Apex Field Research Articles

Lower partial pubicectomy for postoperative complicated posterior urethral stricture

ObjectiveTo report the experience of partial inferior pubicectomy in the treatment of complex posterior urethral stricture after trauma.MethodsA total of 46 patients with post-traumatic posterior urethral stricture admitted to the Department of Urology of our Hospital from January 2013 to September 2021 were selected as the research objects and underwent urethroplasty (including nine patients who had failed previous perineal repair surgery and adopted partial inferior pubicectomy approach). Retrograde urethrograph (RUG) and urine flow measurement were performed at 1, 3, 12 and 18 months after operation, and follow-up was performed when necessary. The clinical data during treatment were statistically analyzed.ResultsAll 46 patients underwent urethroplasty successfully, of which nine were treated with partial pubicectomy, accounting for 19.57% of the total. The causes of the disease were motor vehicle accident in 4 cases, falling collision injury in 2 cases, and rolling injury of military exercise tank in 3 cases. Among the 9 patients, 2 were children (22.22%), aged 8 and 12 years, and 7 were adults (77.78%), aged 19–44 (28.42 ± 1.56) years. Among the 9 patients, 6 had erectile dysfunction, accounting for 66.67%. The length of posterior urinary tract stenosis was (5.12 ± 0.57) cm. The operation time was (290.34 ± 12.35) min from anesthesia induction to skin closure. Five patients received 2 U blood transfusion during operation and three patients received 3 U blood transfusion after operation. The average hospital stay was 12–16 (14.24 ± 1.25) days, and the follow-up was 12–24 (18.24 ± 1.35) months. After surgery, one patient developed HIP abscess, which was successfully treated conservatively. One patient had dysuria 1 month after operation and was successfully treated by transurethral dilatation. One case had postoperative infection and recovered after intravenous administration of potent antibiotics. Cystourethrography was performed 3 months after operation, and there was no difference between patients with wide, long or short anastomotic stretch defects. All patients met the criteria for surgical success.ConclusionPartial inferior pubicectomy is a good surgical procedure for the repair of complicated posterior urethral stricture after operation. It is safe and reliable, can better display the prostatic apex and surgical field, shorten the length of reconstructed urethra, and has good postoperative effect. It has no direct or long-term effect on the stability of pelvis or bladder. However, further studies in a larger cohort of patients with complex posterior urethral strictures after repair are needed to demonstrate the specific indications for partial pubicectomy.

Fast and accurate determination of the curvature-corrected field emission current

The curvature-corrected field emission current density, obtained by linearizing at or below the Fermi energy, is investigated. Two special cases, corresponding to the peak of normal energy distribution and mean normal energy, are considered. It is found that the current density evaluated using the mean normal energy results in errors in the net emission current below 3% for apex radius of curvature Ra≥5 nm and for apex fields Ea in the range of 3–10 V/nm for an emitter having a work function of ϕ=4.5 eV. An analytical expression for the net field emission current is also obtained for local parabolic tips using the generalized cosine law. The errors are found to be below 6% for Ra≥5 nm over an identical range of apex field strengths. The benchmark current is obtained by numerically integrating the current density over the emitter surface and the current density itself computed by integrating over the energy states using the exact Gamow factor and the Kemble form for the WKB transmission coefficient. The analytical expression results in a remarkable speed-up in the computation of the net emission current and is especially useful for large area field emitters having tens of thousands of emission sites.

The transition from thermionic to space charge limited emission for needle-like surfaces—A particle-in-cell simulation study

We perform particle-in-cell simulations of thermionic emission from hemi-ellipsoidal shaped needle emitters. The Schottky corrected Richardson–Dushman equation is used to compute the emitted current from the curved emitter surface. It is shown that the transmitted thermionic current increases with cathode temperature before eventually settling to the enhanced space charge limited (SCL) current. It is further shown that the critical temperature at which transition to the saturation region occurs increases with the height of the emitter, leading to a softening in the transition. This may be attributed to the non-uniformity in the cathode work function as in planar diodes. The SCL current is found to increase linearly with the electrostatic apex field enhancement factor as predicted recently [Singh et al., Phys. Plasmas 27, 104501 (2020)].

