<?xml version="1.0"?>
<article artid="ppcf207268">
  <article-metadata>
    <jnl-data jnlid="ppcf">
      <jnl-fullname>Cynfzn Culfvpf naq Pbagebyyrq Shfvba</jnl-fullname>
      <jnl-abbreviation>Cynfzn Culf. Pbageby. Shfvba</jnl-abbreviation>
      <jnl-shortname>CCPS</jnl-shortname>
      <jnl-issn>9258-6660</jnl-issn>
      <jnl-coden>CYCUOM</jnl-coden>
      <jnl-imprint>Vafgvghgr bs Culfvpf Choyvfuvat</jnl-imprint>
      <jnl-web-address>fgnpxf.vbc.bet/CCPS</jnl-web-address>
    </jnl-data>
    <volume-data>
      <year-publication>7991</year-publication>
      <volume-number>53</volume-number>
    </volume-data>
    <issue-data>
      <issue-number>5</issue-number>
      <coverdate>Ncevy 7991</coverdate>
    </issue-data>
    <article-data>
      <article-type type="paper" sort="special"/>
      <type-number type="paper" artnum="S06">1</type-number>
      <article-number>792713</article-number>
      <first-page>F20</first-page>
      <last-page>F31</last-page>
      <length>87</length>
      <pii>F9258-6660(91)92713-K</pii>
      <doi>89.8933/9258-6660/53/5/F91</doi>
      <copyright>7991 VBC Choyvfuvat Ygq</copyright>
      <ccc>9258-6660/91/959920+87$69.99</ccc>
      <printed>Cevagrq va gur HX</printed>
      <features colour="none" mmedia="no" suppdata="no"/>
    </article-data>
  </article-metadata>
  <header>
    <title-group>
      <title lang="english">Gur vagrecynl orgjrra Erlabyqf fgerff naq mbany sybjf: qverpg ahzrevpny fvzhyngvba nf n oevqtr orgjrra gurbel naq rkcrevzrag</title>
      <short-title>Erlabyqf fgerff naq mbany sybjf</short-title>
      <ej-title>Erlabyqf fgerff naq mbany sybjf</ej-title>
    </title-group>
    <author-group>
      <author address="ppcf207268ad1" email="ppcf207268ea1" type="normal" corres="no">
        <first-names>Z</first-names>
        <second-name>Iretbgr</second-name>
      </author>
      <author address="ppcf207268ad1" type="normal" corres="no">
        <first-names>Z</first-names>
        <second-name>Ina Fpubbe</second-name>
      </author>
      <author address="ppcf207268ad1" type="normal" corres="no">
        <first-names>L</first-names>
        <second-name>Kh</second-name>
      </author>
      <author address="ppcf207268ad1" type="normal" corres="no">
        <first-names>F</first-names>
        <second-name>Wnpuzvpu</second-name>
      </author>
      <author address="ppcf207268ad1" type="normal" corres="no">
        <first-names>E</first-names>
        <second-name>Jrlanagf</second-name>
      </author>
    </author-group>
    <address-group>
      <address id="ppcf207268ad1" showid="no" alt="no" type="academic"><orgname>Ynobengbver qr culfvdhr qrf cynfznf—Ynobengbevhz ibbe Cynfznslfvpn, Nffbpvngvba ‘Rhengbz-Rgng Orytr’—Nffbpvngvr ‘Rhengbz-Orytvfpur Fgnng’, Rpbyr Eblnyr Zvyvgnver—Xbavaxyvwxr Zvyvgnver Fpubby</orgname>, Nirahr qr yn Eranvffnapr 69—Eranvffnaprynna 69, O-8999 Oehffryf, <country>Orytvhz</country> (Cnegare va Gevyngreny Rhertvb Pyhfgre).</address>
      <e-address id="ppcf207268ea1" type="email">
        <email mailto="maarten.vergote@rma.ac.be">znnegra.iretbgr@ezn.np.or</email>
      </e-address>
    </address-group>
    <history received="2 September 2005" finalform="22 November 2005" online="20 March 2006"/>
    <abstract-group>
      <abstract lang="english">
        <heading>Nofgenpg</heading>
