Simple theory for the two-dimensional Child-Langmuir law

Hierarchical Morphing Control of an Ultra-Lightweight Electro-Actuated Polymer Telescope with Thin-Film Actuators

This paper explores advanced shape control techniques for ultra-lightweight electro-actuated polymers with composite ferroelectric thin films. It begins with an overview of PVDF-TrFE film actuators used in the development of thin-shell composites, emphasizing the need to overcome constraints related to the electrode size for successful scalability. Strain generation in thin-film actuators is investigated, including conventional electrode-based methods and non-contact electron flux excitation. Numerical studies incorporate experimentally calibrated ferroelectric parameters, modeling non-contact actuation with an equivalent circuit representation. The potential distribution generated by electron flux injection highlights its potential for reducing print-through actuation issues. Additionally, the paper outlines a vision for the future of large thin-shell reflectors by integrating the discussed methods for charging ferroelectric polymer films. A hierarchical control strategy is proposed, combining macro- and micro-scale techniques to rectify shape errors in lightweight reflectors. These strategies offer the potential to enhance precision and performance in future spaceborne observation systems, benefiting space exploration and communication technologies.

Space-charge-limited current density for nonplanar diodes with monoenergetic emission using Lie-point symmetries

Understanding space-charge-limited current density (SCLCD) is fundamentally and practically important for characterizing many high-power and high-current vacuum devices. Despite this, no analytic equations for SCLCD with nonzero monoenergetic initial velocity have been derived for nonplanar diodes from first principles. Obtaining analytic equations for SCLCD for nonplanar geometries is often complicated by the nonlinearity of the problem and over constrained boundary conditions. In this Letter, we use the canonical coordinates obtained by identifying Lie-point symmetries to linearize the governing differential equations to derive SCLCD for any orthogonal diode. Using this method, we derive exact analytic equations for SCLCD with a monoenergetic injection velocity for one-dimensional cylindrical, spherical, tip-to-tip (t-t), and tip-to-plate (t-p) diodes. We specifically demonstrate that the correction factor from zero initial velocity to monoenergetic emission depends only on the initial kinetic and electric potential energies and not on the diode geometry and that SCLCD is universal when plotted as a function of the canonical gap size. We also show that SCLCD for a t-p diode is a factor of four larger than a t-t diode independent of injection velocity. The results reduce to previously derived results for zero initial velocity using variational calculus and conformal mapping.

ISIS Penning source extraction studies reveal the 3-dimensional Child-Langmuir effect

The standard 1X ISIS negative Penning surface plasma source has reliably produced an H^- beam for ISIS operations for 35 years. In order to meet the 60 mA, 2 ms, and 50 Hz beam current and duty cycle required for the front end test stand (Letchford et al., in Proceedings of IPAC2015, Richmond, VA, USA, 2015), a 2X scaled source has been developed [Faircloth et al., AIP Conf. Proc. 2052, 050004 (2018)]. The 2X source has a plasma chamber twice the linear dimensions of the 1X source. This paper investigates the comparison between different emission areas (plasma electrode aperture dimensions) for both the 1X and 2X sources. Slit and circular extraction schemes are studied. A 3D Child-Langmuir relationship is observed where the space charge limited current density depends on the aspect ratio of the extraction aperture.

Role of the pre-plasma on electron beam currents from a biased laser-plasma

We are investigating laser-plasmas produced in the interaction of a 1 J 9 ns Nd:YAG laser with a solid metal target as a source of electrons. An electron beam pulsed at the laser repetition rate is produced by biasing the target and making the plasma expand in an electric field. In this paper, we focus on the measured beam currents and charge surface distribution of the beam. The peak beam currents are much higher than what is given by a simplified toy model based on the Child-Langmuir limit in a vacuum and the charge surface distributions are inhomogeneous. Both these observations are explained by the presence of a positive preplasma expanding ahead of the laser-plasma front edge.

Novel scaling laws for the Langmuir-Blodgett solutions in cylindrical and spherical diodes

It is found that the Langmuir-Blodgett solutions for the space charge limited current density, for both cylindrical and spherical diodes, may be approximated by Japp=(4/9)ε0sqrt[(2e/m)](Ec3/2/sqrt[D]) over a wide range of parameters, where Ec is the surface electric field on the cathode of the vacuum diode and D is the anode-cathode spacing. This dependence is valid whether Ra/Rc is greater than or less than unity, where Ra and Rc are, respectively, the anode and cathode radius. Minor empirical corrections to the above scaling yield fitting formulas that are accurate to within 5% for 3×10(-5)<Rc/Ra<500. An explanation of this scaling is given. An accurate transit time model yields the Langmuir-Blodgett solutions even in the Coulomb blockade regime for a nanogap, where the electron number may be in the single digits, and the transit time frequency is in the THz range.

