arXiv subjects

Raghwendra Kumar

Publications and source records attributed to Raghwendra Kumar.

17 recordsLinked to original sources

arXiv2022

Semi-analytical theory of emission and transport in a LAFE-based diode

A large area field emitter (LAFE) typically consists of several thousands of nanoscale emitting tips. These are difficult to simulate using purely numerical methods based on finite/boundary element or finite difference methods. We show here that a semi-analytically obtained electrostatic field allows tracking of field emitted electrons of a LAFE fairly accurately using the knowledge of only the LAFE geometry. Using a single and a 9-emitter configuration, the beam parameters calculated using this method are compared with the results of tracking using fields generated by COMSOL. The net emission current, energy conservation and the transverse trace-emittance are found to be reproduced with reasonable accuracy.

physics.app-ph↗

arXiv2021

Predicting space-charge affected field emission current from curved tips

Field emission studies incorporating the effect of space charge reveal that for planar emitters, the steady-state field $E_P$, after initial transients, settles down to a value lower than the vacuum field $E_L$. The ratio $\vartheta = E_P/E_L$ is a measure of the severity of space charge effect with $\vartheta = 0$ being most severe and $\vartheta \simeq 1$ denoting the lack of significant effect. While, $E_L$ can be determined from a single numerical evaluation of the Laplace equation, $E_P$ is largely an unknown quantity whose value can be approximately found using physical models or can be determined `exactly' by particle-in-cell or molecular dynamics codes. We propose here a simple model that applies to planar as well as curved emitters based on an application of Gauss's law. The model is then refined using simple approximations for the magnitude of the anode field and the spread of the beam when it reaches the anode. The predictions are compared with existing molecular dynamics results for the planar case and particle-in-cell simulation results using PASUPAT for curved emitters. In both cases, the agreement is good. The method may also be applied to large area field emitters if the individual enhancement factors are known, for instance, using the hybrid model (D.Biswas, J. Vac. Sci. Technol. B 38, 063201 (2020)).

physics.acc-ph↗

arXiv2021

Approximate universality in the electric field variation on a field-emitter tip in the presence of space charge

The electric field at the surface of a curved emitter is necessary to calculate the field emission current. For smooth parabolic emitting tips where space charge is negligible, variation of the electric field at the surface is known to follow the generalized cosine law. Here we investigate the validity of the cosine law in the regime where space charge due to emitted electrons is important. Particle-in-Cell (PIC) simulations with an emission algorithm based on the cosine law is employed for this study. It is shown that if $E_P$ and $E_L$ be the field at the apex of tip with and without space charge respectively, then for $\vartheta=E_P/E_L \geq 0.9$, the average relative deviation of the electric field from the cosine law is less than $3\%$ over the endcap. Thus, an emission scheme based on cosine law may be used in PIC simulations of field emission of electrons from curved emitter tips in the weak space charge regime. The relation between $\vartheta$ and normalized current $\zeta$ for curved emitters in this regime is also investigated. A linear relation, $\vartheta=1 - \delta \zeta$ (where $\delta$ is a constant), similar to that obtained theoretically for flat emitting surfaces is observed but the value of $\delta$ indicates that the extension of the theory for curved emitters may require incorporation of the field enhancement factor.

physics.app-ph↗

arXiv2020

Simulating multiscale gated field emitters -- a hybrid approach

Multi-stage cathodes are promising candidates for field emission due to the multiplicative effect in local field predicted by the Schottky conjecture and its recent corrected counterpart [J. Vac. Sci. Technol. B 38, 023208 (2020)]. Due to the large variation in length scales even in a 2-stage compound structure consisting of a macroscopic base and a microscopic protrusion, the simulation methodology of a gated field emitting compound diode needs to be revisited. As part of this strategy, the authors investigate the variation of local field on the surface of a compound emitter near its apex and find that the generalized cosine law continues to hold locally near the tip of a multi-scale gated cathode. This is used to emit charges with appropriate distributions in position and velocity components with a knowledge of only the electric field at the apex. The distributions are consistent with contemporary free-electron field emission model and follow from the joint distribution of launch angle, total energy, and normal energy. For a compound geometry with local field enhancement by a factor of around 1000, a hybrid model is used where the vacuum field calculated using COMSOL is imported into the Particle-In-Cell code PASUPAT where the emission module is implemented. Space charge effects are incorporated in a multi-scale adaptation of PASUPAT using a truncated geometry with `open electrostatic boundary' condition. The space charge field, combined with the vacuum field, is used for particle-emission and tracking.