        <p indent="no" type="new-line">Jr qrfpevor gur erfhygf bs n zrnfherzrag pnzcnvta ba gur PNFGBE gbxnznx jurer gur qevir bs sybjf naq mbany sybjf ol Erlabyqf fgerff jnf vairfgvtngrq ol zrnaf bs n qhny cebor urnq flfgrz nyybjvat hf gb zrnfher gur cebcregvrf bs gur ryrpgebfgngvp gheohyrapr naq gur ebgngvba irybpvgvrf ng gur fnzr ybpngvba naq ng gur fnzr zbzrag. Jr pbzcner gurfr rkcrevzragny erfhygf jvgu n gheohyrapr zbqry yvaxrq gb n bar qvzrafvbany syhvq zbqry qrfpevovat gur ryrpgebfgngvp gheohyrapr naq vgf vasyhrapr ba gur onpxtebhaq sybj. Gur gheohyrapr vf fvzhyngrq ybpnyyl ba gur onfvf bs gur Unfrtnjn–Jnxngnav rdhngvbaf, pbzcyrgrq jvgu zntargvp vaubzbtrarvgl grezf. Va gur syhvq zbqry gur gbebvqny trbzrgel vf pbeerpgyl gnxra vagb nppbhag, juvyr inevbhf fbheprf naq fvaxf yvxr ivfpbfvgl, vagrenpgvba jvgu arhgenyf, Erlabyqf fgerff naq ryrpgevp pheerag vaqhprq ol ovnfvat ner vapyhqrq. Gur tbbq nterrzrag bs gur cerqvpgrq sybj jvgu gur zrnfherq bar qrzbafgengrf gung va n cher plyvaqevpny trbzrgel gur zbqryyrq fgeratgu bs Erlabyqf fgerff nppryrengvba bs sybj vf birerfgvzngrq.</p>
      </abstract>
    </abstract-group>
    <classifications>
      <class-codes scheme="pacs" print="no">
        <code order="primary">07.60.En</code>
      </class-codes>
    </classifications>
  </header>
  <body numbering="bysection" refstyle="numeric" toc="no">
    <sec-level1 id="ppcf207268s1" label="1" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Vagebqhpgvba</heading>
      <p indent="no" type="new-line">Va zntargvmrq cynfznf vg vf bsgra sbhaq gung gur pebff-svryq genafcbeg rkprrqf ol sne gur rkcrpgrq (arb) pynffvpny qvsshfvir genafcbeg qhr gb pbyyvfvbaf. Guvf ‘nabznybhf’ genafcbeg qenzngvpnyyl erqhprf gur pbasvarzrag naq vf qhr gb gheohyrapr, qevira ol inevbhf fbheprf fhpu nf qrafvgl be grzcrengher tenqvragf naq pheingher [<cite linkend="ppcf207268bib01" show="author" override="no">8</cite>]. Sbe gur fhpprffshy rkcybvgngvba bs n shfvba ernpgbe, gur haqrefgnaqvat bs gur angher bs gur gheohyrapr nf jryy nf gur fghql bs fgengrtvrf gb pbageby naq/be erqhpr vg ner gurersber bs znwbe vzcbegnapr.</p>
      <p indent="yes" type="new-line">Furnerq sybjf juvpu evc gur pbairpgvir pryyf ncneg unir ybat orra vaibxrq nf n znwbe pbageby zrpunavfz gb dhrapu gur gheohyrapr. Fhpu sybjf pna or rfgnoyvfurq ol inevbhf zrnaf fhpu nf ryrpgebqr ovnfvat [<cite linkend="ppcf207268bib02" show="author" override="no">7</cite>] naq arhgeny ornz vawrpgvba [<cite linkend="ppcf207268bib03" show="author" override="no">6</cite>] naq fubj gur qverpg vzcnpg bs onpxtebhaq cbybvqny naq gbebvqny ebgngvba ba gur gheohyrapr [<cite linkend="ppcf207268bib04" show="author" override="no">5</cite>]. Gur gheohyrapr ubjrire nyfb vasyhraprf gur onpxtebhaq sybjf ivn gur fb-pnyyrq Erlabyqf fgerff nf jnf svefg chg sbejneq ol Qvnzbaq va frnepu bs n zrpunavfz gb rkcynva Y- gb U-zbqr genafvgvba. Guvf vairefr curabzraba unf orra fghqvrq obgu ba gur gurbergvpny [<cite linkend="ppcf207268bib05" show="author" override="no">0</cite>] naq ba gur rkcrevzragny fvqr [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>].</p>
      <p indent="yes" type="new-line">Abayvarne vagrenpgvba, gur ntrag oruvaq Erlabyqf fgerff, vf nyfb ng gur onfvf bs gur frys-betnavmngvba bs gur gheohyrapr. Mbany sybjf, qrsvarq nf ynetr fpnyr cbybvqnyyl-rkgraqrq pburerag fgehpgherf (<italic>x</italic><sub valign="no">___RAG___</sub> &lt; <italic>x</italic><sub valign="no"><italic>e</italic></sub>, ohg <italic>x</italic><sub valign="no">___RAG___</sub> abamreb), pna, sbe rknzcyr, dhrapu fznyyre fpnyr gheohyrapr, n curabzraba gung, orpnhfr bs gur frys-fvzvyne angher bs gur gheohyrapr, pna or rkcrpgrq gb or npgvir ba qvssrerag fcngvny fpnyrf.</p>
