Weibel instability with semirelativistic Maxwellian distribution function
A macroscopic description of the linear Weibel instability, based on semirelativistic distribution in an unmagnetized plasma is presented. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian and semirelativistic Maxwellian...
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| Veröffentlicht in: | Physics of plasmas 2007-07, Vol.14 (7), p.072106-072106-3 |
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| container_end_page | 072106-3 |
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| container_issue | 7 |
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| container_title | Physics of plasmas |
| container_volume | 14 |
| creator | Zaheer, S. Murtaza, G. |
| description | A macroscopic description of the linear Weibel instability, based on semirelativistic distribution in an unmagnetized plasma is presented. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian and semirelativistic Maxwellian distribution functions under the conditions of
ξ
=
ω
k
‖
θ
‖
≫
1
and
≪
1
. The real frequency and the growth rate of the instability for the semirelativistic case now depends upon the factor
χ
generated from the relativistic term in the distribution function. The presence of
χ
which is always greater than unity favors the Weibel instability to occur even for the small anisotropy of temperature. As we increase the value of
χ
large enough that it dominates over other terms, the damping changes into growth. In the limiting case, i.e.,
χ
=
1
, the results approach the Maxwellian situation. |
| doi_str_mv | 10.1063/1.2749254 |
| format | Article |
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ξ
=
ω
k
‖
θ
‖
≫
1
and
≪
1
. The real frequency and the growth rate of the instability for the semirelativistic case now depends upon the factor
χ
generated from the relativistic term in the distribution function. The presence of
χ
which is always greater than unity favors the Weibel instability to occur even for the small anisotropy of temperature. As we increase the value of
χ
large enough that it dominates over other terms, the damping changes into growth. In the limiting case, i.e.,
χ
=
1
, the results approach the Maxwellian situation.</description><identifier>ISSN: 1070-664X</identifier><identifier>EISSN: 1089-7674</identifier><identifier>DOI: 10.1063/1.2749254</identifier><identifier>CODEN: PHPAEN</identifier><language>eng</language><publisher>United States: American Institute of Physics</publisher><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY ; ANISOTROPY ; BOLTZMANN-VLASOV EQUATION ; DAMPING ; DISTRIBUTION FUNCTIONS ; MAXWELL EQUATIONS ; PERMITTIVITY ; PLASMA INSTABILITY ; RELATIVISTIC PLASMA ; RELATIVISTIC RANGE</subject><ispartof>Physics of plasmas, 2007-07, Vol.14 (7), p.072106-072106-3</ispartof><rights>American Institute of Physics</rights><rights>2007 American Institute of Physics</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-69c398361ab07433d01911f9a2457650f7181a3108e97446b4d7d7136c8c24cb3</citedby><cites>FETCH-LOGICAL-c382t-69c398361ab07433d01911f9a2457650f7181a3108e97446b4d7d7136c8c24cb3</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/10.1063/1.2749254$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,776,780,790,881,1553,4498,27903,27904,76130,76136</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/20976621$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Zaheer, S.</creatorcontrib><creatorcontrib>Murtaza, G.</creatorcontrib><title>Weibel instability with semirelativistic Maxwellian distribution function</title><title>Physics of plasmas</title><description>A macroscopic description of the linear Weibel instability, based on semirelativistic distribution in an unmagnetized plasma is presented. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian and semirelativistic Maxwellian distribution functions under the conditions of
ξ
=
ω
k
‖
θ
‖
≫
1
and
≪
1
. The real frequency and the growth rate of the instability for the semirelativistic case now depends upon the factor
χ
generated from the relativistic term in the distribution function. The presence of
