Engineering topics

Garner, Allen L.

Publications and source records attributed to Garner, Allen L..

5 records

DOE OSTI2024

Theoretical Assessment of the Transition Between Electron Emission Mechanisms for Nonplanar Diodes

Theoretically and computationally describing the operation of nanodiodes requires characterizing the transitions between multiple electron emission mechanisms for nanodiodes with complicated geometries. This motivates our development of techniques to determine when simplified theories for individual mechanisms suffice compared to more complete, but more computationally expensive, models. Leveraging recent theories that define a canonical gap distance to translate planar theory to nonplanar diodes, we derive the conditions for the transitions among thermal emission, field emission, and space-charge-limited current density (SCLCD) in vacuum and with collisions for non-Cartesian coordinate systems, including spherical, cylindrical, and prolate spheroidal coordinate systems. Particle-in-cell (PIC) simulations of the current density as a function of applied voltage for a tip-to-plate geometry in vacuum agreed qualitatively with the asymptotes for thermal emission at low voltage and SCLCD at higher voltage using the canonical gap distance. As a result, this demonstrates the utility of this approach for guiding system design and suggests future extensions to save simulation time for more realistic geometries that are more computationally expensive.

Conformal mapping↗

DOE OSTI2024

Limiting current in a collisional crossed-field gap

Crossed-field devices are often used in pulsed power and high-power microwave applications. Previous studies derived closed-form solutions for the limiting current of a vacuum crossed-field system, corresponding to the maximum permissible current for laminar flow, below and above the Hull cutoff B H for magnetic insulation. We extend these studies by introducing collision frequency into the electron force law as a friction term to derive the limiting current in a collisional crossed-field gap. The resulting solution recovers the vacuum crossed-field case in the limit of no collisions and the collisional space-charge limited current with general initial velocity for magnetic field B → 0. In the limit of infinite collisions, we obtain a crossed-field equivalent to the Mott–Gurney law for the maximum current permissible in a collisional, nonmagnetic diode. When the collision frequency ν is less than the electron cyclotron frequency Ω, increasing initial velocity makes the critical current nonmonotonic with increasing ν with the critical current higher at B = B H for ν = Ω. As for a misaligned crossed-field gap where a component of the magnetic field was introduced parallel to the electric field across the gap, magnetic insulation is eliminated and the discontinuity at B = B H for limiting current observed in a vacuum crossed-field gap vanishes. As B → ∞, the limiting current approaches a constant that depends on the initial velocity and the collision frequency.

Breen, Lorin I.↗

DOE OSTI2024

Rapid Demonstration of Bremsstrahlung Diode Optimization

Optimization of the radiation pattern from a Bremsstrahlung target for a given application is possible by controlling the electron beam that impacts the high-atomic-number target. In this work, the electron beam is generated by a 13MV vacuum diode that terminates a coaxial magnetically insulted transmission line (MITL) on the HERMES-III machine at Sandia National Labs. Work by Sanford introduced a geometry for vacuum diodes that can control the flow within bounds. The "indented anode", as coined by Sanford, can straighten out the electron beam in a high-current diode that would otherwise be prone to beam pinching. A straighter beam will produce a more forwardly directed radiation pattern while a pinching electron beam will yield a focal point or hot spot on axis and a more diffuse radiation pattern. Either one of these may be desirable depending on the application. This work serves as a first attempt to optimize the radiation pattern in the former sense of collimating the radiation pattern given a limited parameter space. The optimization is attempted first using electromagnetic particle-in-cell simulations in the EMPIRE code suite. The setup of the models used in EMPIRE is discussed along with some basic theory behind some of the models used in the simulations such as anode heating and secondary ions. Theoretical work performed by Allen Garner and his students at Purdue is included here, which concerns the impact of collisions in these vacuum diodes. The EMPIRE simulations consider both an aggressive and a conservative design. The aggressive design is inherently riskier while the conservative design is chosen as something that, while still a risk, is more likely to perform as expected. The ultimate goal of this work was to validate the EMPIRE code results with experimental data. While the experiment that tested the diode designs proposed by the simulation results fell outside of the fiscal boundaries of this project (and for that reason the results of which are not included in this report), the hardware for the experiment was designed and drafted within those same fiscal boundaries, and is thus included in this report. However, there was yet another experiment performed in this project that tested a key feature of the diode: the hemispherical cathode. Those results are documented here as well, which show that the cathode tip is an important aspect to controlling the diode flow. A short series of simulations on this diode were also performed after the experiment in order to gain a better understanding of the effect of ions. on the flow pattern and faceplate dose profile.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

The transition from field emission to collisional space-charge limited current with nonzero initial velocity

Abstract Multiple electron emission mechanisms often contribute in electron devices, motivating theoretical studies characterizing the transitions between them. Previous studies unified thermionic and field emission, defined by the Richardson-Laue-Dushman (RLD) and Fowler–Nordheim (FN) equations, respectively, with the Child-Langmuir (CL) law for vacuum space-charge limited current (SCLC); another study unified FN and CL with the Mott-Gurney (MG) law for collisional SCLC. However, thermionic emission, which introduces a nonzero injection velocity, may also occur in gas, motivating this analysis to unify RLD, FN, CL, and MG. We exactly calculate the current density as a function of applied voltage over a range of injection velocity (i.e., temperature), mobility, and gap distance. This exact solution approaches RLD, FN, and generalized CL (GCL) and MG (GMG) for nonzero injection velocity under appropriate limits. For nonzero initial velocity, GMG approaches zero for sufficiently small applied voltage and mobility, making these gaps always space-charge limited by either GMG at low voltage or GCL at high voltage. The third-order nexus between FN, GMG, and GCL changes negligibly from the zero initial velocity calculation over ten orders of magnitude of applied voltage. These results provide a closed form solution for GMG and guidance on thermionic emission in a collisional gap.

42 ENGINEERING↗

DOE OSTI2022

Collisional Effects on Electron Trajectories in Crossed-Field Devices

Crossed-field diodes (CFDs) are used in multiple high-power applications and are characterized by an applied magnetic field orthogonal to the electric field, induced by the applied voltage across the anode-cathode gap. In vacuum, the Hull cutoff magnetic field (HCMF) represents the maximum applied magnetic field for which an electron from the cathode can reach the anode. This study investigates the effects of non-vacuum conditions on electron trajectories by introducing electron mobility, which represents particle collisions. We used numerical solutions of the electron force law and particle-in-cell simulations (XPDP1) to assess electron motion for various electron mobilities. For magnetic fields above the HCMF in vacuum, reducing the electron mobility increases the time for an electron emitted from the cathode to reach the anode. Reducing mobility below 22 C s/kg eliminates the HCMF for any magnetic field, meaning that an emitted electron will always cross the gap. We derived the magnetic field, mobility, and electron transit time corresponding to this condition by solving for the condition when the electron velocity in the direction across the anode-cathode gap going to zero at the anode. A parametric study of these conditions using theory and XPDP1 is performed under different gap distances, voltages, and magnetic fields.

42 ENGINEERING↗