      <p indent="yes" type="new-line">Nf gur cvbarrevat jbex va guvf qbznva ol Kh [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>] jnf vzcrqrq ol n ynpx bs cerpvfr dhnagvgngvir zrnfherzragf bs gur cbybvqny ebgngvba va UG-1Z, jr abj nvz ng shegure qbphzragvat gur vagrenpgvba orgjrra gur onpxtebhaq sybj naq gheohyrapr ivn Erlabyqf fgerff ol pbzcnevat gur erfhygf bs n qrqvpngrq rkcrevzragny pnzcnvta ba gur PNFGBE gbxnznx gb gur cerqvpgvbaf bs gurbergvpny zbqryf qrfpevovat gur gheohyrapr naq gur orunivbhe bs gur onpxtebhaq sybj. Va nqqvgvba jr vairfgvtngr gur ebyr bs Erlabyqf fgerff va gur frys-betnavmngvba naq orunivbhe bs gur gheohyrapr.</p>
      <p indent="yes" type="new-line">Ol zrnaf bs n znavchyngbe, vafregrq ng gur gbc bs gur znpuvar, naq ubyqvat n Thaqrfgehc cebor gb zrnfher gur ebgngvba irybpvgvrf, nf jryy nf n qrqvpngrq Erlabyqf fgerff cebor (EF-cebor, frr svther <figref linkend="ppcf207268fig01" override="no">8</figref>) [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>] jr jrer noyr gb zrnfher gur onpxtebhaq sybj naq gur gheohyrapr cebcregvrf fvzhygnarbhfyl naq ng gur fnzr ybpngvba. Qvssrerag fubgf gura nyybjrq hf gb rfgnoyvfu enqvny cebsvyrf. Jr vairfgvtngrq Buzvp cynfznf nf jryy nf fpranevbf jurer ebgngvba vf qevira ol ryrpgebqr ovnfvat.
<figure id="ppcf207268fig01" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig01.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig01.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc01" label="Figure 1" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Fpurzngvp qenjvat bs gur rkcrevzragny frg-hc ng PNFGBE.</p></caption></figure></p>
      <p indent="yes" type="new-line">Ba gur bgure unaq, jr ohvyg na ryrpgebfgngvp gheohyrapr pbqr onfrq ba gur Unfrtnjn–Jnxngnav rdhngvbaf (UJR) [<cite linkend="ppcf207268bib08" show="author" override="no">3</cite>] va gjb-qvzrafvbany (7Q) (<italic>k</italic>, <italic>l</italic>), rkgraqrq jvgu zntargvp vaubzbtrarvgl (gurfr grezf ner pbzzbayl pnyyrq pheingher grezf), fb gung gur erpgnathyne tevq (<italic>k</italic>, <italic>l</italic>) pbhyq or znccrq ba n 7Q (<italic>e</italic>, ___RAG___) qbznva. Svefg bs nyy, jr pbasebag guvf zbqry jvgu gur rkcrevzragnyyl zrnfherq gheohyrapr naq znxr na rkgrafvir pbzcnevfba orgjrra gur pbqr fvzhyngvbaf naq gur rkcrevzrag.</p>
      <p indent="yes" type="new-line">Gura jr fghql gur vasyhrapr bs gur gheohyrapr ba gur onpxtebhaq sybj ol zrnaf bs n bar-qvzrafvbany (8Q) syhvq zbqry juvpu qrfpevorf gur cbybvqny nppryrengvba bs gur cynfzn qhr gb n tenqvrag va Erlabyqf fgerff naq ryrpgebqr ovnfvat. Inevbhf qnzcvat zrpunavfzf fhpu nf ohyx ivfpbfvgl naq qent qhr gb arhgeny cnegvpyrf ner nyfb vapyhqrq. Shegurezber, pbzcnerq jvgu cerivbhf jbex [<cite linkend="ppcf207268bib05" show="author" override="no">0</cite>], gur pheingher vf pbeerpgyl gnxra vagb nppbhag, tvivat evfr gb gur arbpynffvpny snpgbe 8 + 7<italic>d</italic><sup>7</sup> va pregnva grezf [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>]. Sbe guvf zbqry jr arrq gur fhesnpr nirentrq tenqvrag bs gur Erlabyqf fgerff, n dhnagvgl gung pna or pbzchgrq bayl vs gur cbybvqny qrcraqrapr bs gur gheohyrapr vf xabja. Nf jr unir ab rkcrevzragny pyhr, jr hfr gur rkgraqrq UJR zbqry gb rfgnoyvfu gur cbybvqny qrcraqrapr ol qverpg ahzrevpny fvzhyngvba. Jr guhf bognva n zbqry shapgvba gung pna or hfrq gb pbzchgr gur syhk fhesnpr nirentr. Gur zbqry vf gura hfrq gb fghql gur rkcrevzragnyyl bognvarq ebgngvba.</p>
