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Title: Numerical simulation of two-dimensional electron transport in cylindrical nanostructures using Wigner function methods

Abstract

We have constructed a lattice Wigner-Weyl code to expand the Buot-Jensen algorithm to calculation of electron transport in two-dimensional cylindrically symmetric structures. Almost all of the numerical simulations to date have dealt with the restricted problem of one-dimensional 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 four-dimensional 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:
 [1];  [2];  [2]
  1. Applied Electronics Laboratory, Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ 07030 (United States). E-mail: gjr5y@virginia.edu
  2. 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: S0021-9991(05)00136-1; 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; CHARGED-PARTICLE TRANSPORT; COMPUTERIZED SIMULATION; COORDINATES; CYLINDRICAL CONFIGURATION; ELECTRONS; EQUATIONS; FUNCTIONS; MATHEMATICAL EVOLUTION; NANOSTRUCTURES; ONE-DIMENSIONAL CALCULATIONS; PARALLEL PROCESSING; POTENTIALS; TWO-DIMENSIONAL CALCULATIONS; WIGNER THEORY

Citation Formats

Recine, Greg, Rosen, Bernard, and Cui, H.-L.. Numerical simulation of two-dimensional 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 two-dimensional 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 two-dimensional 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 two-dimensional 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 Wigner-Weyl code to expand the Buot-Jensen algorithm to calculation of electron transport in two-dimensional cylindrically symmetric structures. Almost all of the numerical simulations to date have dealt with the restricted problem of one-dimensional 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 four-dimensional 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 two-dimensional (2-D) 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.
  • 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 three-dimensional particle-in-cell 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 Multiplication-Sign B drift at a speed of {approx}1.0 Multiplication-Sign 10{sup 6} m/s (about 37% of the E Multiplication-Sign B drift speed). Local charge separation occurs because the azimuthal local electron density concentration is accompanied by an almost uniform azimuthal ion distribution. The non-axisymmetrical electron density concentration andmore » axisymmetrical ion distribution introduce two azimuthal electric fields with opposite directions in the plasma discharge region. The axial electron shear flow is excited under the additional E{sub {theta}} Multiplication-Sign B field. The anomalous electron transport with the rotating spoke may be attributed to the axial electron shear flow induced by the two azimuthal electric fields with opposite directions as a result of the azimuthal local electron density concentration.« less
  • 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.
  • 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 Multiplication-Sign 10{sup 6} m/s on the surface of the anode. Accompanied by the almost uniform azimuthal ion distribution, the non-axisymmetric 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 » axial electron drift upstream and downstream due to the additional E{sub {theta}} x B field and then the axial shear flow is generated. The axial local charge separation induced by the axial shear electron flow may be compensated by the azimuthal electron transport, finally resulting in the azimuthal electric field rotation and electron transport with the rotating spoke.« less