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Title: Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam

Abstract

Here, we present the design of a volumetric metamaterial (MTM) structure and its interaction with a relativistic electron beam. This novel structure has promising applications in particle beam diagnostics, acceleration, and microwave generation. The volumetric MTM has a cubic unit cell allowing structures of arbitrary size to be configured as an array of identical cells. This structure allows the exploration of the properties of a metamaterial structure without having to consider substrates or other supporting elements. The dispersion characteristics of the unit cell are obtained using eigenmode simulations in the hfss code and also using an effective medium theory with spatial dispersion. Good agreement is obtained between these two approaches. The lowest-order mode of the MTM structure is found to have a negative group velocity in all directions of propagation. The frequency spectrum of the radiation from a relativistic electron beam passing through the MTM structure is calculated analytically and also calculated with the cst code, with very good agreement. The radiation pattern from the relativistic electron beam is found to be backward Cherenkov radiation, which is a promising tool for particle diagnostics. Calculations are also presented for the application of a MTM-based wakefield accelerator as a possible all-metal replacementmore » for the conventional dielectric wakefield structure. The proposed structure may also be useful for MTM-based vacuum electron devices for microwave generation and amplification.« less

Authors:
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1212118
Alternate Identifier(s):
OSTI ID: 1454578
Grant/Contract Number:  
SC0010075; FA 550-12-1-0489
Resource Type:
Published Article
Journal Name:
Physical Review Special Topics. Accelerators and Beams
Additional Journal Information:
Journal Name: Physical Review Special Topics. Accelerators and Beams Journal Volume: 18 Journal Issue: 8; Journal ID: ISSN 1098-4402
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE

Citation Formats

Lu, Xueying, Shapiro, Michael A., and Temkin, Richard J. Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam. United States: N. p., 2015. Web. doi:10.1103/PhysRevSTAB.18.081303.
Lu, Xueying, Shapiro, Michael A., & Temkin, Richard J. Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam. United States. https://doi.org/10.1103/PhysRevSTAB.18.081303
Lu, Xueying, Shapiro, Michael A., and Temkin, Richard J. Tue . "Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam". United States. https://doi.org/10.1103/PhysRevSTAB.18.081303.
@article{osti_1212118,
title = {Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam},
author = {Lu, Xueying and Shapiro, Michael A. and Temkin, Richard J.},
abstractNote = {Here, we present the design of a volumetric metamaterial (MTM) structure and its interaction with a relativistic electron beam. This novel structure has promising applications in particle beam diagnostics, acceleration, and microwave generation. The volumetric MTM has a cubic unit cell allowing structures of arbitrary size to be configured as an array of identical cells. This structure allows the exploration of the properties of a metamaterial structure without having to consider substrates or other supporting elements. The dispersion characteristics of the unit cell are obtained using eigenmode simulations in the hfss code and also using an effective medium theory with spatial dispersion. Good agreement is obtained between these two approaches. The lowest-order mode of the MTM structure is found to have a negative group velocity in all directions of propagation. The frequency spectrum of the radiation from a relativistic electron beam passing through the MTM structure is calculated analytically and also calculated with the cst code, with very good agreement. The radiation pattern from the relativistic electron beam is found to be backward Cherenkov radiation, which is a promising tool for particle diagnostics. Calculations are also presented for the application of a MTM-based wakefield accelerator as a possible all-metal replacement for the conventional dielectric wakefield structure. The proposed structure may also be useful for MTM-based vacuum electron devices for microwave generation and amplification.},
doi = {10.1103/PhysRevSTAB.18.081303},
journal = {Physical Review Special Topics. Accelerators and Beams},
number = 8,
volume = 18,
place = {United States},
year = {2015},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevSTAB.18.081303

Citation Metrics:
Cited by: 4 works
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Figures / Tables:

FIG. 1 FIG. 1: Unit cell design geometry. (a) Face view. The thickness of each face is 0.26 mm. (b) 3D view. In later sections, we will introduce the electron beam that goes through the center of the beam holes of the cells lying on the beam line.