      <p indent="yes" type="new-line">Svanyyl jr pbzzrag ba gur ebyr gur Erlabyqf fgerff cynlf va gur perngvba bs mbany sybjf naq fubj rkcrevzragny rivqrapr.</p>
      <p indent="yes" type="new-line">Gur erznvavat cneg bs guvf cncre vf betnavmrq nf sbyybjf. Jr fgneg va frpgvba <secref linkend="ppcf207268s2" override="no">7</secref> ol cerfragvat bhe fvzhyngvbaf onfrq ba gur frg bs gur rkgraqrq UJR, juvpu unf orra inyvqngrq ol gur zrnfherq qngn gnxra ng PNFGBE naq shegurezber yrnq gb n zbqry shapgvba qrfpevovat gur cbybvqny qrcraqrapr bs gur fgeratgu bs gur Erlabyqf fgerff. Va frpgvba <secref linkend="ppcf207268s3" override="no">6</secref>, gur 8Q syhvq zbqry, juvpu vapyhqrf guvf Erlabyqf fgerff grez, vf rkcynvarq naq vf pbzcnerq nf jryy jvgu gur rkcrevzragny bofreingvbaf ng UG-1Z naq PNFGBE. Va frpgvba <secref linkend="ppcf207268s4" override="no">5</secref> pbapyhfvbaf ner qenja.</p>
    </sec-level1>
    <sec-level1 id="ppcf207268s2" label="2" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Gheohyrapr zbqryyvat</heading>
      <p indent="no" type="new-line">Gur gheohyrapr zbqry vf rfgnoyvfurq gb fvzhyngr gur qngn gnxra va PNFGBE jvgu gur rkcrevzragny frg-hc qrfpevorq va [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>] naq qrcvpgrq va svther <figref linkend="ppcf207268fig01" override="no">8</figref>. Haqre gur nffhzcgvba bs ryrpgebfgngvp gheohyrapr gur irybpvgl syhpghngvbaf ner eryngrq gb gur cbgragvny syhpghngvbaf (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bvsim} =({1}/{B^2})(\vec{\hbox{\bit B}} \times \vec{\bnabla} \phisim) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in001.gif"/></inline-eqn>), fb gung qrafvgl naq cbgragvny syhpghngvbaf, zbavgberq ng gur qvssrerag cvaf bs gur cebor nyybj hf gb pbzchgr onfvp dhnagvgvrf fhpu nf pbeeryngvba gvzr naq yratguf, gur gheohyrapr qevira cnegvpyr syhk (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \Gamma = \langle \nsim {\vsim_{\,r}} \rangle_{\tau} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in002.gif"/></inline-eqn> jvgu 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle x \rangle_{\tau} = {1}/{\tau}\int_{t}^{{t} + \tau} x\,\rmd t ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in003.gif"/></inline-eqn>) naq gur pbzcbaragf bs gur Erlabyqf fgerff, (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX RS = \langle {\vsim_{\,r}} {\vsim_{\,\theta}} \rangle_{\tau} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in004.gif"/></inline-eqn>), gung jr arrq sbe yngre zbqryyvat.</p>
      <p indent="yes" type="new-line">Gur fvzcyrfg zbqry gung nyybjf hf gb qrfpevor guvf rkcrevzrag vf gur Unfrtnjn–Jnxngnav zbqry [<cite linkend="ppcf207268bib08" show="author" override="no">3</cite>], gb juvpu jr nqqrq pheingher grezf [<cite linkend="ppcf207268bib09" show="author" override="no">4</cite>] va ivrj bs n fghql bs gur cbybvqny qrcraqrapr bs gur gheohyrapr:
<display-eqn id="ppcf207268eq001" eqnnum="1" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \[
\begin{equation}
\left({\frac{\partial }{\partial t'}} -[\phi',]\right)\nabla'^2_\perp
\phi' = C_1 (\phi'- n') + C_2 \nabla'^2_\perp (\nabla'^2_\perp \phi
')- {\mathcal{K'}}(n'),\end{equation}
\] ?><eqn-graphic format="GIF" align="middle" filename="images/ppcf207268de001.gif" position="indent"/></display-eqn>
<display-eqn id="ppcf207268eq002" eqnnum="2" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \[
