Implementation of the Wigner-Boltzmann transport equation within particle Monte Carlo simulation

Querlioz, Damien; Saint-Martin, Jérôme; Dollfus, Philippe

doi:10.1007/s10825-010-0319-6

Cited by 13 publications

(6 citation statements)

References 35 publications

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“…In these cases, it might be more efficient to consider decomposition of the partially coherent light into orthogonal mutually incoherent modes and to include the diffraction effects on each mode separately. Nonlinear optical elements similarly pose a challenge for an efficient WDF transport, even though examples of Monte Carlo quantum transport using the Wigner distribution are finding increasing application for the semiconductor devices [46]. Borrowing some of these techniques may yield a practical method capable of including all the relevant phenomena for the x-ray transport line design.…”

Section: Discussionmentioning

confidence: 99%

Synchrotron radiation representation in phase space

Bazarov

2012

Phys. Rev. ST Accel. Beams

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The notion of brightness is efficiently conveyed in geometric optics as density of rays in phase space. Wigner has introduced his famous distribution in quantum mechanics as a quasiprobability density of a quantum system in phase space. Naturally, the same formalism can be used to represent light including all the wave phenomena as originally done by Walther and for synchrotron radiation by Kim. It provides a natural framework for radiation propagation and optics matching by transferring the familiar ''baggage'' of accelerator physics ( function, emittance, phase-space transforms, etc.) to synchrotron radiation. More specifically, the use of Wigner distribution formalism allows a rigorous description of partially coherent non-Gaussian sources, which is generally the case for synchrotron radiation from an undulator with a high degree of transverse coherence. This paper reviews many of the properties of the Wigner distribution starting from quantum mechanics and provides examples of how its use enables physically insightful description of partially coherent synchrotron radiation in phase space. The concepts of diffraction limit and coherence are given an exact correspondence to their quantum mechanical counterparts. In particular, it is shown that the undulator radiation on resonance by a single electron is not diffraction limited though fully coherent. An extension of how to account for practically important cases of electron beams with nearly diffraction limited emittances is presented along with a discussion of appropriate figures of merit suitable for comparing future light sources.

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Section: Discussionmentioning

confidence: 99%

Synchrotron radiation representation in phase space

Bazarov

2012

Phys. Rev. ST Accel. Beams

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“…Page 123 of 127 (E) directed along the tube axis, can be described as electron propagation along the CNT interrupted instantaneously by emission or absorption of phonon. Nonequilibrium field dependent electron distribution f(k) in conduction bands, obtained from steady-state Boltzmann transport equation solved in k space, is used to calculate drift velocity [16,17,9]. Electron distribution in the presence of uniform electric field oriented along the tube axis is calculated numerically by solving multi-band Boltzmann transport equation given by…”

Section: Electron Transport Equationmentioning

confidence: 99%

Current Distribution Dependence on Electric Field in Helically Coiled Carbon Nanotubes

Popović

Vuković

Nikolić

et al. 2017

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Experimentally is confirmed that helically coiled carbon nanotube (HCCNT) could be used as a small solenoid for generating spatially localized magnetic field. Current distribution during diffusive electronic transport likewise the inductivity of this quantum conductor depends on electric field. Despite slightly lower electron mobility in HCCNTs than that of the straight single wall carbon nanotubes, the coiled nanotubes are attractive for application as nonlinear nano-solenoids. Nonequilibrium electron distribution functions obtained by solving Boltzmann transport equation are used to predict average helical radius of current flow as a function of electric field intensity. Change of spatial distribution of electronic flow with applied electric field is considered and nonlinear inductivity of HCCNT is predicted.

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“…which is solved numerically [6] with commonly used simplification, known as low density approximation 𝑓𝑓(𝑘𝑘, 𝑚𝑚) ≪ 1. All permitted channels [15] are found numerically and accounted in total scattering rate of accelerated electrons, often distributed in different bands.…”

Section: Electron-phonon Interaction and Boltzmann Transport Equationmentioning

confidence: 99%

Prediction of Electron Drift Velocity in Helically Coiled Carbon Nanotubes

Popović

Vuković

Nikolić

et al. 2016

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We studied electron transport in single wall carbon nanotubes placed in stationary homogeneous electric fields, oriented along tubes. Electron distributions for various electric fields are determined by solving stationary multi bands Boltzmann transport equation in presence of electron phonon scattering mechanisms. Contributions of all possible scattering channels, allowed by selection rules and energy conservation, are taken into account for finding scattering rate and collision integrals. As it is previously predicted, large electron drift velocities in straight single wall carbon nanotubes are obtained. Frequent electron scattering as well as low group velocity have strong impact on reduction of drift velocity in helically coiled carbon nanotubes.

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Implementation of the Wigner-Boltzmann transport equation within particle Monte Carlo simulation

Cited by 13 publications

References 35 publications

Synchrotron radiation representation in phase space

Synchrotron radiation representation in phase space

Current Distribution Dependence on Electric Field in Helically Coiled Carbon Nanotubes

Prediction of Electron Drift Velocity in Helically Coiled Carbon Nanotubes

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