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Works referenced in this record:

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C.</span> </li> <li> Physical Review D, Vol. 36, Issue 8</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevD.36.2283" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevD.36.2283<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevLett.61.2756" target="_blank" rel="noopener noreferrer" class="name">Experimental Demonstration of Wake-Field Effects in Dielectric Structures<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1988-12-01">December 1988</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Gai, W.; Schoessow, P.; Cole, B.</span> </li> <li> Physical Review Letters, Vol. 61, Issue 24</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevLett.61.2756" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevLett.61.2756<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1063/1.4897392" target="_blank" rel="noopener noreferrer" class="name">Sub-wavelength waveguide loaded by a complementary electric metamaterial for vacuum electron devices<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-10-01">October 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Duan, Zhaoyun; Hummelt, Jason S.; Shapiro, Michael A.</span> </li> <li> Physics of Plasmas, Vol. 21, Issue 10</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1063/1.4897392" class="text-muted" target="_blank" rel="noopener noreferrer">10.1063/1.4897392<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1088/0953-8984/20/29/295222" target="_blank" rel="noopener noreferrer" class="name">Taming spatial dispersion in wire metamaterial<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2008-07-01">July 2008</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Demetriadou, A.; Pendry, J. B.</span> </li> <li> Journal of Physics: Condensed Matter, Vol. 20, Issue 29</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1088/0953-8984/20/29/295222" class="text-muted" target="_blank" rel="noopener noreferrer">10.1088/0953-8984/20/29/295222<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevLett.108.244801" target="_blank" rel="noopener noreferrer" class="name">Dielectric Wakefield Acceleration of a Relativistic Electron Beam in a Slab-Symmetric Dielectric Lined Waveguide<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2012-06-01">June 2012</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Andonian, G.; Stratakis, D.; Babzien, M.</span> </li> <li> Physical Review Letters, Vol. 108, Issue 24</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevLett.108.244801" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevLett.108.244801<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevE.70.016608" target="_blank" rel="noopener noreferrer" class="name">Robust method to retrieve the constitutive effective parameters of metamaterials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2004-07-01">July 2004</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Chen, Xudong; Grzegorczyk, Tomasz M.; Wu, Bae-Ian</span> </li> <li> Physical Review E, Vol. 70, Issue 1</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevE.70.016608" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevE.70.016608<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1364/OL.31.002051" target="_blank" rel="noopener noreferrer" class="name">Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-01-01">January 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Shapiro, M. A.; Shvets, G.; Sirigiri, J. R.</span> </li> <li> Optics Letters, Vol. 31, Issue 13</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1364/OL.31.002051" class="text-muted" target="_blank" rel="noopener noreferrer">10.1364/OL.31.002051<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1126/science.1133628" target="_blank" rel="noopener noreferrer" class="name">Metamaterial Electromagnetic Cloak at Microwave Frequencies<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-11-10">November 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Schurig, D.; Mock, J. J.; Justice, B. J.</span> </li> <li> Science, Vol. 314, Issue 5801</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1126/science.1133628" class="text-muted" target="_blank" rel="noopener noreferrer">10.1126/science.1133628<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevE.71.036617" target="_blank" rel="noopener noreferrer" class="name">Electromagnetic parameter retrieval from inhomogeneous metamaterials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2005-03-01">March 2005</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Smith, D. R.; Vier, D. C.; Koschny, Th.</span> </li> <li> Physical Review E, Vol. 71, Issue 3</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1103/PhysRevE.71.036617" class="text-muted" target="_blank" rel="noopener noreferrer">10.1103/PhysRevE.71.036617<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1070/PU1968v010n04ABEH003699" target="_blank" rel="noopener noreferrer" class="name">THE ELECTRODYNAMICS OF SUBSTANCES WITH SIMULTANEOUSLY NEGATIVE VALUES OF $\epsilon$ AND μ<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1968-04-30">April 1968</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#5C7B2D;"> Veselago, Viktor G.