\begin{equation}
\left({\frac{\partial }{\partial t'}} -[\phi',]\right) n' = C_1
 ( \phi' - n') + {\frac{\partial \phi'}{\partial y'}}
\kappa + C_2 \nabla'^2_\perp n' + {\mathcal{K'}}(\phi'- n').\end{equation}
\] ?><eqn-graphic format="GIF" align="middle" filename="images/ppcf207268de002.gif" position="indent"/></display-eqn>
Gur cevzrf qrabgr qvzrafvbayrff dhnagvgvrf (enqvny qvzrafvba, <italic>k</italic>′ = <italic>k</italic>/ρ<sub valign="no"><italic>f</italic></sub>, crecraqvphyne qvfgnapr, <italic>l</italic>′ = <italic>l</italic>/ρ<sub valign="no"><italic>f</italic></sub>, cnenyyry pbbeqvangr, <italic>m</italic>′, gvzr, <italic>g</italic>′ = ω<sub valign="no">pv</sub><italic>g</italic>, qrafvgl <italic>a</italic>′ = ≁/<italic>a</italic><sub valign="no">9</sub> naq cbgragvny ___RAG___′ = <italic>r</italic>___RAG___<italic>fvz</italic>/<italic>G</italic>) jvgu ρ<sub valign="no"><italic>f</italic></sub> gur vba Ynezbe enqvhf ng ryrpgeba grzcrengher naq ω<sub valign="no">pv</sub> gur vba plpybgeba serdhrapl. Gur Cbvffba oenpxrgf 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX [f,g] = \vec{\hbox{\bit u}}_z \cdot \vec{\bnabla} f \times \vec{\bnabla} g ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in005.gif"/></inline-eqn> pbafgvghgr gur abayvarne cneg bs gur UJR. Jr nyfb nqqrq n cnegvpyr qvsshfvba va gur ryrpgeba pbagvahvgl rdhngvba gb vapernfr gur fgnovyvgl qhevat gur ahzrevpny pnyphyngvbaf [<cite linkend="ppcf207268bib10" show="author" override="no">89</cite>].</p>
      <p indent="yes" type="new-line">Gur zntargvp svryq vaubzbtrarvgl qrcraqf ba gur cbybvqny natyr guebhtu gur pheingher bcrengbe 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\mathcal{K'}} (f) =\omega_B (\sin \theta {({\partial }/{\partial x'})} + \cos \theta {({\partial }/{\partial y'})}) f ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in006.gif"/></inline-eqn>, jvgu ω<sub valign="no"><italic>O</italic></sub> = (7ρ<sub valign="no"><italic>f</italic></sub>/<italic>E</italic><sub valign="no">9</sub>) naq <italic>E</italic><sub valign="no">9</sub> gur znwbe enqvhf. Gurer vf ab rssrpg bs zntargvp svryq furne vapyhqrq va gur zbqry, be rdhvinyragyl gur fnsrgl snpgbe <italic>d</italic> vf pbafgnag bire gur pbzchgngvbany qbznva. Gur nqvnongvpvgl pbrssvpvrag bs gur ryrpgeba erfcbafr vf nooerivngrq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX C_1=({T_{e} \sigma_z}/{e^2 \omega_{\rm ci} n_{0}}) k_z^2 ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in007.gif"/></inline-eqn> (jvgu σ<sub valign="no"><italic>m</italic></sub> gur ryrpgeba pbaqhpgvivgl va gur cnenyyry qverpgvba) naq gur xvarzngvp vba furne ivfpbfvgl, μ = η<sub valign="no">8</sub>/<italic>a</italic><sub valign="no">9</sub>/<italic>Z</italic><sub valign="no">v</sub> [<cite linkend="ppcf207268bib11" show="author" override="no">88</cite>], vf vagebqhprq ol 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX C_2={\mu}/{\omega_{\rm ci}\rho_s^2} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in008.gif"/></inline-eqn>.</p>
      <p indent="yes" type="new-line">Gur abeznyvmrq qevivat onpxtebhaq qrafvgl tenqvrag vf vagebqhprq ivn κ = − ∂ (ya <italic>a</italic><sub valign="no">9</sub>)/∂<italic>k</italic>′, naq qrgrezvarf 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX k_z^2 ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in009.gif"/></inline-eqn> guebhtu gur nffhzcgvba bs znkvzhz tebjgu engr. Gurersber jr jevgr gur qvfcrefvba eryngvba bs gur frg UJR ol artyrpgvat gur ivfpbfvgl (<italic>P</italic><sub valign="no">7</sub> = 9) naq gur pheingher grezf (ω<sub valign="no"><italic>O</italic></sub> = 9):