physics.app-ph↗

arXiv2020

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 diode configuration, the space charge limited (SCL) current density from a planar emitting patch is given by the Child-Langmuir (CL) law $J_{CL} \sim V_g^{3/2}/D^2$ where $V_g$ is the potential difference across the diode and $D$ is the separation between the anode and 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 $J_{SCL} \sim \gamma_a V_g^{3/2}/D^2$ where $\gamma_a$ is the apex field enhancement factor of the curved emitter. For an emitter with large height ($h$) to apex radius of curvature ($R_a$) ratio, the limiting current far exceeds the planar value. The result is verified using the particle-in-cell code PASUPAT for two curved emitters shapes.

physics.plasm-ph↗

arXiv2019

A simple metamaterial absorber associated with Fano-like resonance

A simple metamaterial absorber suitable for fabrication over large areas associated with a Fano like resonance is proposed. The proposed designed of the metamaterial absorber consists of photoresist disk arrays on a silicon substrate followed by the deposition of a tri layer of Au, ZnS and Au on the top of the structure. Due to the tri layer, there is a formation of a cavity between the substrate and gold layer on the top of photoresist disk and a waveguide in the ZnS layer in between the gold layers on the substrate and the ZnS layer itself. The Fano like resonance arises due to the interference of the cavity mode and the guided-mode resonance as well as the Woods anomaly. The cavity mode resonance works as continuum mode whereas the guided mode resonance and Woods anomaly work as discrete modes. The spectral position of the resonance can be tuned by just controlling the thickness of the tri layer instead of the structural size and shape modification of the micro and nano-structures as usually done in conventional metamaterial absorbers. This design can be easily scaled for fabrication over large areas as it separates the structuring and deposition processes and makes them sequential thereby avoiding expensive and complex lift off or etching processes which are usually required for conventional metamaterial processing.

physics.optics↗

arXiv2017

Variation of field enhancement factor near the emitter tip

The field enhancement factor at the emitter tip and its variation in a close neighbourhood determines the emitter current in a Fowler-Nordheim like formulation. For an axially symmetric emitter with a smooth tip, it is shown that the variation can be accounted by a $\cos{\tilde{\theta}}$ factor in appropriately defined normalized co-ordinates. This is shown analytically for a hemi-ellipsoidal emitter and confirmed numerically for other emitter shapes with locally quadratic tips.

physics.app-ph↗

arXiv2015

Boundary conditions for the solution of the 3-dimensional Poisson equation in open metallic enclosures

Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable boundary condition at the open end. In this paper, methods for solving the Poisson equation are investigated for various charge densities and aspect ratios of the open ends. It is found that a mixture of second order and third order local asymptotic boundary condition (ABC) is best suited for large aspect ratios while a proposed non-local matching method, based on the solution of the Laplace equation, scores well when the aspect ratio is near unity for all charge density variations, including ones where the centre of charge is close to an open end or the charge density is non-localized. The two methods complement each other and can be used in electrostatic calculations where the computational domain needs to be terminated at the open boundaries of the metallic enclosure.

physics.comp-ph↗

arXiv2015

Thermally Induced Nonlinear Optical Absorption in Metamaterial Perfect Absorbers

A metamaterial perfect absorber consisting of a tri-layer (Al/ZnS/Al) metal-dielectric-metal system with top aluminium nano-disks is fabricated by laser-interference lithography and lift-off processing. The metamaterial absorber had peak resonant absorbance at 1090 nm and showed nonlinear absorption for 600ps laser pulses at 1064 nm wavelength. A nonlinear saturation of reflectance was measured to be dependent on the average laser power incident and not the peak laser intensity. The nonlinear behaviour is shown to arise from the heating due to the absorbed radiation and photo-thermal changes in the dielectric properties of aluminium. The metamaterial absorber is seen to be damage resistant at large laser intensities of 25 MW/cm2.

physics.optics↗

arXiv2014

Anisotropic energy transfers in quasi-static magnetohydrodynamic turbulence

We perform direct numerical simulations of quasi-static magnetohydrodynamic turbulence, and compute various energy transfers including the ring-to-ring and conical energy transfers, and the energy fluxes of the perpendicular and parallel components of the velocity field. We show that the rings with higher polar angles transfer energy to ones with lower polar angles. For large interaction parameters, the dominant energy transfer takes place near the equator (polar angle $\theta \approx \frac{\pi}{2}$). The energy transfers are local both in wavenumbers and angles. The energy flux of the perpendicular component is predominantly from higher to lower wavenumbers (inverse cascade of energy), while that of the parallel component is from lower to higher wavenumbers (forward cascade of energy). Our results are consistent with earlier results, which indicate quasi two-dimensionalization of quasi-static magnetohydrodynamic (MHD) flows at high interaction parameters.

physics.flu-dyn↗

arXiv2013

Calculating field emission currents in nanodiodes - a multi-group formalism with space charge and exchange-correlation effects

