters into account. It is found that at a gas pressure of 102 Pa the electron two-stream instability is excited. As a consequence, the electrostatic plasma wave propagates from the cathode to the anode. The trapping of electrons by this wave contributes noticeably to the heating of the plasma. At a larger gas pressure, this instability is not excited. As a consequence, plasma electrons are heated only because of the generation of energetic electrons in ionization events and the scattering of emitted electrons.
As the size of a positively biased electrode increases, the nature of the interface formed between the
electrode and the host plasma undergoes a transition from an electron-rich structure (electron sheath)
to an intermediate structure containing both ion and electron rich regions (double layer) and ultimately
forms an electron-depleted structure (ion sheath). In this study, measurements are performed to further
test how the size of an electron-collecting electrode impacts the plasma discharge the electrode is
immersed in. This is accomplished using a segmented disk electrode in which individual segments are
individually biased to change the effective surface area of the anode. Measurements of bulk plasma parameters
such as the collected current density, plasma potential, electron density, electron temperature
and optical emission are made as both the size and the bias placed on the electrode are varied. Abrupt
transitions in the plasma parameters resulting from changing the electrode surface area are identified
in both argon and helium discharges and are compared to the interface transitions predicted by global
current balance [S. D. Baalrud, N. Hershkowitz, and B. Longmier, Phys. Plasmas 14, 042109 (2007)].
While the size-dependent transitions in argon agree, the size-dependent transitions observed in helium
systematically occur at lower electrode sizes than those nominally derived from prediction. The discrepancy
in helium is anticipated to be caused by the finite size of the interface that increases the effective
area offered to the plasma for electron loss to the electrode
Under analytical and numerical study are the kinetic phenomena inherent for nonlinear oscillations in 1D diodes in which charged particles are supplied from an emitter and move with no collision in the interelectrode spacing. An original numerical method (E,K code) is used to build up the ion and electron velocity distribution functions as well to study the structures forming in the course of the nonlinear oscillations both in the vacuum diode with monoenergetic electron beam and in the Knudsen diode with surface ionization. The oscillations are shown to occur owing to the Bursian-Pierce instability.
The exact theoretical expressions involved in the formation of sheath in
front of an electron emitting electrode immersed in a low-density plasma
have been derived. The potential profile in the sheath region has been
calculated for subcritical, critical, and supercritical emissions. The
potential profiles of critical and supercritical emissions reveals that
we must take into account a small, instead of zero, electric field at
the sheath edge to satisfy the boundary conditions used to integrate the
Poisson's equation. The I-V curves for critical emission shows that only
high values of plasma-electron to emitted-electron temperature ratio can
meet the floating potential of the emissive electrode. A one-dimensional
fluid like model is assumed for ions, while the electron species are
treated as kinetic. The distribution of emitted-electron from the
electrode is assumed to be half Maxwellian. The plasma-electron enters
the sheath region at sheath edge with half Maxwellian velocity
distribution, while the reflected ones have cut-off velocity
distribution due to the absorption of super thermal electrons by the
electrode. The effect of varying emitted-electron current on the sheath
structure has been studied with the help of a parameter G (the ratio of
emitted-electron to plasma-electron densities).
The spatial distribution of the plasma and beam electrons in a region whose extension from a hot cathode is larger than the Debye length, but smaller than the electron mean free path, is analyzed. In addition, the influence of electrons thermionically emitted from a hot cathode and the ratio of electron-to-ion mass on the Bohm velocity and on the ion and electron densities at the plasma-sheath boundary in a gas discharge are studied. It is shown that thermionic emission has the effect of increasing the Bohm velocity, and this effect is more pronounced for lighter ions. In addition, it is shown that the Bohm velocity cannot be increased to more than 24% above its value when there is no electron emission.
The time-dependent current collection by a cylindrical Langmuir probe, whose bias is suddenly changed from zero to a positive or negative finite value, is studied with a novel direct Vlasov code. The numerical algorithm is based on finite-difference formulas to approximate spatial and velocity derivatives and the time integration is carried out with an explicit Runge-Kutta method, or in the case of probe radius small compared with the Debye length, by using the unconditionally stable backward Euler scheme. Both electrons and ions are treated kinetically by the code, which implements initial and boundary conditions that are consistent with the presence of the probe. Within the considered parameter range, the plasma sheath around the probe exhibited an overshoot and it later recovered a steady state. Phase space diagrams of the particle trajectories revealed the presence of a trapped population of particles. The dependence of this population as a function of the probe radius is presented as well as a comparison with the stationary theory. The performance of the code and a comparison with previously used particle-in-cell algorithms are discussed.
