Excitation of Longitudinal Waves in a Bounded Collisionless Plasma
The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is...
Gespeichert in:
| Veröffentlicht in: | Physics of Fluids (U.S.) 1963-09, Vol.6 (9), p.1305-1312 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1312 |
|---|---|
| container_issue | 9 |
| container_start_page | 1305 |
| container_title | Physics of Fluids (U.S.) |
| container_volume | 6 |
| creator | Taylor, Edward C. |
| description | The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant
κ=[1−ω
p
2
/ω
2
(1−5KT/2mc
2
)]
, unless the driving frequency lies in the small band
ω
p
2
(1−5KT/2mc
2
) |
| doi_str_mv | 10.1063/1.1706899 |
| format | Article |
| fullrecord | <record><control><sourceid>scitation_osti_</sourceid><recordid>TN_cdi_scitation_primary_10_1063_1_1706899</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>scitation_primary_10_1063_1_1706899</sourcerecordid><originalsourceid>FETCH-LOGICAL-c291t-53832b09ac5dc7e7083bc63e943611aae5c636faf973faf108bedb9041916d353</originalsourceid><addsrcrecordid>eNp90E1LxDAQBuAgCtbVg_8geFPommnatDm6Zf2Agh4UjyFNU410E-l0xf33Rrpevcww8DDMvIScA1sCE_wallAyUUl5QJIMBE9zKatDkjDGIZVQwjE5QfxgLMsh5wlZrb-Nm_Tkgqehp03wb27ads7rgb7qL4vUearpKmx9Zztah2FwGPFgEenToHGjT8lRrwe0Z_u-IC-36-f6Pm0e7x7qmyY1mYQpLXjFs5ZJbYrOlLZkFW-N4FbmXABobYs4iV73suSxAqta27WS5SBBdLzgC3Ix7w04OYXxbGveTfDemknlQsT3q4guZ2TGgDjaXn2ObqPHnQKmfhNSoPYJRXs1W_yL4B_8Axf5ZL4</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Excitation of Longitudinal Waves in a Bounded Collisionless Plasma</title><source>Alma/SFX Local Collection</source><creator>Taylor, Edward C.</creator><creatorcontrib>Taylor, Edward C. ; Aerospace Corp., Los Angeles</creatorcontrib><description>The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant
κ=[1−ω
p
2
/ω
2
(1−5KT/2mc
2
)]
, unless the driving frequency lies in the small band
ω
p
2
(1−5KT/2mc
2
)<ω
2
<ω
p
2
(1+KT/2mc
2
)
. When the driving frequency satisfies the inequality, then the plasma also supports standing waves which satisfy the relativistic dispersion relation for longitudinal waves.</description><identifier>ISSN: 0031-9171</identifier><identifier>EISSN: 2163-4998</identifier><identifier>DOI: 10.1063/1.1706899</identifier><identifier>CODEN: PFLDAS</identifier><language>eng</language><subject>CHARGED PARTICLES ; CONFIGURATION ; DEBYE LENGTH ; DIELECTRICS ; DIFFERENTIAL EQUATIONS ; ELECTRIC FIELDS ; EQUATIONS ; EXCITATION ; FREQUENCY ; INTERACTIONS ; OSCILLATIONS ; PHYSICS ; PLASMA ; PLASMA WAVES ; REFLECTION ; RELATIVITY THEORY ; SHIELDING ; SURFACES ; VLASOV EQUATION</subject><ispartof>Physics of Fluids (U.S.), 1963-09, Vol.6 (9), p.1305-1312</ispartof><rights>The American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c291t-53832b09ac5dc7e7083bc63e943611aae5c636faf973faf108bedb9041916d353</citedby><cites>FETCH-LOGICAL-c291t-53832b09ac5dc7e7083bc63e943611aae5c636faf973faf108bedb9041916d353</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/4660638$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Taylor, Edward C.</creatorcontrib><creatorcontrib>Aerospace Corp., Los Angeles</creatorcontrib><title>Excitation of Longitudinal Waves in a Bounded Collisionless Plasma</title><title>Physics of Fluids (U.S.)</title><description>The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant
κ=[1−ω
p
2
/ω
2
(1−5KT/2mc
2
)]
, unless the driving frequency lies in the small band
ω
p
2
(1−5KT/2mc
2
)<ω
2
<ω
p
2
(1+KT/2mc
2
)
. When the driving frequency satisfies the inequality, then the plasma also supports standing waves which satisfy the relativistic dispersion relation for longitudinal waves.</description><subject>CHARGED PARTICLES</subject><subject>CONFIGURATION</subject><subject>DEBYE LENGTH</subject><subject>DIELECTRICS</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>ELECTRIC FIELDS</subject><subject>EQUATIONS</subject><subject>EXCITATION</subject><subject>FREQUENCY</subject><subject>INTERACTIONS</subject><subject>OSCILLATIONS</subject><subject>PHYSICS</subject><subject>PLASMA</subject><subject>PLASMA WAVES</subject><subject>REFLECTION</subject><subject>RELATIVITY THEORY</subject><subject>SHIELDING</subject><subject>SURFACES</subject><subject>VLASOV EQUATION</subject><issn>0031-9171</issn><issn>2163-4998</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1963</creationdate><recordtype>article</recordtype><recordid>eNp90E1LxDAQBuAgCtbVg_8geFPommnatDm6Zf2Agh4UjyFNU410E-l0xf33Rrpevcww8DDMvIScA1sCE_wallAyUUl5QJIMBE9zKatDkjDGIZVQwjE5QfxgLMsh5wlZrb-Nm_Tkgqehp03wb27ads7rgb7qL4vUearpKmx9Zztah2FwGPFgEenToHGjT8lRrwe0Z_u-IC-36-f6Pm0e7x7qmyY1mYQpLXjFs5ZJbYrOlLZkFW-N4FbmXABobYs4iV73suSxAqta27WS5SBBdLzgC3Ix7w04OYXxbGveTfDemknlQsT3q4guZ2TGgDjaXn2ObqPHnQKmfhNSoPYJRXs1W_yL4B_8Axf5ZL4</recordid><startdate>196309</startdate><enddate>196309</enddate><creator>Taylor, Edward C.