Modeling basic tip forms and its effective field emission parameters

One of the important parameters of the single-tip emission system is the total emission current from the tip. To obtain the distribution of the field enhancement factor over the tip surface, we provided comsol simulation for different tip shapes. Current-voltage characteristics are obtained by integrating the current density over the emitter surface. Several types of current density formulas with different degrees of accuracy were used. The basic criterion for the calculation of the peak current was the satisfaction of the apex electric field to field emission test conditions. A “hemisphere on a cylindrical post” emitter was shown to offer compelling advantages in both total emission current and threshold voltage values. The comparison of the effective values of the field enhancement factor and emission area with the apex field enhancement factor and formal emission area is carried out.

Looped carbon nanotube fibers as cathodes with giant field enhancement factors

Structures with a sharp apex amplify an applied macroscopic field, FM, substantially and generate significant field electron emission (FE). The apex barrier field, Fa, is related to FM by the apex field enhancement factor (aFEF), γa≡Fa/FM. In this Letter, we provide a theoretical explanation for extremely high-effective FEFs (104 ≲ γeff ≲ 105) recently extracted from an orthodoxy theory analysis of the emission current–voltage characteristics of looped carbon nanotube (CNT) fibers, making them promising candidates for FE applications. In this work, we found a dependence of γa on the geometrical parameters for an isolated conductive looped CNT fiber, modeled via the finite element technique. The aFEF of looped CNT fibers is found to scale as γa=2+[hf/rfiber][ln (2h/rfiber)]−1, where f≡1+θ[rfiber/b]α[ln (2h/rfiber)−1], in which h is the height of a looped fiber standing on an emitter plate, b is its base length, rfiber is the radius of the fiber, and θ and α are fitting parameters that have a nonlinear dependence on the scaling parameter h/b. Our results show that the scaling law predicts that 10 ≲ γa ≲ 100 for looped CNT fibers with parameters: 10 μm ≤rfiber≤ 100 μm, 0.4 ≤h/b≤ 2, and d/h≥1, where d is the distance between the apex of the looped fiber and the anode. However, scanning electron microscopy images reveal the presence of microfibrils protruding from the looped CNT fiber surface close to its apex. We show that the modeling of a combined two-stage structure (looped CNT fiber + fibrils) leads to aFEF values in excellent agreement with an orthodoxy theory analysis of FE experiments performed on these fibers.

Enhanced space charge limited current for curved electron emitters

The maximum current that can be transported across a vacuum diode is limited by forces arising due to space charge. In a planar thermionic or explosive emission diode, the space charge limited current density from an emitting patch is given by the Child–Langmuir law JCL∼Vg3/2/D2, where Vg is the potential difference across the diode and D is the separation between the anode and the cathode. We show here, analytically using the nonlinear line charge model, that for a curved emitter in a planar diode configuration, the limiting current obeys the scaling relationship JSCL∼γaVg3/2/D2, where γa is the apex field enhancement factor of the curved emitter. For an emitter with a large height (h) to the apex radius of curvature (Ra) ratio, the limiting current far exceeds the planar value. The result is verified using the particle-in-cell code PASUPAT for two curved emitter shapes.

Electrostatic shielding versus anode-proximity effect in large area field emitters

Field emission of electrons crucially depends on the enhancement of the local electric field around nanotips. The enhancement is maximum when individual emitter-tips are well separated. As the distance between two or more nanotips decreases, the field enhancement at individual tips reduces due to the shielding effect. The anode-proximity effect acts in quite the opposite way, increasing the local field as the anode is brought closer to the emitter. For isolated emitters, this effect is pronounced when the anode is at a distance less than three times the height of the emitter. It is shown here that for a large area field emitter (LAFE), the anode-proximity effect increases dramatically and can counterbalance shielding effects to a large extent. Also, it is significant even when the anode is far away. The apex field enhancement factor for an LAFE in the presence of an anode is derived using the line charge model. It is found to explain the observations well and can accurately predict the apex enhancement factors. The results are supported by numerical studies using comsol multiphysics.