The measured potential profiles of unmagnetized plasma sheath near a stainless steel plate exhibit deep virtual cathode structures caused by secondary electrons produced by high-speed ions hitting the surface of the plate. The depth and thickness of the virtual cathode depend on the ion streaming energy and gas pressure. The experimental results are in agreement with numerical calculations.
A one-dimensional kinetic theory of sheaths surrounding planar, electron-emitting surfaces is presented which accounts for plasma electrons lost to the surface and the temperature of the emitted electrons. It is shown that ratio of plasma electron temperature to emitted electron temperature significantly affects the sheath potential when the plasma electron temperature is within an order of magnitude of the emitted electron temperature. The sheath potential goes to zero as the plasma electron temperature equals the emitted electron temperature, which can occur in the afterglow of an rf plasma and some low-temperature plasma sources. These results were validated by particle in cell simulations. The theory was tested by making measurements of the sheath surrounding a thermionically emitting cathode in the afterglow of an rf plasma. The measured sheath potential shrunk to zero as the plasma electron temperature cooled to the emitted electron temperature, as predicted by the theory.
A macroscopic model of the interaction of a plasma with two parallel, electron-emitting walls is presented. Zero Debye-length and total thermalization of the secondary electron emission (SEE) are assumed. The SEE is treated as a free beam within each thin, collisionless sheath, but as part of a single electron population within the presheath. Plasma models with three and two species result in sheath and presheath, respectively. The ion flow at the presheath/sheath transition is sonic, and the sound speed there determines the relation between the temperature of the confined electron populations in sheath and presheath. For the general case of a plasma flowing axially between two annular walls the complete dimensionless solution depends on five parameters. Potential drops in the presheath can be larger than in the sheaths, mainly when charge-saturation is reached in the sheath or for a large effective ion friction in the presheath. The losses of plasma current to the walls are determined totally by the presheath problem, whereas the sheath problem and wall material determine the energy lost by impacting particle. Energy losses change drastically from zero SEE to a SEE yield about 100% when the charge-saturated regime is reached.
A particle injection algorithm has been developed for its use in electrostatic particle-in-cell (PIC) simulations of the ion sheath which takes place in the surroundings of a planar electrode immersed in a plasma when negatively biased. The algorithm takes into account the acceleration of ions along the presheath and evaluates their flux and velocity distribution when entering the simulation at the sheath edge. It has been verified by comparing the results obtained from the PIC simulation with those provided by fluid models of the ion sheath. The algorithm can be easily extended to cylindrical or spherical geometries and, in fact, it has already been successfully used to study the transition from radial to orbital behaviour of ions in the surroundings of cylindrical Langmuir probes.
The potential structures around a moderate negative biased electron-emitting cylindrical probe in low-density isotropic plasma are calculated in the collisionless sheath region. The formalisms, equations, and solutions for the entire electron emitting range (i.e., subcritical, critical, and supercritical) from the cylindrical emitter and collector surface are discussed. The plasma-electron and emitted-electron are assumed to have half Maxwellian velocity distributions at their respective sheath entering boundaries with cold plasma ions. Poisson's equation is solved numerically in the sheath region for the subcritical, critical, and supercritical emissions. The I-V characteristics for these three cases are presented in tabular form. The results show that we need very high emitted-electron current to solve Poisson's equation for the critical and spercritical emissions. Thus, the floating potential is far away in these scenarios. Also, the number density of emitted-and plasma-electron are comparable at the sheath edge so we cannot neglect the density of former in comparison with latter at the sheath edge.
The first results of particle-in-cell simulations of the electrostatic sheath and magnetic pre-sheath of thermionically emitting planar tungsten surfaces in fusion plasmas are presented. Plasma conditions during edge localized modes (ELMs) and during inter-ELM periods have been considered for various inclinations of the magnetic field and for selected surface temperatures. All runs have been performed under two assumptions for the sheath potential drop; fixed or floating. The primary focus lies on the evaluation of the escaping thermionic current and the quantification of the suppression due to the combined effects of space-charge and Larmor gyration. When applicable, the results are compared with the predictions of analytical models. The heat balance in the presence of thermionic emission as well as the contribution of the escaping thermionic current to surface cooling are also investigated. Regimes are identified where emission needs to be considered in the energy budget.