χ
which is always greater than unity favors the Weibel instability to occur even for the small anisotropy of temperature. As we increase the value of
χ
large enough that it dominates over other terms, the damping changes into growth. In the limiting case, i.e.,
χ
=
1
, the results approach the Maxwellian situation.</description><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</subject><subject>ANISOTROPY</subject><subject>BOLTZMANN-VLASOV EQUATION</subject><subject>DAMPING</subject><subject>DISTRIBUTION FUNCTIONS</subject><subject>MAXWELL EQUATIONS</subject><subject>PERMITTIVITY</subject><subject>PLASMA INSTABILITY</subject><subject>RELATIVISTIC PLASMA</subject><subject>RELATIVISTIC RANGE</subject><issn>1070-664X</issn><issn>1089-7674</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp9kF9LwzAUxYMoOKcPfoOCTwqduUmaNC-CDP8MFF8UfQtpmrJI144k29y3t6UDBZlP93D53cO5B6FzwBPAnF7DhAgmScYO0AhwLlPBBTvstcAp5-zjGJ2E8IkxZjzLR2j2bl1h68Q1IerC1S5uk42L8yTYhfO21tGtXYjOJM_6a2Pr2ukmKbuNd8UqurZJqlVjenGKjipdB3u2m2P0dn_3On1Mn14eZtPbp9TQnMSUS0NlTjnoAgtGaYlBAlRSE5YJnuFKQA6adtmtFIzxgpWiFEC5yQ1hpqBjdDH4tl0sFYyL1sxN2zTWREWwFJwT6KjLgTK-DcHbSi29W2i_VYBV35QCtWuqY28GtjfT_S_74aEu9asutekMrvYZrFv_c6yWZfUf_DfaN9aBjH8</recordid><startdate>20070701</startdate><enddate>20070701</enddate><creator>Zaheer, S.</creator><creator>Murtaza, G.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>20070701</creationdate><title>Weibel instability with semirelativistic Maxwellian distribution function</title><author>Zaheer, S. ; Murtaza, G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-69c398361ab07433d01911f9a2457650f7181a3108e97446b4d7d7136c8c24cb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</topic><topic>ANISOTROPY</topic><topic>BOLTZMANN-VLASOV EQUATION</topic><topic>DAMPING</topic><topic>DISTRIBUTION FUNCTIONS</topic><topic>MAXWELL EQUATIONS</topic><topic>PERMITTIVITY</topic><topic>PLASMA INSTABILITY</topic><topic>RELATIVISTIC PLASMA</topic><topic>RELATIVISTIC RANGE</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zaheer, S.</creatorcontrib><creatorcontrib>Murtaza, G.</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>Zaheer, S.</au><au>Murtaza, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weibel instability with semirelativistic Maxwellian distribution function</atitle><jtitle>Physics of plasmas</jtitle><date>2007-07-01</date><risdate>2007</risdate><volume>14</volume><issue>7</issue><spage>072106</spage><epage>072106-3</epage><pages>072106-072106-3</pages><issn>1070-664X</issn><eissn>1089-7674</eissn><coden>PHPAEN</coden><abstract>A macroscopic description of the linear Weibel instability, based on semirelativistic distribution in an unmagnetized plasma is presented. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian and semirelativistic Maxwellian distribution functions under the conditions of
ξ
=
ω
k
‖
θ
‖
≫
1
and
≪
1
. The real frequency and the growth rate of the instability for the semirelativistic case now depends upon the factor
χ
generated from the relativistic term in the distribution function. The presence of
χ
which is always greater than unity favors the Weibel instability to occur even for the small anisotropy of temperature. As we increase the value of
χ
large enough that it dominates over other terms, the damping changes into growth. In the limiting case, i.e.,
χ
=
1
, the results approach the Maxwellian situation.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><doi>10.1063/1.2749254</doi><tpages>3</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1070-664X |
| ispartof | Physics of plasmas, 2007-07, Vol.14 (7), p.072106-072106-3 |
| issn | 1070-664X 1089-7674 |
| language | eng |
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| source | AIP Journals Complete; AIP Digital Archive |
| subjects | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY ANISOTROPY BOLTZMANN-VLASOV EQUATION DAMPING DISTRIBUTION FUNCTIONS MAXWELL EQUATIONS PERMITTIVITY PLASMA INSTABILITY RELATIVISTIC PLASMA RELATIVISTIC RANGE |
| title | Weibel instability with semirelativistic Maxwellian distribution function |
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