Inclusion of electron-electron interaction is essential in nano-diodes to understand the underlying physical phenomenon and tailor devices accordingly. However, both space charge and exchange-correlation interactions involve electrons at different energies and hence a self-consistent multi-energy-group solution of the Schr\{o}dinger-Poisson system is required. It is shown here that the existence of a limiting density-dependent potential at low applied voltages allows calculation of the field emission current. Despite additional interactions, a Fowler-Nordheim behaviour is observed. It is also found that the exchange-correlation potential dominates at these voltages in nanogaps and possibly leads to a higher turn-on voltage.

cond-mat.mes-hall↗

arXiv2013

The Child-Langmuir law in the quantum domain

It is shown using dimensional analysis that the maximum current density J_{QCL} transported on application of a voltage V_g across a gap of size D follows the relation J_{QCL} ~ \hbar^{3 - 2\alpha} V_g^\alpha /D^{5 - 2\alpha}. The classical Child-Langmuir result is recovered at \alpha = 3/2 on demanding that the scaling law be independent of \hbar. For a nanogap in the deep quantum regime, additional inputs in the form of appropriate boundary conditions and the behaviour of the exchange-correlation potential show that \alpha = 5/14. This is verified numerically for several nanogaps. It is also argued that in this regime, the limiting mechanism is quantum reflection from a downhill potential due to a sharp change in slope seen by the electron on emerging through the barrier.

cond-mat.mes-hall↗

arXiv2011

Transport across nanogaps using semiclassically consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density, J_c, is found to obey the local scaling law J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.

cond-mat.mes-hall↗

arXiv2006

Relation between space charge limited current and power loss in open drift tubes

Drift space is a region free from externally applied fields. It is an important part of many devices involving charged particle beams. The space charge effect imposes a limit on the current that can be transported through a drift space. A reasonable estimate of the space charge limited current density (J_{SCL}^{c}) in 'closed' drift tubes can be obtained from electrostatic considerations despite the fact that charge particle transport results in electromagnetic radiation. We deal here with the situation where the drift tube is 'open' to electromagnetic radiation, for instance due to the presence of a dielectric window. In such cases, electromagnetic radiation leaks out of the window which results in a decrease in the average kinetic energy of electrons. If the injected current density is much lower than J_{SCL}^{c}, power loss does not result in a change in the transmitted current. As the injected current density is increased, power loss increases and at a critical value lower than J_{SCL}^{c}, reflection of electrons begins to occur. We also show that the lowering of the space charge limited current on account of power loss can be incorporated in the standard electrostatic picture by introducing an effective voltage for the collection plate.

physics.plasm-ph↗

arXiv2005

Power loss in open cavity diodes and a modified Child Langmuir Law

Diodes used in most high power devices are inherently open. It is shown that under such circumstances, there is a loss of electromagnetic radiation leading to a lower critical current as compared to closed diodes. The power loss can be incorporated in the standard Child-Langmuir framework by introducing an effective potential. The modified Child-Langmuir law can be used to predict the maximum power loss for a given plate separation and potential difference as well as the maximum transmitted current for this power loss. The effectiveness of the theory is tested numerically.

physics.plasm-ph↗

arXiv2004

Generalization of Child-Langmuir Law for Non-Zero Injection Velocities in a Planar Diode

The Child-Langmuir law relates the voltage applied across a planar diode to the saturation value J_CL of current density that can be transmitted through it in case the injection velocity of electrons into the diode is zero. The Child-Langmuir current density J_CL is, at the same time, (i) the maximum current density that can be transmitted through a planar diode, (ii) the current density below which the flow is steady and unidirectional in the long time limit and (iii) the average transmitted current density for {\em any} value of injected current density above J_CL. Existing generalizations of Child-Langmuir law to non-zero velocities of injection are based on the characteristics (i) and (ii) of J_CL. This paper generalizes the law to non-zero velocities of injection based on the characteristic (iii) by deriving an analytical expression for the saturation value of current density. The analytical expression for the saturation current density is found to be well supported by numerical computations. A reason behind preferring the saturation property of the Child-Langmuir current density as the basis for its generalization is the importance of that property in numerical simulations of high current diode devices.

physics.plasm-ph↗

arXiv2004

Absence of saturation for finite injected currents in axially symmetric cavity diode

The Child-Langmuir law is investigated numerically using a fully electromagnetic particle-in-cell code for a closed axially symmetric diode. It is found that the average current transmitted to the anode increases with the injected current even after the formation of virtual cathode in both the non-relativistic and relativistic cases. The increase is found to be a power law. In other words, the time averaged fraction $f$ of electrons reaching the anode varies with the input current as, $f\sim J_{\rm IN}^{-β}$ where $β< 1$. In contrast, for an infinite parallel plate diode, $f \sim J_{\rm IN}^{-1}$. The possibility of asymptotic saturation is also discussed.

physics.plasm-ph↗