Schottky conjecture and beyond

The “Schottky conjecture” deals with the electrostatic field enhancement at the tip of compound structures such as a hemiellipsoid on top of a hemisphere. For such a 2-primitive compound structure, the apex field enhancement factor γa(C) is conjectured to be multiplicative (γa(C)=γa(1)γa(2)), provided the structure at the base (labeled 1, e.g., the hemisphere) is much larger than the structure on top (referred to as crown and labeled 2, e.g., the hemiellipsoid). The author first demonstrates numerically that, for generic smooth structures, the conjecture holds in the limiting sense when the apex radius of curvature of the primitive-base Ra(1) is much larger than the height of the crown h2 (i.e., h2/Ra(1)→0). If the condition is somewhat relaxed, the author shows that it is the electric field above the primitive-base (i.e., in the absence of the crown), averaged over the height of the crown, that gets magnified instead of the field at the apex of the primitive-base. This observation leads to the corrected Schottky conjecture (CSC), which, for 2-primitive structures, reads as γa(C)≃⟨γa(1)⟩γa(2), where ⟨⋅⟩ denotes the average value over the height of the crown. For small protrusions (h2/h1 typically less than 0.2), ⟨γa(1)⟩ can be approximately determined using the line charge model so that γa(C)≃γa(1)γa(2)(2Ra(1)/h2)ln⁡(1+h2/2Ra(1)). The error is found to be within 1% for h2/Ra(1)<0.05, increasing to about 3% (or less) for h2/Ra(1)=0.1 and bounded below 5% for h2/Ra(1) as large as 0.5. The CSC is also found to give good results for 3-primitive compound structures. The relevance of the CSC for field emission is discussed.

Verification of shielding effect predictions for large area field emitters

A recent analytical model for large area field emitters [D. Biswas and R. Rudra, Phys. Plasmas 25, 083105 (2018)], based on the line charge model (LCM), provides a simple approximate formula for the field enhancement on hemiellipsoidal emitter tips in terms of the ratio of emitter height to pairwise distance between neighboring emitters. The formula, verified against the exact solution of the linear LCM, was found to be adequate, provided that the mean separation between emitters is larger than half the emitter height, h. In this paper, we subject the analytical predictions to a more stringent test by simulating (i) an infinite regular array and (ii) an isolated cluster of 10 random emitters, using the finite element software COMSOL v5.4. In the case of the array, the error in the apex field enhancement factor (AFEF) is found to be less than 0.25% for an infinite array when the lattice constant c ≥ 1.5h, increasing to 2.9% for c = h and 8.1% for c = 0.75h. For an isolated random cluster of 10 emitters, the error in large AFEF values is found to be small. Thus, the error in the net emitted current is small for a random cluster compared to a regular infinite array with the same (mean) spacing. The LCM thus provides a reasonable analytical tool for optimizing a large area field emitter.

Electrostatic field enhancement on end-caps of cylindrical field-emitters

The apex field enhancement factor (AFEF) γa of a cylindrical emitter depends sensitively on its end-cap geometry. The hemispherical end-cap is well studied due to its simplicity, but, in general, a cylindrical emitter may terminate in a variety of end-cap shapes. It is well known that the AFEF depends on the ratio h/Ra, where h is the total height of the emitter and Ra is the apex radius of curvature. The authors show here that there can be a large variation in γa as the end-cap geometry is altered while keeping h/Ra fixed. They carry out a systematic numerical study and determine an approximate formula for γa in terms of measurable end-cap geometry parameters such as its height H, the radius of the cylinder R, and the apex radius of curvature Ra. They show that the formula is robust and can predict the net field emission current with errors generally less than 40%.