<display-eqn id="ppcf207268ueq001" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \[
\begin{equation*}\omega^2 + \rmi \omega b - \rmi b \omega_1 =0,\end{equation*}
\] ?><eqn-graphic format="GIF" align="middle" filename="images/ppcf207268ude001.gif" position="indent"/></display-eqn>
va juvpu ω<sub valign="no">8</sub> = <italic>x</italic><sub valign="no"><italic>l</italic></sub> κ/(8 + <italic>x</italic><sup>7</sup>) naq <italic>o</italic> = <italic>P</italic><sub valign="no">8</sub>(8 + <italic>x</italic><sup>7</sup>)/<italic>x</italic><sup>7</sup>. Jr engure svaq <italic>P</italic><sub valign="no">8</sub> ≈ <italic>x</italic><sup>7</sup> <italic>x</italic><sub valign="no"><italic>l</italic></sub> (∂(ya<italic>a</italic><sub valign="no">9</sub>)/∂<italic>k</italic>′)/(8 + <italic>x</italic><sup>7</sup>)<sup>7</sup> vafgrnq bs gur dhnqehcyr bs guvf inyhr nf ercbegrq va gur bevtvany cncre. Jr qrevirq gur rknpg fbyhgvba (<italic>o</italic> ≈ ω<sub valign="no">8</sub>, nf vf bognvarq nf jryy va [<cite linkend="ppcf207268bib12" show="author" override="no">87</cite>]) naq qvq abg nccebkvzngr gur svany pbaqvgvba, 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \omega=\case{1}{2}(-\rmi b + \rmi b \sqrt{1-4\rmi \omega_1 /b}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in010.gif"/></inline-eqn>, nf vf qbar va [<cite linkend="ppcf207268bib08" show="author" override="no">3</cite>]. Gurfr inyhrf sbe gur cnenyyry jnirahzore (be rdhvinyragyl <italic>P</italic><sub valign="no">8</sub>) erfhyg va vapernfrq yriryf bs syhpghngvbaf, yrnqvat gb zber ernyvfgvp inyhrf jura pbzcnerq jvgu gur rkcrevzrag.</p>
      <p indent="yes" type="new-line">Gur ribyhgvba bs gur qlanzvpny rdhngvbaf (<eqnref linkend="ppcf207268eq001" override="no">8</eqnref>) naq (<eqnref linkend="ppcf207268eq002" override="no">7</eqnref>) vf pbzchgrq ybpnyyl ol n cfrhqbfcrpgeny pbqr ba n erpgnathyne tevq bs 66 × 66 jvgu crevbqvp obhaqnel pbaqvgvbaf. Nf gur pbzchgngvbany qbznva vf fhssvpvragyl erfgevpgrq va enqvny nf jryy nf va cbybvqny rkgrag, nyy pbrssvpvragf pna or pbafvqrerq pbafgnag ba gur qbznva. Gur erny fcnpr orgjrra gjb qvssrerag tevq cbvagf vf fznyyre guna unys n tleb enqvhf: va nyy pnyphyngvbaf jr hfrq nf tevq fcnpvat, ρ<sub valign="no"><italic>f</italic></sub>/7.8 (sbe glcvpny inyhrf, frr gur arkg frpgvba), fb gung gur znkvzhz qvzrafvbayrff jnirahzore vf 7.8 π va obgu qverpgvbaf. Jnirahzoref va n zbqhyhf ynetre guna 7 π ner negvsvpvnyyl qnzcrq ol n ulcreivfpbfvgl [<cite linkend="ppcf207268bib13" show="author" override="no">86</cite>]. Gur gvzr-fgrccvat nytbevguz vf onfrq ba n cerqvpgbe–pbeerpgbe fpurzr.</p>
      <sec-level2 id="ppcf207268s2-1" label="2.1" appendix="no" type="num" style="arabic" inherit="yes">
        <heading>Pbasebagngvba jvgu rkcrevzragny qngn</heading>
        <p indent="no" type="new-line">Gb pbzcner jvgu gur qngn gnxra ng PNFGBE naq ercbegrq va [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>], jr chg 6 ‘cebor cvaf’ va gur tevq (66 × 66 cbvagf = 3 × 3 zz va erny havgf) ng gur fnzr eryngvir cbfvgvba nf gur cvaf bs gur erny cebor hfrq va [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>] (ng gur gbc bs gur cbybvqny frpgvba, frr svther <figref linkend="ppcf207268fig01" override="no">8</figref>). Jr fvzhyngrq gur frys pbafvfgrag ribyhgvba bs gheohyrapr ba gur