SIMULATION OF HIGH CURRENT FIELD EMISSION FROM VERTICALLY WELL-ALIGNED METALLIC CARBON NANOTUBES

We have studied the intense electron beams emitted from multiple metallic, vertical and well-aligned Carbon Nanotube (CNT) field emitters. A two-dimensional (2D) particle-in-cell simulation code MAGIC2D is used to obtain the I–V characteristics near to the apex of the emitters' surface for a given applied electric field and field enhancement factor over a wide range of parameters. The effects of electron space charge and electric field shielding from neighboring emitters are compared in low current and high current regimes. It is found that the electron space charge is dominant in high current regime, where the Fowler–Nordheim (FN) law becomes the 2D Child–Langmuir (CL) law. The emitter spacing, number of emitters, and emitter's uniformity are also particularly studied, and they are more critical in low current regime. Smooth transition from the FN law to CL law is demonstrated.

Interpretation and implementation of an ion sensitive probe as a plasma potential diagnostic

An ion sensitive probe (ISP) is developed as a robust diagnostic for measuring plasma potentials (Φ(P)) in magnetized plasmas. The ISP relies on the large difference between the ion and electron gyroradii (ρ(i)/ρ(e)∼60) to reduce the electron collection at a collector recessed behind a separately biased wall distance ∼ρ(i). We develop a new ISP method to measure the plasma potential that is independent of the precise position and shape of the collector. Φ(P) is found as the wall potential when charged current to the probe collector vanishes during the voltage sweep. The plasma potentials obtained from the ISP match Φ(P) measured with an emissive probe over a wide range of plasma conditions in a small magnetized plasma.

Space-charge modulation in vacuum microdiodes at THz frequencies

We investigate the dynamics of a space-charge limited, photoinjected, electron beam in a microscopic vacuum diode. Because of the small nature of the system it is possible to conduct high-resolution simulations where the number of simulated particles is equal to the number of electrons within the system. In a series of simulations of molecular dynamics type, where electrons are treated as point charges, we address and analyze space-charge effects in a micrometer-scale vacuum diode. We have been able to reproduce breakup of a single pulse injected with a current density beyond the Child-Langmuir limit, and we find that continuous injection of current into the diode gap results in a well-defined train of electron bunches corresponding to THz frequency. A simple analytical explanation of this behavior is given.

Nonlinear theory for a quantum diode in a dense Fermi magnetoplasma

We present a simple analytical nonlinear theory for quantum diodes in a dense Fermi magnetoplasma. By using the steady-state quantum hydrodynamical equations for a dense Fermi magnetoplasma, we derive coupled nonlinear Schrödinger and Poisson equations. The latter are numerically solved to show the effects of the quantum statistical pressure, the quantum tunneling (or the quantum diffraction), and the external magnetic field strength on the potential and electron density profiles in a quantum diode at nanometer scales. It is found that the quantum statistical pressure introduces a lower bound on the steady electron flow in the quantum diode, while the quantum diffraction effect allows the electron tunneling at low flow speeds. The magnetic field acts as a barrier, and larger potentials are needed to drive currents through the quantum diode.

Ultrashort-pulse child-langmuir law in the quantum and relativistic regimes

This Letter presents a consistent quantum and relativistic model of short-pulse Child-Langmuir (CL) law, of which the pulse length tau is less than the electron transit time in a gap of spacing D and voltage V. The classical value of the short-pulse CL law is enhanced by a large factor due to quantum effects when the pulse length and the size of the beam are, respectively, in femtosecond duration and nanometer scale. At high voltage larger than the electron rest mass, relativistic effects will suppress the enhancement of short-pulse CL law, which is confirmed by particle-in-cell simulation. When the pulse length is much shorter than the gap transit time, the current density is proportional to V, and to the inverse power of D and tau.

New scaling of child-langmuir law in the quantum regime

This paper presents a consistent quantum mechanical model of Child-Langmuir (CL) law, including electron exchange-correlation interaction, electrode's surface curvature, and finite emitter area. The classical value of the CL law is increased by a larger factor due to the electron tunneling through the space-charge potential, and the electron exchange-correlation interaction becomes important when the applied gap voltage Vg and the gap spacing D are, respectively, on the order of Hartree energy level, and nanometer scale. It is found that the classical scaling of Vg(3/2) and D(-2) is no longer valid in the quantum regime, and a new scaling of Vg(1/2) and D(-4) is established. The smooth transition from the classical regime to the quantum regime is also demonstrated.

Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field

An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.