Derivation of a current-voltage-type plot beyond the Fowler-Nordheim one: The role of the voltage-dependency on the emission area

A dependency of the emission area on the applied voltage has been recently confirmed in reliable cold field emission experiments considering emitters in a large area form. In this work, we show that the inclusion of this dependency leads to a more general theory and then to a derivation of a more general current-voltage plot. This derivation is patent to a precise field emitter characterization, even in a single tip emitter form. We confirmed our analytical predictions using first-principles electrostatic calculations for a hemisphere on a cylindrical post and for ellipsoidal conducting emitters. As a consequence, a new plot is proposed beyond the Fowler-Nordheim one. This plot is experimentally feasible and provides, with high precision, the apex field enhancement factor from orthodox current-voltage characteristics.

Why converting field emission voltages to macroscopic fields before making a Fowler-Nordheim plot has often led to spurious characterization results

An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor γC. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot. Several years ago, the development of an “orthodoxy test” allowed a sample of 19 published FN plots relating to LAFEs to be tested, and it was found that about 40% of the related papers were reporting spuriously high values for γC. In technological papers relating to LAFE characterization, the common practice is to preconvert the measured voltage into an (apparent) value of the macroscopic field before making and analyzing an FN plot. This paper suggests that the cause of the “spurious field enhancement factor value” problem is the widespread use of a preconversion equation that is defective (for example, not compatible with ordinary electrical circuit theory) when it is applied to so-called “nonideal” field emission devices/systems. Many real devices/systems are nonideal. The author argues that FN plots should be made using raw experimental current-voltage data, that an orthodoxy test should be applied to the resulting FN plot before any more-detailed analysis, and that (in view of growing concerns over the reliability of published “scientific” results) reviewers should scrutinize field emission materials characterization papers with enhanced care.

The anode proximity effect for generic smooth field emitters

The proximity of the anode to a curved field electron emitter alters the electric field at the apex and its neighborhood. A formula for the apex field enhancement factor, γa(D), for generic smooth emitters is derived using the line charge model when the anode is at a distance D from the cathode plane. The resulting approximately modular form is such that the anode proximity contribution can be calculated separately (using geometric quantities such as the anode-cathode distance D, the emitter height h, and the emitter apex radius of curvature Ra) and substituted into the expression for γa(∞). It is also shown that the variation of the enhancement factor on the surface of the emitter close to the apex is unaffected by the presence of the anode and continues to obey the generalized cosine law. These results are verified numerically for various generic emitter shapes using COMSOL Multiphysics®. Finally, the theory is applied to explain experimental observations on the scaling behavior of the I–V field emission curve.

Simulation-Based Model of Randomly Distributed Large-Area Field Electron Emitters

With a large-area field electron emitter (LAFE), it is desirable to choose the spacings of individual emitters in such a way that the LAFE-average emission current density and total current are maximised, when the effects of electrostatic depolarization (mutual screening) are taken into account. This paper uses simulations based on a finite element method to investigate how to do this for a LAFE with randomly distributed emitters. The approach is based on finding the apex field enhancement factor and the specific emission current for an emitter, as a function of the average nearest neighbor spacing between emitters. Using electrostatic simulations based on the finite element method, the influence of neighboring emitters on a reference emitter being placed at the LAFE centre is investigated. Arrays with 25 ideal (identical) conical emitters with rounded tops are studied for different emitter densities and applied macroscopic fields. A theoretical average spacing is derived from the Poisson Point Process Theory. An optimum average spacing, and hence optimum emitter density, can be predicted for each macroscopic field.