</span> </li> <li> Soviet Physics Uspekhi, Vol. 10, Issue 4</li> <li> <span class="text-muted related-url">DOI: <a href="https://doi.org/10.1070/PU1968v010n04ABEH003699" class="text-muted" target="_blank" rel="noopener noreferrer">10.1070/PU1968v010n04ABEH003699<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="sr-only">Previous Page</span><span class="fa fa-angle-left"></span></a> <ul class="pagination d-inline-block" style="padding-left:.2em;"></ul> <a class="pure-button next page" href="#" rel="next"><span class="sr-only">Next Page</span><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All References</a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="journal"><span class="fa fa-angle-right"></span> journal<small class="text-muted"> (28)</small></a></li> </ul> <div style="margin-top:2em;"> <form class="pure-form small text-muted reference-search"> <label for="reference-search-text" class="sr-only">Search</label> <input class="search form-control pure-input-1" id="reference-search-text" placeholder="Search" style="margin-bottom:10px;" /> <fieldset aria-label="Sort By"> <legend class="legend-filters sr-only">Sort by:</legend> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort" name="references-sort" data-sort="name" style="position:relative;top:2px;" id="reference-search-sort-name"><label for="reference-search-sort-name" style="margin-left: .3em;">Sort by title</label></div> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort" name="references-sort" data-sort="date" data-order="desc" style="position:relative;top:2px;" id="reference-search-sort-date"><label for="reference-search-sort-date" style="margin-left: .3em;">Sort by date</label></div> </fieldset> <div class="text-left" style="margin-left:1em;"> <a href="" class="filter-clear clearfix" title="Clear filter / sort" style="font-weight:normal; float:none;">[ × clear filter / sort ]</a> </div> <input type="submit" id="sort_submit_references" name="submit" aria-label="submit" style="display: none;"/> </form> </div> </div> </div> </section> <section id="biblio-images" class="tab-content tab-content-sec osti-curated" data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;"><span id="image-type-label">Figures / Tables</span> found in this record:</p> <div class="list clearfix"> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 2" data-order="1" data-imgid="1212118-img64221" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064221.png" data-title="FIG. 1" data-desc="Unit cell design geometry. (a) Face view. The thickness of each face is 0.26 mm. (b) 3D view. In later sections, we will introduce the electron beam that goes through the center of the beam holes of the cells lying on the beam line." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64221" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64221"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 1 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064221.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 2" data-order="2" data-imgid="1212118-img64222" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064222.png" data-title="FIG. 2" data-desc="Brillouin diagram of a unit cell. (a) Different regions in the first Brillouin zone. (b) Γ − X region dispersion showing the intersection with the light line." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64222" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64222"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 2 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064222.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 3" data-order="3" data-imgid="1212118-img64224" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064224.png" data-title="FIG. 3" data-desc="Field patterns of the longitudinal eigenmodes in the Γ − X region. The cutting plane is the middle plane going through the center of the beam hole. Black arrows denote possible beam paths for the purpose of later sections. Waves propagate to the right. The fields are shown on a linear scale. (a) Mode 1 (the negative index mode); y and z directions are symmetric. (b) Mode 3 (the positive index mode). (c) Cutting plane and future beam position. (d) Axial field patterns at the synchronized points with a relativistic beam at the speed of light." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64224" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64224"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 3 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 3)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064224.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 4" data-order="4" data-imgid="1212118-img64225" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064225.png" data-title="FIG. 4" data-desc="Fitting results of the dispersion curves. HFSS results are in dotted lines, and the fitting curves are in solid lines. The optimized parameters are $α_1$ = −0.0209, $α_2$ = −0.0209, and $α_3$ = 0.0156. (a) Γ − X. (b) Γ −M. (c) Γ − R. Modes 1, 2, 3, and 4 are denoted with black, red, blue, and magenta, respectively. In the Γ −M region, mode 4 splits into two modes." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64225" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64225"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 4 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 4)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064225.