</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>196309</creationdate><title>Excitation of Longitudinal Waves in a Bounded Collisionless Plasma</title><author>Taylor, Edward C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-53832b09ac5dc7e7083bc63e943611aae5c636faf973faf108bedb9041916d353</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1963</creationdate><topic>CHARGED PARTICLES</topic><topic>CONFIGURATION</topic><topic>DEBYE LENGTH</topic><topic>DIELECTRICS</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>ELECTRIC FIELDS</topic><topic>EQUATIONS</topic><topic>EXCITATION</topic><topic>FREQUENCY</topic><topic>INTERACTIONS</topic><topic>OSCILLATIONS</topic><topic>PHYSICS</topic><topic>PLASMA</topic><topic>PLASMA WAVES</topic><topic>REFLECTION</topic><topic>RELATIVITY THEORY</topic><topic>SHIELDING</topic><topic>SURFACES</topic><topic>VLASOV EQUATION</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Taylor, Edward C.</creatorcontrib><creatorcontrib>Aerospace Corp., Los Angeles</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Physics of Fluids (U.S.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Taylor, Edward C.</au><aucorp>Aerospace Corp., Los Angeles</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Excitation of Longitudinal Waves in a Bounded Collisionless Plasma</atitle><jtitle>Physics of Fluids (U.S.)</jtitle><date>1963-09</date><risdate>1963</risdate><volume>6</volume><issue>9</issue><spage>1305</spage><epage>1312</epage><pages>1305-1312</pages><issn>0031-9171</issn><eissn>2163-4998</eissn><coden>PFLDAS</coden><abstract>The relativistic form of the Vlasov equation is used to derive an integral equation for an externally produced electric field oscillating with frequency ω in a plasma bounded by two specularly reflecting walls. A tentative solution is constructed from exact solutions of the half‐space problem. It is shown that the exact equation is satisfied by the tentative solution up to terms which are exponentially small in the number of Debye lengths across the plasma. It happens that the bounded plasma acts like a medium with a dielectric constant
κ=[1−ω
p
2
/ω
2
(1−5KT/2mc
2
)]
, unless the driving frequency lies in the small band
ω
p
2
(1−5KT/2mc
2
)<ω
2
<ω
p
2
(1+KT/2mc
2
)
. When the driving frequency satisfies the inequality, then the plasma also supports standing waves which satisfy the relativistic dispersion relation for longitudinal waves.</abstract><doi>10.1063/1.1706899</doi><tpages>8</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0031-9171 |
| ispartof | Physics of Fluids (U.S.), 1963-09, Vol.6 (9), p.1305-1312 |
| issn | 0031-9171 2163-4998 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_1706899 |
| source | Alma/SFX Local Collection |
| subjects | CHARGED PARTICLES CONFIGURATION DEBYE LENGTH DIELECTRICS DIFFERENTIAL EQUATIONS ELECTRIC FIELDS EQUATIONS EXCITATION FREQUENCY INTERACTIONS OSCILLATIONS PHYSICS PLASMA PLASMA WAVES REFLECTION RELATIVITY THEORY SHIELDING SURFACES VLASOV EQUATION |
| title | Excitation of Longitudinal Waves in a Bounded Collisionless Plasma |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-28T21%3A11%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-scitation_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Excitation%20of%20Longitudinal%20Waves%20in%20a%20Bounded%20Collisionless%20Plasma&rft.jtitle=Physics%20of%20Fluids%20(U.S.)&rft.au=Taylor,%20Edward%20C.&rft.aucorp=Aerospace%20Corp.,%20Los%20Angeles&rft.date=1963-09&rft.volume=6&rft.issue=9&rft.spage=1305&rft.epage=1312&rft.pages=1305-1312&rft.issn=0031-9171&rft.eissn=2163-4998&rft.coden=PFLDAS&rft_id=info:doi/10.1063/1.1706899&rft_dat=%3Cscitation_osti_%3Escitation_primary_10_1063_1_1706899%3C/scitation_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |