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

Journal Article · · Physical Review Special Topics. Accelerators and Beams
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
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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.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); US Air Force Office of Scientific Research (AFOSR)
Grant/Contract Number:
SC0010075; FA 550-12-1-0489
OSTI ID:
1212118
Alternate ID(s):
OSTI ID: 1454578
Journal Information:
Physical Review Special Topics. Accelerators and Beams, Journal Name: Physical Review Special Topics. Accelerators and Beams Vol. 18 Journal Issue: 8; ISSN 1098-4402
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 12 works
Citation information provided by
Web of Science

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C.</li> <li class="mb-0-5 source"> <span class="mr-1">Physical Review D, Vol. 36, Issue 8</span> <span class="text-muted"><a href="https://doi.org/10.1103/PhysRevD.36.2283" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevD.36.2283<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1987-10-01">October 1987</span></td> </tr><tr> <td> <a href="https://doi.org/10.1103/PhysRevLett.61.2756" target="_blank" rel="noopener noreferrer" class="title" data-title="Experimental Demonstration of WakeField Effects in Dielectric Structures">Experimental Demonstration of Wake-Field Effects in Dielectric Structures<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Gai, W.; Schoessow, P.; Cole, B.</li> <li class="mb-0-5 source"> <span class="mr-1">Physical Review Letters, Vol. 61, Issue 24</span> <span class="text-muted"><a href="https://doi.org/10.1103/PhysRevLett.61.2756" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevLett.61.2756<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1988-12-01">December 1988</span></td> </tr><tr> <td> <a href="https://doi.org/10.1063/1.4897392" target="_blank" rel="noopener noreferrer" class="title" data-title="Subwavelength waveguide loaded by a complementary electric metamaterial for vacuum electron devices">Sub-wavelength waveguide loaded by a complementary electric metamaterial for vacuum electron devices<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Duan, Zhaoyun; Hummelt, Jason S.; Shapiro, Michael A.</li> <li class="mb-0-5 source"> <span class="mr-1">Physics of Plasmas, Vol. 21, Issue 10</span> <span class="text-muted"><a href="https://doi.org/10.1063/1.4897392" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1063/1.4897392<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2014-10-01">October 2014</span></td> </tr><tr> <td> <a href="https://doi.org/10.1088/0953-8984/20/29/295222" target="_blank" rel="noopener noreferrer" class="title" data-title="Taming spatial dispersion in wire metamaterial">Taming spatial dispersion in wire metamaterial<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Demetriadou, A.; Pendry, J. B.</li> <li class="mb-0-5 source"> <span class="mr-1">Journal of Physics: Condensed Matter, Vol. 20, Issue 29</span> <span class="text-muted"><a href="https://doi.org/10.1088/0953-8984/20/29/295222" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1088/0953-8984/20/29/295222<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2008-07-01">July 2008</span></td> </tr><tr> <td> <a href="https://doi.org/10.1103/PhysRevLett.108.244801" target="_blank" rel="noopener noreferrer" class="title" data-title="Dielectric Wakefield Acceleration of a Relativistic Electron Beam in a SlabSymmetric Dielectric Lined Waveguide">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> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Andonian, G.; Stratakis, D.; Babzien, M.</li> <li class="mb-0-5 source"> <span class="mr-1">Physical Review Letters, Vol. 108, Issue 24</span> <span class="text-muted"><a href="https://doi.org/10.1103/PhysRevLett.108.244801" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevLett.108.244801<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2012-06-01">June 2012</span></td> </tr><tr> <td> <a href="https://doi.org/10.1103/PhysRevE.70.016608" target="_blank" rel="noopener noreferrer" class="title" data-title="Robust method to retrieve the constitutive effective parameters of metamaterials">Robust method to retrieve the constitutive effective parameters of metamaterials<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Chen, Xudong; Grzegorczyk, Tomasz M.; Wu, Bae-Ian</li> <li class="mb-0-5 source"> <span class="mr-1">Physical Review E, Vol. 70, Issue 1</span> <span class="text-muted"><a href="https://doi.org/10.1103/PhysRevE.70.016608" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevE.70.016608<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2004-07-01">July 2004</span></td> </tr><tr> <td> <a href="https://doi.org/10.1364/OL.31.002051" target="_blank" rel="noopener noreferrer" class="title" data-title="Spatial dispersion in metamaterials with negative dielectric permittivity and its effect on surface waves">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> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Shapiro, M. A.; Shvets, G.; Sirigiri, J. R.