Physics-based derivation of a formula for the mutual depolarization of two post-like field emitters

Recent analyses of the apex field enhancement factor (FEF) for many forms of field emitter have revealed that the depolarization effect is more persistent with respect to the separation between the emitters than originally assumed. It has been shown that, at sufficiently large separations, the fractional reduction of the FEF decays with the inverse cube power of separation, rather than exponentially. The behavior of the fractional reduction of the FEF encompassing both the range of technological interest (c being the separation and h is the height of the emitters) and large separations () has not been predicted by the existing formulas in field emission literature, for post-like emitters of any shape. In this work, we use first principles to derive a simple two-parameter formula for fractional reduction that can be useful for experimentalists for modeling and interpreting the FEFs for small clusters of emitters or arrays at separations of interest. For the structures tested, the agreement between numerical and analytical data is ∼1%.

Evidence of universal inverse-third power law for the shielding-induced fractional decrease in apex field enhancement factor at large spacings: a response via accurate Laplace-type calculations

Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, L, and the height, H, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, ε, in the calculation of the apex-FEF as a function of H and L. Importantly, our results show that the effects of H and L on ε are scale invariant, allowing one to predict ε for ratios L/h and H/h, where h is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, δ, from a single emitter, , and a pair, . We show that small relative errors in (i.e. ), due to the finite domain size, are sufficient to alter the functional dependence , where c is the distance from the emitters in the pair. We show that obeys a recently proposed power law decay (Forbes 2016 J. Appl. Phys. 120 054302), at sufficiently large distances in the limit of infinite domain size (, say), which is not observed when using a long time established exponential decay (Bonard et al 2001 Adv. Mater. 13 184) or a more sophisticated fitting formula proposed recently by Harris et al (2015 AIP Adv. 5 087182). We show that the inverse-third power law functional dependence is respected for various systems like infinity arrays and small clusters of emitters with different shapes. Thus, , with m = 3, is suggested to be a universal signature of the charge-blunting effect in small clusters or arrays, at sufficient large distances between emitters with any shape. These results improve the physical understanding of the field electron emission theory to accurately characterize emitters in small clusters or arrays.

Physical electrostatics of small field emitter arrays/clusters

This paper aims to improve qualitative understanding of electrostatic influences on apex field enhancement factors (AFEFs) for small field emitter arrays/clusters. Using the “floating sphere at emitter-plate potential” (FSEPP) model, it re-examines the electrostatics and mathematics of three simple systems of identical post-like emitters. For the isolated emitter, various approaches are noted. An adequate approximation is to consider only the effects of sphere charges and (for significantly separated emitters) image charges. For the 2-emitter system, formulas are found for charge-transfer (“charge-blunting”) effects and neighbor-field effects, for widely spaced and for “sufficiently closely spaced” emitters. Mutual charge-blunting is always the dominant effect, with a related (negative) fractional AFEF-change δtwo. For sufficiently small emitter spacing c, |δtwo| varies approximately as 1/c; for large spacing, |δtwo| decreases as 1/c3. In a 3-emitter equispaced linear array, differential charge-blunting and differential neighbor-field effects occur, but differential charge-blunting effects are dominant, and cause the “exposed” outer emitters to have higher AFEF (γ0) than the central emitter (γ1). Formulas are found for the exposure ratio Ξ = γ0/γ1, for large and for sufficiently small separations. The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge models (LCMs) are an alternative, but an apparent difficulty with recent LCM implementations is identified. Better descriptions of array electrostatics may involve developing good fitting equations for AFEFs derived from accurate numerical solution of Laplace's equation, perhaps with equation form(s) guided qualitatively by FSEPP-model results. In existing fitting formulas, the AFEF-reduction decreases exponentially as c increases, which is different from the FSEPP-model formulas. This discrepancy needs to be investigated, using systematic Laplace-based simulations and appropriate results analysis. FSEPP models might provide a useful provisional guide to the qualitative behaviour of small field emitter clusters larger than those investigated here.

