Numerical simulation of twodimensional electron transport in cylindrical nanostructures using Wigner function methods
Abstract
We have constructed a lattice WignerWeyl code to expand the BuotJensen algorithm to calculation of electron transport in twodimensional cylindrically symmetric structures. Almost all of the numerical simulations to date have dealt with the restricted problem of onedimensional transport. In real devices, electrons are not confined to a single transport dimension and the coulombic potential is fully present and felt in three dimensions. We show the derivation of the 2D equation in cylindrical coordinates as well as approximations employed in the calculation of the fourdimensional convolution integral of the Wigner function and the potential. We work under the assumption that longitudinal transport is more dominant than radial transport and employ parallel processing techniques. The total transport is calculated in two steps: (1) transport the particles in the longitudinal direction in each shell separately, then (2) each shell exchanges particles with its nearest neighbor. Most of this work is concerned with the former step: A 1D space and 2D momentum transport problem. Time evolution simulations based on these method are presented for three different cases. Each case lead to numerical results consistent with expectations. Discussions of future improvements are discussed.
 Authors:
 Applied Electronics Laboratory, Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ 07030 (United States). Email: gjr5y@virginia.edu
 Applied Electronics Laboratory, Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ 07030 (United States)
 Publication Date:
 OSTI Identifier:
 20687260
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 209; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2005.03.009; PII: S00219991(05)001361; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; CHARGEDPARTICLE TRANSPORT; COMPUTERIZED SIMULATION; COORDINATES; CYLINDRICAL CONFIGURATION; ELECTRONS; EQUATIONS; FUNCTIONS; MATHEMATICAL EVOLUTION; NANOSTRUCTURES; ONEDIMENSIONAL CALCULATIONS; PARALLEL PROCESSING; POTENTIALS; TWODIMENSIONAL CALCULATIONS; WIGNER THEORY
Citation Formats
Recine, Greg, Rosen, Bernard, and Cui, H.L.. Numerical simulation of twodimensional electron transport in cylindrical nanostructures using Wigner function methods. United States: N. p., 2005.
Web. doi:10.1016/j.jcp.2005.03.009.
Recine, Greg, Rosen, Bernard, & Cui, H.L.. Numerical simulation of twodimensional electron transport in cylindrical nanostructures using Wigner function methods. United States. doi:10.1016/j.jcp.2005.03.009.
Recine, Greg, Rosen, Bernard, and Cui, H.L.. Tue .
"Numerical simulation of twodimensional electron transport in cylindrical nanostructures using Wigner function methods". United States.
doi:10.1016/j.jcp.2005.03.009.
@article{osti_20687260,
title = {Numerical simulation of twodimensional electron transport in cylindrical nanostructures using Wigner function methods},
author = {Recine, Greg and Rosen, Bernard and Cui, H.L.},
abstractNote = {We have constructed a lattice WignerWeyl code to expand the BuotJensen algorithm to calculation of electron transport in twodimensional cylindrically symmetric structures. Almost all of the numerical simulations to date have dealt with the restricted problem of onedimensional transport. In real devices, electrons are not confined to a single transport dimension and the coulombic potential is fully present and felt in three dimensions. We show the derivation of the 2D equation in cylindrical coordinates as well as approximations employed in the calculation of the fourdimensional convolution integral of the Wigner function and the potential. We work under the assumption that longitudinal transport is more dominant than radial transport and employ parallel processing techniques. The total transport is calculated in two steps: (1) transport the particles in the longitudinal direction in each shell separately, then (2) each shell exchanges particles with its nearest neighbor. Most of this work is concerned with the former step: A 1D space and 2D momentum transport problem. Time evolution simulations based on these method are presented for three different cases. Each case lead to numerical results consistent with expectations. Discussions of future improvements are discussed.},
doi = {10.1016/j.jcp.2005.03.009},
journal = {Journal of Computational Physics},
number = 2,
volume = 209,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}

Turbulent transport with trapped electrons is simulated with a twodimensional (2D) representation. The trapped particles are lumped into hot and cold fluids to treat temperature gradient effects. The ion temperature gradient and dissipative trapped electron modes are simultaneously present. The hot and cold lumped fluid model was found to represent the true kinetic model linearly. The numerically simulated transport compares very well with detailed quasilinear expressions. A plasma particle pinch is found only at extremely low collisionalities and a heat conduction pinch is found at moderate collisionalities, although there is no energy flow pinch seen.

Threedimensional numerical investigation of electron transport with rotating spoke in a cylindrical anode layer Hall plasma accelerator
The effects of increased magnetic field and pressure on electron transport with a rotating spoke in a cylindrical anode layer Hall plasma accelerator are investigated by threedimensional particleincell numerical simulation. The azimuthal rotation of electron transport with the spoke has a frequency of 12.5 MHz. It propagates in the direction of the E MultiplicationSign B drift at a speed of {approx}1.0 MultiplicationSign 10{sup 6} m/s (about 37% of the E MultiplicationSign B drift speed). Local charge separation occurs because the azimuthal local electron density concentration is accompanied by an almost uniform azimuthal ion distribution. The nonaxisymmetrical electron density concentration andmore » 
Comment on 'Threedimensional numerical investigation of electron transport with rotating spoke in a cylindrical anode layer Hall plasma accelerator'[Phys. Plasmas 19, 073519 (2012)]
The oscillation behavior described by Tang et al.[Phys. Plasmas 19, 073519 (2012)] differs too greatly from previous experimental and numerical studies to claim observation of the same phenomenon. Most significantly, the rotation velocity by Tang et al.[Phys. Plasmas 19, 073519 (2012)] is three orders of magnitude larger than that of typical 'rotating spoke' phenomena. Several physical and numerical considerations are presented to more accurately understand the numerical results of Tang et al.[Phys. Plasmas 19, 073519 (2012)] in light of previous studies. 
Response to 'Comment on 'Threedimensional numerical investigation of electron transport with rotating spoke in a cylindrical anode layer Hall plasma accelerator''[Phys. Plasmas 20, 014701 (2013)]
The numerical simulation described in our paper [D. L. Tang et al., Phys. Plasmas 19, 073519 (2012)] shows a rotating dense plasma structure, which is the critical characteristic of the rotating spoke. The simulated rotating spoke has a frequency of 12.5 MHz with a rotational speed of {approx}1.0 MultiplicationSign 10{sup 6} m/s on the surface of the anode. Accompanied by the almost uniform azimuthal ion distribution, the nonaxisymmetric electron distribution introduces two azimuthal electric fields with opposite directions. The azimuthal electric fields have the same rotational frequency and speed together with the rotating spoke. The azimuthal electric fields excite themore »