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 5" data-order="5" data-imgid="1212118-img64226" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064226.png" data-title="FIG. 5" data-desc="Longitudinal wake impedance spectrum. Peaks are located at 16.6 and 18.7 GHz, corresponding to eigenmode 1 and 3, respectively." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64226" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64226"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 5 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064226.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 5" data-order="6" data-imgid="1212118-img64227" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064227.png" data-title="TABLE I" data-desc="Comparison of wave-beam interaction frequencies (unit, GHz)." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64227" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64227"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">TABLE I <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">table</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064227.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 6" data-order="7" data-imgid="1212118-img64219" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064219.png" data-title="FIG. 6" data-desc="Radiation pattern with a relativistic beam. (a) Illustration of the bulk structure. The beam passes through the line of y = z = 0. (b) Longitudinal E field ($E_x$) on y = 0middle cutting plane for the MTM structure. The MTM region is enclosed in the black rectangles. (c) The same result for the volume mode of a dielectric with ε = 1.5." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64219" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64219"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 6 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 6)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064219.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 6" data-order="8" data-imgid="1212118-img64220" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064220.png" data-title="FIG. 7" data-desc="The 3D properties. (a) Radiated Ex field on an oblique cutting plane rotated 45° around the $x$ axis starting from the $y$ = 0 plane. (b) Radiation pattern on the cutting plane of $x$ = const; i.e., the cutting plane is perpendicular to the longitudinal direction." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64220" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64220"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 7 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 6)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064220.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> <div class="col-sm-3 float-left biblio-image-tile" data-apporder="p. 7" data-order="9" data-imgid="1212118-img64223" data-imgsrc="/biblio/1212118/image/000/909/0009098/1/0064223.png" data-title="FIG. 8" data-desc="(a) Structure for wakefield acceleration demonstration. Part of the waveguide is removed to show the inside structure. (b) Phase space evolution in the x direction of the drive bunch (the top group) and the witness bunch (the bottom group). The time interval between every two snapshots is 0.02 ns. The plots of the two bunches at the same time are represented with the same color. The witness bunch is injected into the structure 25 mm after the drive bunch." data-ostiid="1212118" style="padding-bottom: 2em; border-bottom: 1px solid #ddd;"> <a href="#img" class="biblio-image-tile-a ga-click-event" data-imgid="1212118-img64223" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64223"> <div style=" padding: .5em; border: 1px solid #eee; background-color: #fff; "> <small class="name">FIG. 8 <small class="pull-right" style="margin-right: .5em;color:#999;top: 3px;position: relative;">(p. 7)</small><span class="d-none type">figure</span></small> <div style=" background-image:url('/biblio/1212118/image/000/909/0009098/1/t0064223.png'); background-repeat:no-repeat; background-size:contain; background-position-x: center; width: 100%; height: 175px; margin-top:.5em; "> </div> </div> </a> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-images" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All Images</a></li> <li class="small" style="margin-left:.75em; 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padding:1em;"> <em>Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.</em> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar Records in DOE PAGES and OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1656740-coherent-high-power-rf-wakefield-generation-electron-bunch-trains-metamaterial-structure" itemprop="url">Coherent high-power RF wakefield generation by electron bunch trains in a metamaterial structure</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Lu, Xueying</span> ; <span class="author">Picard, Julian F.</span> ; <span class="author">Shapiro, Michael A.