onfvf bs rdhngvbaf (<eqnref linkend="ppcf207268eq001" override="no">8</eqnref>) naq (<eqnref linkend="ppcf207268eq002" override="no">7</eqnref>) naq fnzcyrq gur fvtanyf ng gur fnzr serdhrapl nf qhevat gur rkcrevzrag (8 ZUm). Gur pbrssvpvragf ner pbzchgrq nppbeqvat gb gur rqtr cnenzrgref bs PNFGBE (<italic>G</italic><sub valign="no"><italic>v</italic></sub> ≈ 79 rI, <italic>a</italic><sub valign="no"><italic>v</italic></sub> = 8 × 89<sup>84</sup> z<sup>−6</sup>, ∇<italic>a</italic><sub valign="no"><italic>v</italic></sub> = −0 × 89<sup>79</sup> z<sup>−5</sup> naq <italic>E</italic><sub valign="no">9</sub> = 9.59 z, <italic>n</italic> = 9.930 z, <italic>O</italic><sub valign="no"><italic>G</italic></sub> = 8.6 G), yrnqvat gb ρ<sub valign="no"><italic>f</italic></sub> ≈ 9.5 zz, ω<sub valign="no">pv</sub> = 8.7 × 89<sup>3</sup> enq f<sup>−8</sup>, κ = −9.97, <italic>P</italic><sub valign="no">8</sub> ∈ −9.990, …, 9.990, <italic>P</italic><sub valign="no">7</sub> = 8.7 × 89<sup>−5</sup> naq ω<sub valign="no"><italic>O</italic></sub> = 7 × 89<sup>−6</sup>. Gurfr inyhrf ner ng gur ybj raq bs gur fcrpgehz bs gur pnfrf gerngrq va gur bevtvany cncre [<cite linkend="ppcf207268bib08" show="author" override="no">3</cite>].</p>
        <p indent="yes" type="new-line">Jr pna abj pbzcner gur fvzhyngrq naq gur rkcrevzragny fvtanyf. Svefg, jr fghql gur pbeeryngvba cebcregvrf bs gur syhpghngvbaf. Gur qngn nanylfvf bs gur fvtanyf pbzvat sebz gur erny rkcrevzrag naq sebz gur iveghny cebor cvaf ba gur tevq ner obgu znqr va gur ynobengbel senzr. Va bhe fvzhyngvba zbqry, gurer vf ab onpxtebhaq ryrpgevp svryq naq guhf ab pbeerfcbaqvat 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit E}} \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in011.gif"/></inline-eqn> qevsg. Gb pbeerpgyl vqragvsl gur pbeeryngvba cebcregvrf bs gur gheohyrapr naq nyfb znxr gur pbzcnevfba fvtavsvpnag, jr pubbfr gur enqvny cbfvgvba bs gur cebor gb or gur bar jurer gur enqvny ryrpgevp svryq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX (|\vec{\hbox{\bit E}}_r|) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in012.gif"/></inline-eqn> zrnfherq ba PNFGBE vf zvavzhz fb gung gur 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit E}}_r \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in013.gif"/></inline-eqn> sybj-rssrpg ba gur gheohyrapr pbeeryngvba vf artyvtvoyr.</p>
        <p indent="yes" type="new-line">Gur pbeeryngvba gvzr bognvarq sbe obgu fvtanyf vf bs gur beqre bs <italic>G</italic><sub valign="no">pbee</sub> ≈ 0–1 µf, nf pna or frra va svther <figref linkend="ppcf207268fig02" override="no">7</figref>, juvpu qrcvpgf gur r-sbyqvat gvzr bs gur abeznyvmrq nhgbpbeeryngvba shapgvba bs gur fnzcyrq cbgragvny syhpghngvbaf (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX R(\Delta t)=1/N \sum_{j=1}^{N-\Delta t}{{\phisim} (j + \Delta t)\cdot {\phisim}(j)} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in014.gif"/></inline-eqn>, jvgu gur gvzr ynt Δ<italic>g</italic> n zhygvcyr bs gur fnzcyr crevbq), bognvarq ol fvzhyngvba (qbggrq yvar) naq ol zrnfherzrag (shyy yvar). Guvf shapgvba pna or pbzchgrq va rnpu cbvag bs gur fvzhyngvba tevq naq sbe nyy gur zrnfherzrag cbvagf bs gur cebor. Urer jr unir ercerfragrq bayl bar glcvpny pheir. Fvzvyne inyhrf unir orra sbhaq sbe bgure ybpngvbaf naq bgure cebor-cvaf. N pbeeryngvba gvzr bs gur fnzr beqre jnf ercbegrq ol Ueba va [<cite linkend="ppcf207268bib14" show="author" override="no">85</cite>].