</li> <li class="mb-0-5 source"> <span class="mr-1">Optics Letters, Vol. 31, Issue 13</span> <span class="text-muted"><a href="https://doi.org/10.1364/OL.31.002051" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1364/OL.31.002051<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2006-01-01">January 2006</span></td> </tr><tr> <td> <a href="https://doi.org/10.1126/science.1133628" target="_blank" rel="noopener noreferrer" class="title" data-title="Metamaterial Electromagnetic Cloak at Microwave Frequencies">Metamaterial Electromagnetic Cloak at Microwave Frequencies<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Schurig, D.; Mock, J. J.; Justice, B. J.</li> <li class="mb-0-5 source"> <span class="mr-1">Science, Vol. 314, Issue 5801</span> <span class="text-muted"><a href="https://doi.org/10.1126/science.1133628" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1126/science.1133628<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2006-11-10">November 2006</span></td> </tr><tr> <td> <a href="https://doi.org/10.1103/PhysRevE.71.036617" target="_blank" rel="noopener noreferrer" class="title" data-title="Electromagnetic parameter retrieval from inhomogeneous metamaterials">Electromagnetic parameter retrieval from inhomogeneous metamaterials<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Smith, D. R.; Vier, D. C.; Koschny, Th.</li> <li class="mb-0-5 source"> <span class="mr-1">Physical Review E, Vol. 71, Issue 3</span> <span class="text-muted"><a href="https://doi.org/10.1103/PhysRevE.71.036617" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevE.71.036617<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2005-03-01">March 2005</span></td> </tr><tr> <td> <a href="https://doi.org/10.1007/978-3-642-69247-5" target="_blank" rel="noopener noreferrer" class="title" data-title="Principles of Plasma Electrodynamics">Principles of Plasma Electrodynamics<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Alexandrov, Andrey F.; Bogdankevich, Larisa S.; Rukhadze, Anri A.</li> <li class="mb-0-5 source"> <span class="text-muted"><a href="https://doi.org/10.1007/978-3-642-69247-5" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/978-3-642-69247-5<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="book">book</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1984-01-01">January 1984</span></td> </tr><tr> <td> <a href="https://doi.org/10.1070/PU1968v010n04ABEH003699" target="_blank" rel="noopener noreferrer" class="title" data-title="THE ELECTRODYNAMICS OF SUBSTANCES WITH SIMULTANEOUSLY NEGATIVE VALUES OF epsilon AND ">THE ELECTRODYNAMICS OF SUBSTANCES WITH SIMULTANEOUSLY NEGATIVE VALUES OF $\epsilon$ AND μ<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Veselago, Viktor G.</li> <li class="mb-0-5 source"> <span class="mr-1">Soviet Physics Uspekhi, Vol. 10, Issue 4</span> <span class="text-muted"><a href="https://doi.org/10.1070/PU1968v010n04ABEH003699" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1070/PU1968v010n04ABEH003699<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="journal">journal</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1968-04-30">April 1968</span></td> </tr></tbody></table> </div> </div> </section> <hr class="mt-2 mb-2"/> <section id="section-images" data-list="list_img" class="tab-content-sec osti-curated biblio-section section-scroll" style="scroll-margin-top:110px;"> <div class="biblio-section-navbar active row"> <div class="col"> <h2 class="abstract biblio-section-title mt-0 mb-0-5" style="cursor:pointer;"><span class="fa indicator"></span> Figures / Tables (9) <span class="text-muted list-table-filternum"></span></h2> </div> <div class="col-md-12 col-lg-auto"> <form class="pure-form reference-filter d-print-none"> <div class="small biblio-section-navbar-tool"> <label for="list-table-search-figures" class="sr-only">Search figures / tables: </label> <input type="text" class="list-table-search mt-0 mb-0-5 ml-1" id="list-table-search-figures" placeholder="Search figures / tables ..."> </div> <div class="small biblio-section-navbar-tool"> <select class="list-table-sort mt-0 mb-0-5"> <option value="date">Sort by Date</option> <option value="title">Sort by Title</option> </select> </div> <div class="small biblio-section-navbar-tool"> <button type="reset" class="pure-button list-table-reset mt-0 mb-0-5">↺</button> </div> </form> </div> </div> <div class="row"> <div class="col-sm-12"> <table id="list-table-images" class="truncate-rows list-table list-table-images table-to-tiles" data-rows="1" style="width:100%;"><tbody class="list"> <tr class="biblio-image-tile "><td class="col-sm-3"> <a id="img-1212118-img64221" data-pos="first" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64221" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64221" 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 1<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 1" src="/biblio/1212118/image/000/909/0009098/1/t0064221.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile "><td class="col-sm-3"> <a id="img-1212118-img64222" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64222" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64222" 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 2<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 2)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 2" src="/biblio/1212118/image/000/909/0009098/1/t0064222.