</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Applied Physics Letters</span> </span> </div> <div class="abstract">In this paper, we present an experimental study of coherent high-power wakefield generation in a metamaterial (MTM) structure at 11.7 GHz by 65 MeV electron bunch trains at the Argonne Wakefield Accelerator (AWA), following a previous experiment, the Stage-I experiment, at the AWA. Both the Stage-II experiment, reported in this paper, and the Stage-I experiment were conducted using MTM structures, which are all-metal periodic structures with the period being much smaller than the wavelength. Differences between the two experiments include (1) structure length (Stage-I 8 cm and Stage-II 20 cm); (2) number of bunches used to excite the structure (Stage-I<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> with two bunches, up to 85 nC of total charge; Stage-II with eight bunches, up to 224 nC of total charge); and (3) highest peak power measured (Stage-I 80 MW in a 2 ns pulse and Stage-II 380 MW in a 10 ns pulse). High-power radio frequency pulses were generated by reversed Cherenkov radiation of the electron beam due to the negative group velocity in the MTM structures. Because the radiation is coherent, a train of bunches with a proper spacing can build up to achieve a high peak power. The observed output power levels are very promising for future applications in direct collinear wakefield acceleration or in transfer to a second accelerator for two-beam acceleration.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/5.0012671" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1656740" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1063/5.0012671</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1656740" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1656740" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/958534-wakefield-generation-metamaterial-loaded-waveguides" itemprop="url">Wakefield generation in metamaterial-loaded waveguides.</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Power, J G</span> ; <span class="author">Gai, W</span> ; <span class="author">Liu, W</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - J. Appl. Phys.</span> </span> </div> <div class="abstract">Metamaterials (MTMs) are artificial structures made of periodic elements and are designed to obtain specific electromagnetic properties. As long as the periodicity and the size of the elements are much smaller than the wavelength of interest, an artificial structure can be assigned a permittivity and permeability, just like natural materials. Metamaterials can be customized to have the permittivity and permeability desired for a particular application. When the permittivity and permeability are made simultaneously negative in some frequency range, the metamaterial is called double-negative or left-handed and has some unusual properties. For example, Cherenkov radiation (CR) in a left-handed metamaterial is<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> backward; radiated energy propagates in the opposite direction to particle velocity. This property can be used to improve the design of particle detectors. Waveguides loaded with metamaterials are of interest because the metamaterials can change the dispersion relation of the waveguide significantly. Slow backward waves, for example, can be produced in a MTM-loaded waveguide without corrugations. In this paper we present theoretical studies of waveguides loaded with an anisotropic and dispersive medium (metamaterial). The dispersion relation of a MTM-loaded waveguide has several interesting frequency bands which are described. We present a universal method to simulate wakefield (CR) generation in a waveguide loaded with a dispersive and anisotropic medium. This method allows simulation of different waveguide cross sections, any transverse beam distribution, and any physical dispersion, of the medium. The method is benchmarked against simple cases, which can be theoretically calculated. Results show excellent agreement.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1557637-sub-wavelength-waveguide-loaded-complementary-electric-metamaterial-vacuum-electron-devices" itemprop="url">Sub-wavelength waveguide loaded by a complementary electric metamaterial for vacuum electron devices</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Duan, Zhaoyun</span> ; <span class="author">Hummelt, Jason S.</span> ; <span class="author">Shapiro, Michael A.</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Physics of Plasmas</span> </span> </div> <div class="abstract">This work reviews the electromagnetic properties of a waveguide loaded by complementary electric split ring resonators (CeSRRs) and the application of the waveguide in vacuum electronics. The S-parameters of the CeSRRs in free space are calculated using the HFSS code and are used to retrieve the effective permittivity and permeability in an effective medium theory. The dispersion relation of a waveguide loaded with the CeSRRs is calculated by two methods: by direct calculation with HFSS and by calculation with the effective medium theory; the results are in good agreement. An improved agreement is obtained using a fitting procedure for the<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> permittivity tensor in the effective medium theory. The gain of a backward wave mode of the CeSRR-loaded waveguide interacting with an electron beam is calculated by two methods: by using the HFSS model and traveling wave tube theory; and by using a dispersion relation derived in the effective medium model. Results of the two methods are in very good agreement. The introduced all-metal structure may be useful in miniaturized vacuum electron devices.