Benjamin Ragan-Kelley

Jupyter Notebooks—a publishing format for reproducible computational workflows

It is increasingly necessary for researchers in all fields to write computer code, and in order to reproduce research results, it is important that this code is published. We present Jupyter notebooks, a document format for publishing code, results and explanations in a form that is both readable and executable. We discuss various tools and use cases for notebook documents.

Two-dimensional axisymmetric Child–Langmuir scaling law

The classical one-dimensional (1D) Child–Langmuir law was previously extended to two dimensions by numerical calculation in planar geometries. By considering an axisymmetric cylindrical system with axial emission from a circular cathode of radius r, outer drift tube radius R>r, and gap length L, we further examine the space charge limit in two dimensions. Simulations were done with no applied magnetic field as well as with a large (100 T) longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit JCL2 to the theoretical 1D value JCL1 is found to be a monotonically decreasing function of the ratio of emission radius to gap separation r/L. This result is in agreement with the planar results, where the emission area is proportional to the cathode width W. The drift tube in axisymmetric systems is shown to have a small but measurable effect on the space charge limit. Strong beam edge effects are observed with J(r)/J(0) approaching 3.5. Two-dimensional ax...

Collaborative cloud-enabled tools allow rapid, reproducible biological insights

Microbial ecologists today face critical computational barriers. The rapid increase in the quantity of data acquired by modern sequencing instruments makes analysis by hand infeasible, and even software developed just a few years ago cannot scale to modern data sets. As a result, making advanced, scalable algorithms and large-scale computational resources available to end-users is necessary to advancing our understanding of microbial ecology.

Modeling a thermionic energy converter using finite-difference time-domain particle-in-cell simulations

A thermionic energy converter (TEC) is a static device that converts heat directly into electricity by boiling electrons from a hot emitter surface across a small inter electrode gap to a cooler collector surface. The main challenge in TECs is overcoming the space charge limit, which limits the amount of current that can transmit across a gap of a given voltage and width. In this preliminary work, it is found that the OOPD1 simulation results is in good agreement with analytical results. We have verified the feasibility of studying and developing a TEC using a bounded finite-difference time-domain particle-in-cell plasma simulation code, OOPD1 developed by PTSG, UC Berkeley.

Optimizing physical parameters in 1-D particle-in-cell simulations with Python

Abstract A particle-in-cell (PIC) simulation tool, OOPD1, is wrapped in the Python programming language, enabling automated algorithmic optimization of physical and numerical parameters. The Python-based environment exposes internal variables, enabling modification of simulation parameters, as well as run-time generation of new diagnostics based on calculations with internal data. For problems requiring an iterative optimization approach, this enables a programmable interactive feedback loop style simulation model, where the input to one simulation is a programmable function of the output of the previous one. This approach is applied to field-emission of electrons in a diode, in order to explore space charge effects in bipolar flow. We find an analytical solution for maximizing the space-charge limited current through a diode with an upstream ion current, and confirm the result with simulations, demonstrating the efficacy of the feedback scheme. We also demonstrate and analyze a modeling approach for scaling the ion mass, which can shorten simulation time without changing the ultimate result. The methods presented can be generalized to handle other applications where it is desirable to evolve simulation parameters based on algorithmic results from the simulation, including models in which physical or numerical parameter tuning is used to converge or optimize a system in one or more variables.

A relativistic self-consistent model for studying enhancement of space charge limited field emission due to counter-streaming ions

Recently, field emission has attracted increasing attention despite the practical limitation that field emitters operate below the Child-Langmuir space charge limit. By introducing counter-streaming ion flow to neutralize the electron charge density, the space charge limited field emission (SCLFE) current can be dramatically enhanced. In this work, we have developed a relativistic self-consistent model for studying the enhancement of SCLFE by a counter-streaming ion current. The maximum enhancement is found when the ion effect is saturated, as shown analytically. The solutions in non-relativistic, intermediate, and ultra-relativistic regimes are obtained and verified with 1-D particle-in-cell simulations. This self-consistent model is general and can also serve as a benchmark or comparison for verification of simulation codes, as well as extension to higher dimensions.

PPPS-2013: Relaxing assumptions in field-limited emission, and an iterative approach to a scaling law for space-charge limited flow in axisymmetric 2D

Summary form only given. Field-limited emission is an approach for using Gausss Law to to satisfy the space charge limit for emitting current in Particle-in-Cell simulations. A thorough analysis is done of the assumptions made in prior implementations, and corrections are introduced for cylindrical geometry, non-zero injection velocity, and non-zero surface field. Particular care is taken to determine special conditions for the outermost node, where we find that forcing a balance of Gausss Law would be incorrect. The scheme is then applied to determine a scaling law for the Child-Langmuir limit in an axisymmetric planar diode, with finite initial velocity. We find that the new scheme reproduces prior results, in significantly less computation time, due to no longer needing to overinject and to rapid convergence of the surface field using our new algorithmic optimization wrapper to seek the local limiting current along an emitter.

Two-dimensional axisymmetric Child-Langmuir scaling law

The one-dimensional Child-Langmuir law has been extended to two dimensions by numerical simulation in planar geometries . The space charge limit in two dimensions is examined. Simulations were done with no applied magnetic field as well as with a large longitudinal magnetic field to restrict motion of particles to 1D. The ratio of the observed current density limit JCL2 to the theoretical one-dimensional value JCL1 is found to be a mono- tonically decreasing function of the ratio of emission radius (r) to gap separation (L). This result is in agreement with the planar results, where the emission area is proportional to the cathode width. The simulations were run in the particle in cell code. Least-squares fits to a log-log plot for no applied magnetic field.