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile "><td class="col-sm-3"> <a id="img-1212118-img64224" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64224" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64224" 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 3<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 3)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 3" src="/biblio/1212118/image/000/909/0009098/1/t0064224.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile "><td class="col-sm-3"> <a id="img-1212118-img64225" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64225" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64225" 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 4<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 4)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 4" src="/biblio/1212118/image/000/909/0009098/1/t0064225.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile tr-striped"><td class="col-sm-3"> <a id="img-1212118-img64226" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64226" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64226" 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 5<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 5" src="/biblio/1212118/image/000/909/0009098/1/t0064226.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile tr-striped"><td class="col-sm-3"> <a id="img-1212118-img64227" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64227" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64227" 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"> <div class="biblio-image-tile-inner"> <small class="name">TABLE I<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 5)</small><span class="d-none type">table</span></small> <img class="img-responsive mt-0-5" alt="TABLE I" src="/biblio/1212118/image/000/909/0009098/1/t0064227.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile tr-striped"><td class="col-sm-3"> <a id="img-1212118-img64219" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64219" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64219" 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 <em>y = z </em>= 0. (b) Longitudinal <em>E</em> 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 6<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 6)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 6" src="/biblio/1212118/image/000/909/0009098/1/t0064219.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile tr-striped"><td class="col-sm-3"> <a id="img-1212118-img64220" data-pos="" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64220" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64220" 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 E<sub>x</sub> 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 7<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 6)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 7" src="/biblio/1212118/image/000/909/0009098/1/t0064220.png"/> </div> </a> </td></tr> <tr class="biblio-image-tile "><td class="col-sm-3"> <a id="img-1212118-img64223" data-pos="last" href="#modal-image" data-modal-toggle="true" class="biblio-image-tile-a ga-click-event apporder order title desc" data-imgid="1212118-img64223" data-lityx data-category="Extracted Images" data-label="biblio: image thumbnail" data-value="1212118-img64223" 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 <em>x</em> 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"> <div class="biblio-image-tile-inner"> <small class="name">FIG. 8<small class="pull-right text-muted" style="margin-right: .5em;top: 3px;position: relative;">(p. 7)</small><span class="d-none type">figure</span></small> <img class="img-responsive mt-0-5" alt="FIG. 8" src="/biblio/1212118/image/000/909/0009098/1/t0064223.png"/> </div> </a> </td></tr> </tbody></table> </div> </div> </section> <div id="modal-image" class="modal"> <div class="modal-content"> <div class="modal-header"> <span class="close" data-modal-close="true">×</span> <header id="modal-image_label" style="margin:0px;">Image title</header> </div> <div id="modal-image_body" class="modal-body"> </div> </div> </div> <hr class="mt-2 mb-2"/> <section id="section-similar" class="tab-content-sec osti-curated biblio-section section-scroll" style="scroll-margin-top:110px;"> <div class="row"> <div class="col-8" style="padding-right:40px;"> <h2 class="abstract">Similar Records</h2> <div class="" style="line-height:1.6rem;"> <a href="/biblio/1880525" target="_blank">Modeling of the interaction of a volumetric metallic metamaterial structure with a relativistic electron beam</a> <div class="small" style="line-height:1.4rem;"> Dataset <span style="padding-left: 0.75rem;padding-right: 0.75rem;">·</span> Wed Dec 12 00:00:00 EST 2018 <span style="padding-left: 0.75rem;padding-right: 0.75rem;">·</span> <span class="text-muted" style="padding-right:0.5em;">OSTI ID:</span>1212118 </div> <div class="small" style="line-height:1.4rem;"> <span class="author-link"><a href="/search/author:"Lu, Xueying"" class="btn btn-link btn-sm"><span class="author" itemprop="author">Lu, Xueying; 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