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 23<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/1.4897392" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1557637" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1063/1.4897392</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1557637" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1557637" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/pages/biblio/1779093-metamaterial-inspired-vacuum-electron-devices-accelerators" itemprop="url">Metamaterial-Inspired Vacuum Electron Devices and Accelerators</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Duan, Zhaoyun</span> ; <span class="author">Shapiro, Michael A.</span> ; <span class="author">Schamiloglu, Edl</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - IEEE Transactions on Electron Devices</span> </span> </div> <div class="abstract">Metamaterials (MTMs) are structured materials with subwavelength features that can be engineered to have some unique properties not found in nature, such as negative refractive index, reversed Doppler effect, and reversed Cherenkov radiation. Based on these novel MTMs, several important research groups have made great attempts to develop novel MTM-inspired vacuum electron devices (VEDs) and accelerators. Just as solid-state power devices are innovated by incessant emerging of new semiconductor materials, VEDs can also be inspired by MTMs to have very remarkable advantages, such as smaller size, higher power, higher efficiency, and/or larger gain relative to conventional VEDs, such as traveling-wave<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> tubes, backward-wave oscillators, and klystrons. Similarly, relative to conventional accelerators, MTM-inspired accelerators have obvious advantages, such as smaller size and higher accelerating gradient. Furthermore, MTM-inspired devices have promising applications in areas such as radar, communication, electronic warfare, microwave heating, and imaging.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 6<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1109/ted.2018.2878242" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1779093" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1109/ted.2018.2878242</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/pages/servlets/purl/1779093" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1779093" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="5" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1775450-coherent-high-power-rf-wakefield-generation-electron-bunch-trains-metamaterial-structure" itemprop="url">Coherent high-power RF wakefield generation by electron bunch trains in a metamaterial structure</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Lu, Xueying</span> ; <span class="author">Picard, Julian F.</span> ; <span class="author">Shapiro, Michael A.</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Applied Physics Letters</span> </span> </div> <div class="abstract">We present an experimental study of coherent high-power wakefield generation in a metamaterial (MTM) structure at 11.7 GHz by 65 MeV electron bunch trains at the Argonne Wakefield Accelerator (AWA), following a previous experiment, the Stage-I experiment, at the AWA. Both the Stage-II experiment, reported in this paper, and the Stage-I experiment were conducted using MTM structures, which are all-metal periodic structures with the period being much smaller than the wavelength. Differences between the two experiments include (1) structure length (Stage-I 8 cm and Stage-II 20 cm); (2) number of bunches used to excite the structure (Stage-I with two bunches,<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> up to 85 nC of total charge; Stage-II with eight bunches, up to 224 nC of total charge); and (3) highest peak power measured (Stage-I 80 MW in a 2 ns pulse and Stage-II 380 MW in a 10 ns pulse). High-power radio frequency pulses were generated by reversed Cherenkov radiation of the electron beam due to the negative group velocity in the MTM structures. Because the radiation is coherent, a train of bunches with a proper spacing can build up to achieve a high peak power. The observed output power levels are very p</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1063/5.0012671" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1775450" data-product-type="Journal Article" data-product-subtype="AC" >https://doi.org/10.1063/5.0012671</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="hidden-xs">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/pages/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="sr-only">Facebook</span><em class="fa fa-facebook" style=""></em></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="sr-only">Twitter</span><em class="fa fa-twitter" style=""></em></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="sr-only">YouTube</span><em class="fa fa-youtube-play" style=""></em></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/pages/css/pages.fonts.220120.1828.css" rel="stylesheet"> <script src="/pages/js/pages.220120.1828.js"></script><noscript></noscript> <script defer src="/pages/js/pages.biblio.220120.1828.js"></script><noscript></noscript> <script defer src="/pages/js/lity.js"></script><noscript></noscript> <script async�type="text/javascript" src="/pages/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- DOE PAGES v.220120.1828 --> </html>