Volumetric measurement of artificial pure ground-glass nodules at low-dose CT: Comparisons between hybrid iterative reconstruction and filtered back projection

PurposeTo compare hybrid iterative reconstruction (HIR) with filtered back projection (FBP) in the volumetry of artificial pure ground-glass nodules (GGNs) with low-dose computed tomography (CT). Materials and methodsArtificial GGNs (10mm-diameter, 523.6mm3, −660HU) in an anthropomorphic chest phantom were scanned by a 256-row multi-slice CT with three dose levels (10, 30, 100mAs). Each scan was repeated six times. Each set was reconstructed by FBP and HIR at 0.625-mm thickness. The volumes of artificial GGNs placed at the lung apex and middle lung field of the chest phantom were measured by two observers. Semi-automated measurements were performed by clicking the cursor in the center of GGNs, and manual measurements were performed by tracing GGNs on axial section. Modification of the trace was added on a sagittal or coronal section if necessary. Measurement errors were calculated for both the FBP and HIR at each dose level. We used the Wilcoxon signed rank test to identify any significant difference between the measurement errors of the FBP and HIR. Inter-observer, intra-observer, and inter-scan variabilities were evaluated by Bland Altman analysis with limits of agreements given by 95% confidence intervals. ResultsThere were significant differences in measurement errors only at the lung apex between FBP and HIR with 10mAs in both the semi-automated (observer 1, −37% vs. 7.2%; observer 2, −39% vs. 1.9%) and manual methods (observer 1, −29% vs. 7.5%; observer 2, −30% vs. 1.1%), respectively (P<0.05). HIR provided each variability equal to or less than one half of that of FBP at 10mAs in both methods. In the semi-automated method, the inter-observer and intra-observer variabilities obtained by HIR at 10mAs were −11% to 17% and −6.7% to 6.7%, whereas those for FBP at 10mAs were −29% to 30% and −38% to 20%, respectively. The inter-scan variability for FBP at 100mAs vs. HIR at 10mAs was −9.5% to 11%, and that for FBP at 100mAs vs. FBP at 10mAs was −73% to 32%. In the manual method, the inter-observer and intra-observer variabilities for HIR at 10mAs were −14% to 22% and −9.8% to 22%, and those for FBP at 10mAs were −45% to 36% and −31% to 28%, respectively. The inter-scan variability for FBP at 100mAs vs. HIR at 10mAs was −7.4% to 23%, and that for FBP at 100mAs vs. FBP at 10mAs was −52% to 26%. ConclusionHIR is superior to FBP in the volumetry of artificial pure GGNs at lung apex with low-dose CT.

Discrete space charge affected field emission: Flat and hemisphere emitters

Models of space-charge affected thermal-field emission from protrusions, able to incorporate the effects of both surface roughness and elongated field emitter structures in beam optics codes, are desirable but difficult. The models proposed here treat the meso-scale diode region separate from the micro-scale regions characteristic of the emission sites. The consequences of discrete emission events are given for both one-dimensional (sheets of charge) and three dimensional (rings of charge) models: in the former, results converge to steady state conditions found by theory (e.g., Rokhlenko et al. [J. Appl. Phys. 107, 014904 (2010)]) but show oscillatory structure as they do. Surface roughness or geometric features are handled using a ring of charge model, from which the image charges are found and used to modify the apex field and emitted current. The roughness model is shown to have additional constraints related to the discrete nature of electron charge. The ability of a unit cell model to treat field emitter structures and incorporate surface roughness effects inside a beam optics code is assessed.

UNSTEADY LAMINAR FREE CONVECTION FLOW PAST A NON-ISOTHERMAL VERTICAL CONE IN THE PRESENCE OF A MAGNETIC FIELD

An analysis is performed to study the effects of unsteady incompressible flow past a vertical cone with variable surface temperature varying as a power function of distance from the apex (x = 0) and magnetic field applied normal to the surface. The dimensionless coupled partial differential boundary layer equations are solved numerically using an efficient and unconditionally stable finite-difference scheme of the Crank-Nicolson type. The velocity and temperature fields have been studied for various combinations of physical parameters (Prandtl number, Pr, exponent in power law variation in surface temperature, n, and magnetic field parameter, M). The local as well as average skin friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in the literature and are found to be in good agreement.