Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas
This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B&J) [Phys....
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description | This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B&J) [Phys. Fluids
30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B&J model is a generalization of the well-known Tonks–Langmuir (T&L) [Phys. Rev.
34, 876 (1929)] discharge model characterized by a “cold” ion source. Unlike the T&L model, which can be readily solved analytically, attempts to solve the B&J model with a “warm” ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B&J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B&J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc.
74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures. |
doi_str_mv | 10.1063/1.3223556 |
format | Article |
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30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B&J model is a generalization of the well-known Tonks–Langmuir (T&L) [Phys. Rev.
34, 876 (1929)] discharge model characterized by a “cold” ion source. Unlike the T&L model, which can be readily solved analytically, attempts to solve the B&J model with a “warm” ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B&J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B&J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc.
74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures.]]></description><identifier>ISSN: 1070-664X</identifier><identifier>EISSN: 1089-7674</identifier><identifier>DOI: 10.1063/1.3223556</identifier><identifier>CODEN: PHPAEN</identifier><language>eng</language><publisher>United States</publisher><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY ; BESSEL FUNCTIONS ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; DISTRIBUTION FUNCTIONS ; GAUSS FUNCTION ; INTEGRAL EQUATIONS ; ION TEMPERATURE ; IONS ; NUMERICAL SOLUTION ; PLASMA SHEATH ; PLASMA SIMULATION</subject><ispartof>Physics of plasmas, 2009-09, Vol.16 (9)</ispartof><rights>American Institute of Physics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-3d07f2d495cb055140fa40d3cc294781c4c21d58c2c5ce2e90417810268812003</citedby><cites>FETCH-LOGICAL-c327t-3d07f2d495cb055140fa40d3cc294781c4c21d58c2c5ce2e90417810268812003</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/pop/article-lookup/doi/10.1063/1.3223556$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,780,784,794,885,1559,4512,27924,27925,76384,76390</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/21282132$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Kos, L.</creatorcontrib><creatorcontrib>Jelić, N.</creatorcontrib><creatorcontrib>Kuhn, S.</creatorcontrib><creatorcontrib>Duhovnik, J.</creatorcontrib><title>Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas</title><title>Physics of plasmas</title><description><![CDATA[This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B&J) [Phys. Fluids
30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B&J model is a generalization of the well-known Tonks–Langmuir (T&L) [Phys. Rev.
34, 876 (1929)] discharge model characterized by a “cold” ion source. Unlike the T&L model, which can be readily solved analytically, attempts to solve the B&J model with a “warm” ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B&J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B&J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc.
74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures.]]></description><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</subject><subject>BESSEL FUNCTIONS</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>DISTRIBUTION FUNCTIONS</subject><subject>GAUSS FUNCTION</subject><subject>INTEGRAL EQUATIONS</subject><subject>ION TEMPERATURE</subject><subject>IONS</subject><subject>NUMERICAL SOLUTION</subject><subject>PLASMA SHEATH</subject><subject>PLASMA SIMULATION</subject><issn>1070-664X</issn><issn>1089-7674</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNp9kEtKBDEQhoMoOI4uvEHAlUKPefZjqcP4YsCNgrsQ04ndkk6aJA668w7e0JPY7Qy6EFxVUfXVB_UDcIjRDKOcnuIZJYRynm-BCUZllRV5wbbHvkBZnrOHXbAX4zNCiOW8nIBu8Zq0i6130BuYGg3P2xi1tZ_vHze-cXFY9FbGTmax0TI1sPO1ttD4AGXf21bJNB4nD83LqMmCtnolXYLS1fBJOx2k3SjiPtgx0kZ9sKlTcH-xuJtfZcvby-v52TJTlBQpozUqDKlZxdUj4hwzZCRDNVWKVKwosWKK4JqXiiiuNNEVYngYI5KXJSYI0Sk4Wnt9TK2Iqk1aNco7p1USBJOSYEoG6nhNqeBjDNqIPrSdDG8CIzGmKbDYpDmwJ2t2lH2__AOvfPgFRV-b_-C_5i-3nYQu</recordid><startdate>20090901</startdate><enddate>20090901</enddate><creator>Kos, L.</creator><creator>Jelić, N.</creator><creator>Kuhn, S.</creator><creator>Duhovnik, J.</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20090901</creationdate><title>Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas</title><author>Kos, L. ; Jelić, N. ; Kuhn, S. ; Duhovnik, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-3d07f2d495cb055140fa40d3cc294781c4c21d58c2c5ce2e90417810268812003</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</topic><topic>BESSEL FUNCTIONS</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>DISTRIBUTION FUNCTIONS</topic><topic>GAUSS FUNCTION</topic><topic>INTEGRAL EQUATIONS</topic><topic>ION TEMPERATURE</topic><topic>IONS</topic><topic>NUMERICAL SOLUTION</topic><topic>PLASMA SHEATH</topic><topic>PLASMA SIMULATION</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kos, L.</creatorcontrib><creatorcontrib>Jelić, N.</creatorcontrib><creatorcontrib>Kuhn, S.</creatorcontrib><creatorcontrib>Duhovnik, J.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Physics of plasmas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kos, L.</au><au>Jelić, N.</au><au>Kuhn, S.</au><au>Duhovnik, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas</atitle><jtitle>Physics of plasmas</jtitle><date>2009-09-01</date><risdate>2009</risdate><volume>16</volume><issue>9</issue><issn>1070-664X</issn><eissn>1089-7674</eissn><coden>PHPAEN</coden><abstract><![CDATA[This article presents an approach to solving a special Fredholm-type integral equation of the first kind with a particular kernel containing a modified Bessel function for applications in plasma physics. From the physical point of view, the problem was defined by Bissell and Johnson (B&J) [Phys. Fluids
30, 779 (1987)] as a task to find the potential profile and the ion velocity distribution function in a plane-parallel discharge with a Maxwellian ion source. The B&J model is a generalization of the well-known Tonks–Langmuir (T&L) [Phys. Rev.
34, 876 (1929)] discharge model characterized by a “cold” ion source. Unlike the T&L model, which can be readily solved analytically, attempts to solve the B&J model with a “warm” ion source have been done only numerically. However, the validity of numerical solutions up to date remains constrained to a rather limited range of a crucial independent parameter of the B&J integral equation, which mathematically is the width of a Gaussian distribution and physically represents the ion temperature. It was solved only for moderately warm ion sources. This paper presents the exact numerical solution of the B&J model, which is valid without any restriction regarding the above-mentioned parameter. It is shown that the ion temperature is very different from the temperature of the ion source. The new results with high-temperature ion sources are not only of particular importance for understanding and describing the plasma-sheath boundary in fusion plasmas, but are of considerable interest for discharge problems in general. The eigenvalue of the problem, found analytically by Harrison and Thompson [Proc. Phys. Soc.
74, 145 (1959)] for the particular case of a cold ion source, is here extended to arbitrary ion-source temperatures.]]></abstract><cop>United States</cop><doi>10.1063/1.3223556</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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subjects | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY BESSEL FUNCTIONS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DISTRIBUTION FUNCTIONS GAUSS FUNCTION INTEGRAL EQUATIONS ION TEMPERATURE IONS NUMERICAL SOLUTION PLASMA SHEATH PLASMA SIMULATION |
title | Extension of the Bissell–Johnson plasma-sheath model for application to fusion-relevant and general plasmas |
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