A method for treatment of boundary conditions and particle loading in a self-consistent semi-infinite Particle-In-Cell/Monte Carlo simulation is presented. A non-ionizing, collisional plasma in contact with an electrode was assumed. The simulation was performed for a spherical probe with constant probe potential. The motion of charged particles was calculated in three dimensions, but only the radial charge distribution and thus only radial electric field were assumed. The particle loading has to be done with an appropriate velocity distribution with a radial drift velocity. This drift velocity has to be calculated from the probe current, and therefore, a self-consistent (iterative) approach is necessary. Furthermore, correct values of particle densities and electric field potential at the outer boundary of the computational domain have to be set using asymptotic formulae for particle density and electric field potential. This approach removes the “source sheath” which is created artificially, if incorrect boundary conditions and velocity distributions of loaded particles are used. This approach is, however, feasible only for the case of a negative probe where asymptotic formulae are known.
This paper is devoted to studying how the inter-electrode distance affects the voltage drop across electrodes, the cathode sheath thickness, and the axial distribution of plasma parameters. The experiment demonstrates the simultaneous growth of both the voltage drop across the electrodes and the cathode sheath thickness when on increasing the gap the anode is moved away from the cathode while remaining in the negative glow. This effect is most clearly pronounced under low gas pressure and high current values when the negative glow length is large. The discharge axial structure dynamics is studied with the Langmuir probe technique and with the OOPIC Pro code. The inter-electrode gap growth with the current fixed is found to be accompanied by the plasma concentration increase in the negative glow. The positive plasma potential is shown to cause the current to the grounded anode to be transported by fast electrons accelerated in the cathode sheath. Moving the anode away from the cathode through the negative glow weakens the flow of fast electrons coming to the anode, thus decreasing the discharge current. In order to restore the discharge current, one has to increase the voltage across the electrodes, leading to the cathode sheath thickness increase and the plasma concentration growth in the negative glow.
Two floating sheath solutions with strong electron emission in planar geometry have been proposed, a “space-charge limited” (SCL) sheath and an “inverse” sheath. SCL and inverse models contain different assumptions about conditions outside the sheath (e.g., the velocity of ions entering the sheath). So it is not yet clear whether both sheaths are possible in practice, or only one. Here we treat the global presheath-sheath problem for a plasma produced volumetrically between two planar walls. We show that all equilibrium requirements (a) floating condition, (b) plasma shielding, and (c) presheath force balance, can indeed be satisfied in two different ways when the emission coefficient γ > 1. There is one solution with SCL sheaths and one with inverse sheaths, each with sharply different presheath distributions. As we show for the first time in 1D-1V simulations, a SCL and inverse equilibrium are both possible in plasmas with the same upstream properties (e.g., same N and Te). However, maintaining a true SCL equilibrium requires no ionization or charge exchange collisions in the sheath, or else cold ion accumulation in the SCL's “dip” forces a transition to the inverse. This suggests that only a monotonic inverse type sheath potential should exist at any plasma-facing surface with strong emission, whether be a divertor plate, emissive probe, dust grain, Hall thruster channel wall, sunlit object in space, etc. Nevertheless, SCL sheaths might still be possible if the ions in the dip can escape. Our simulations demonstrate ways in which SCL and inverse regimes might be distinguished experimentally based on large-scale presheath effects, without having to probe inside the sheath.
Electron transpiration cooling (ETC) is a recently proposed approach to manage the high heating loads experienced at the sharp leading edges of hypersonic vehicles. Computational fluid dynamics (CFD) can be used to investigate the feasibility of ETC in a hypersonic environment. A modeling approach is presented for ETC, which includes developing the boundary conditions for electron emission from the surface, accounting for the space-charge limit effects of the near-wall plasma sheath. The space-charge limit models are assessed using 1D direct-kinetic plasma sheath simulations, taking into account the thermionically emitted electrons from the surface. The simulations agree well with the space-charge limit theory proposed by Takamura et al. for emitted electrons with a finite temperature, especially at low values of wall bias, which validates the use of the theoretical model for the hypersonic CFD code. The CFD code with the analytical sheath models is then used for a test case typical of a leading edge radius in a hypersonic flight environment. The CFD results show that ETC can lower the surface temperature of sharp leading edges of hypersonic vehicles, especially at higher velocities, due to the increase in ionized species enabling higher electron heat extraction from the surface. The CFD results also show that space-charge limit effects can limit the ETC reduction of surface temperatures, in comparison to thermionic emission assuming no effects of the electric field within the sheath.
The formation of a plasma sheath in front of a negative wall emitting secondary electron is studied by a one-dimensional fluid model. The model takes into account the effect of the ion temperature. With the secondary electron emission (SEE) coefficient obtained by integrating over the Maxwellian electron velocity distribution for various materials such as Be, C, Mo, and W, it is found that the wall potential depends strongly on the ion temperature and the wall material. Before the occurrence of the space-charge-limited (SCL) emission, the wall potential decreases with increasing ion temperature. The variation of the sheath potential caused by SEE affects the sheath energy transmission and impurity sputtering yield. If SEE is below SCL emission, the energy transmission coefficient always varies with the wall materials as a result of the effect of SEE, and it increases as the ion temperature is increased. By comparison of with and without SEE, it is found that sputtering yields have pronounced differences for low ion temperatures but are almost the same for high ion temperatures.
The Bohm sheath criterion is studied with laser-induced fluorescence in three ion species plasmas using two tunable diode lasers. Krypton is added to a low pressure unmagnetized DC hot filament discharge in a mixture of argon and xenon gas confined by surface multi-dipole magnetic fields. The argon and xenon ion velocity distribution functions are measured at the sheath-presheath boundary near a negatively biased boundary plate. The potential structures of the plasma sheath and presheath are measured by an emissive probe. Results are compared with previous experiments with Ar–Xe plasmas, where the two ion species were observed to reach the sheath edge at nearly the same speed. This speed was the ion sound speed of the system, which is consistent with the generalized Bohm criterion. In such two ion species plasmas, instability enhanced collisional friction was demonstrated [Hershkowitz et al., Phys. Plasmas 18(5), 057102 (2011).] to exist which accounted for the observed results. When three ion species are present, it is demonstrated under most circumstances the ions do not fall out of the plasma at their individual Bohm velocities. It is also shown that under most circumstances the ions do not fall out of the plasma at the system sound speed. These observations are also consistent with the presence of the instabilities.
An important unresolved question in plasma physics concerns the effect of strong electron emission on plasma-surface interactions. Previous papers reported solutions with negative and positive floating potentials relative to the plasma edge. The two models give very different predictions for particle and energy balance. Here we show that the positive potential state is the only possible equilibrium in general. Even if a negative floating potential existed at t=0, the ionization collisions near the surface will force a transition to the positive floating potential state. This transition is demonstrated with a new simulation code.
Recent papers claim that a one dimensional (1D) diode with a time-varying voltage drop can transmit current densities that exceed the Child-Langmuir (CL) limit on average, apparently contradicting a previous conjecture that there is a hard limit on the average current density across any 1D diode, as t → ∞, that is equal to the CL limit. However, these claims rest on a different definition of the CL limit, namely, a comparison between the time-averaged diodecurrent and the adiabatic average of the expression for the stationary CL limit. If the current were considered as a function of the maximum applied voltage, rather than the average applied voltage, then the original conjecture would not have been refuted.
The performance capabilities of the PINK, a plasma generator with a thermionic cathode mounted in the cavity of a hollow cathode, depending for its operation on a non-self-sustained low-pressure gas discharge have been investigated. It has been shown that when a single-filament tungsten
cathode 2 mm in diameter is used and the peak filament current is equal to or higher than 100 A, the self-magnetic field of the filament current significantly affects the discharge current and voltage waveforms. This effect is due to changes in the time and space distributions of the emission current density from the hot cathode. When the electron mean free path is close to the characteristic dimensions of the thermionic cathode, the synthesized plasma density distribution is nonuniform and the cathode is etched nonuniformly. The cathode lifetime in this case is 8–12 h. Using a cathode consisting of several parallel-connected tungsten filaments ∼0.8 mm in diameter moderates the effect of the self-magnetic field of the filament current and nearly doubles the cathode lifetime. The use of this type of cathode together with a discharge igniting electrode reduces the minimum operating pressure in the plasma generator to about one third of that required for the generator operation with a single-filament cathode (to 0.04 Pa).
Here is both a textbook for beginners and a handbook for specialists in plasma physics and gaseous electronics. The book contains much useful data: results of experiments and calculations, and reference data. It provides estimates of typical parameters and formulas in forms suitable for computations. Gas discharges of all important types are discussed: breakdown, glow, arc, spark and corona at radio frequency, microwave and optical frequences. The generation of plasma, and its application to high power gas lasers are treated in detail.
The region between a Maxwellian plasma source and an absorbing surface that emits cool electrons is modeled numerically with dynamic, electrostatic particle simulation and theoretically with a static, kinetic plasma‐sheath model. Steady‐state emission results are applied specifically to secondary electrons that are induced by either incident ions or electrons, but are also valid for thermionic and photoelectrons. The ratio of the emitted electron current to incident electron current is varied up to and beyond the critical emission coefficient (ratio) that causes electric field reversal at the collector. Results from these models agree very well over the range from zero to five times the critical emission coefficient. Increasing the secondary emission coefficient is found to reduce the collector potential and decrease the ion energy deposited, yet increase the total energy flux to the collector. In the simulation, some heating of the secondary electron stream is observed to gradually evolve over many Debye lengths, possibly because of a beam–plasma interaction. This heating increases potential fluctuations but causes only small deviations from the predictions with static theory.
Photon-enhanced thermionic emission from semiconducting cathodes is a promising means of increasing cathode current density in low temperature vacuum thermionic energy devices [J. W. Schwede et al., Nature Mater. 9, 762 (2010)]. However, the space charge resulting from high emission current densities prevents emitted electrons from reaching the collector, even with gaps as small as 100 μm and at voltages as high as 1 V. We demonstrate by particle-in-cell simulations that one possible solution to overcoming the space charge is to add cesium filling and generation of a space charge-neutralizing plasma by continuous laser excitation of the cesium resonance level.
A negative potential barrier on the low-potential side of a moving double layer gives rise to a current limitation in a collisionless plasma terminated by a positively biased cold collector plate in a Q machine. The double layer is produced in front of the plasma source and moves toward the collector during the limitation. When the double layer arrives at the collector, the barrier dissolves and the current increases, causing a rise in potential along the whole plasma column. The double layer then reforms at the source.
An analytical study is presented for an one-dimensional, steady-state plasma bound between two perfectly absorbing walls that are biased with respect to each other. Starting from a description of the plasma sheaths formed at both walls, an expression relating the bulk plasma potential to the wall currents is derived, showing that the plasma potential undergoes an abrupt transition when currents cross a critical value. This result is confirmed by numerical simulations performed with a particle-in-cell code.
The discharge modes of a thermionic low pressure discharge (p<1Pa) are investigated with the one‐dimensional particle‐in‐cell simulation codes PDP1 and XPDP1 [C. K. Birdsall, IEEE Trans. Plasma Sci. 19, 65 (1991)]. The simulation results provide a model approach for stable discharge modes, hysteresis, and for nonlinear relaxation‐oscillations. During this potential‐relaxation instability, nonlinear structures, e.g. electron holes and double layers, are observed. A Pierce–Buneman‐mode is suggested as a trigger mechanism for the onset of the instability. The detailed oscillation process can be subdivided into three distinct phases: expansion phase, double layer phase, and relaxation phase. This allows one to explain the parameter dependencies of the oscillation frequency. For a periodically driven discharge, mode‐locking in a period‐2 state is found and explained by the model. The mode‐locking phenomenon is studied systematically. The results of the simulations are well confirmed by experimental observations presented in Part II of this paper [T. Klinger et al., Phys. Plasmas 2, 1822 (1995)].
A theoretical treatment of the double sheath in a hot-cathode low-pressure discharge is presented. The current density of thermionically produced electrons is found to have an upper limit. The energy of ions entering the sheath from the plasma region is calculated, and the spatial structure of the double sheath is computed.
DOI:https://doi.org/10.1103/PhysRev.2.450