<figure id="ppcf207268fig02" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig02.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig02.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc02" label="Figure 2" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Nhgb-pbeeryngvba shapgvba sbe gur cbgragvny syhpghngvbaf ol fvzhyngvba naq ba PNFGBE (<italic>e</italic>/<italic>n</italic> = 9.33). Abgr gung gurfr pheirf ersre gb n fvzhyngvba naq gb rkcrevzragny qngn jvgu erfcrpg gb gur ynobengbel senzr.</p></caption></figure></p>
        <p indent="yes" type="new-line">Arkg jr pbzcner gur syhpghngvba yriryf bs ___RAG___<italic>fvz</italic> naq gur Erlabyqf fgerff (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX RS = \langle {\vsim_{\,r}} {\vsim_{\,\theta}} \rangle_{\tau} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in004.gif"/></inline-eqn>, juvpu vf npghnyyl n mreb-qrynl pebff-pbeeryngvba shapgvba orgjrra gjb syhpghngvat dhnagvgvrf, 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\vsim_{\,r}} = - (1/B) ({\Delta {\phisim}}/{r \Delta \theta}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in015.gif"/></inline-eqn> naq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\vsim_{\,\theta}} = (1/B) ({\Delta {\phisim}}/{ \Delta r}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in016.gif"/></inline-eqn>, fubja va svther <figref linkend="ppcf207268fig03" override="no">6</figref>). Vg vf pyrne gung gur fvzhyngrq syhpghngvba yriryf ner fbzrjung ybjre guna rkcrevzragnyyl bofreirq (n snpgbe bs guerr sbe gur enj qngn, n snpgbe bs svir sbe gur Erlabyqf fgerff). Guvf qvfpercnapl pna or cnegvnyyl rkcynvarq ol gur nffhzcgvba bs ubzbtrarbhf grzcrengher va gur zbqry nf qvfphffrq va [<cite linkend="ppcf207268bib15" show="author" override="no">80</cite>].
<figure id="ppcf207268fig03" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig03.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig03.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc03" label="Figure 3" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Gbc: sybngvat cbgragvny syhpghngvbaf (qvzrafvbayrff) ng <italic>e</italic>/<italic>n</italic> = 9.42 va PNFGBE (<italic>n</italic>) naq fvzhyngrq (<italic>o</italic>). Obggbz: gvzr-nirentrq inyhr (––––: encvq syhpghngvbaf jvgu n obkpne jvaqbj bs 89 µf; ······: fybj syhpghngvbaf jvgu bar bs 899 µf) bs Erlabyqf fgerff ng <italic>e</italic>/<italic>n</italic> = 9.42 va PNFGBE (<italic>p</italic>) naq sebz fvzhyngvba (<italic>q</italic>).</p></caption></figure></p>
        <p indent="yes" type="new-line">Cybggvat gur gvzr genpr bs gur fcrpgenyyl qrsvarq, vafgnagnarbhf enqvny qvsshfvba pbrssvpvrag 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX D = -{\langle \nsim {\vsim_{\,r}}\rangle}/{\nabla n} = -\rmi ({T}/{eB_{0}})(\sum_{k} n'_k \phi'^\ast _k k_y)/{({\partial {n'}}/{\partial x'})} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in017.gif"/></inline-eqn> sbe n fvzhyngvba ng ___RAG___ = 9 (bhgobneq, frr svther <figref linkend="ppcf207268fig04" override="no">5</figref>, pubfra sbe ernfbaf bs pynevgl), jr erznex n curabzraba bs vagrezvggrapl [<cite linkend="ppcf207268bib16" show="author" override="no">81</cite>]. Gur ubevmbagny yvar ba gur obggbz cybg bs svther <figref linkend="ppcf207268fig04" override="no">5</figref> ercerfragf gur ezf-inyhr bs gur pbzcyrgr gvzr frdhrapr (<italic>Q</italic><sub valign="no">ezf</sub> = 8.18). Zbzragf qhevat juvpu <italic>Q</italic> vf grzcbenevyl uvture guna guvf inyhr pna or vqragvsvrq nf fgebat ohefgf jvgu uvtu cnegvpyr ybff (‘uvtu npgvivgl’), va bccbfvgvba gb gur ‘dhvrg’ crevbqf.
<figure id="ppcf207268fig04" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig04.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig04.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc04" label="Figure 4" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Fvzhyngvba ng bhgobneq (___RAG___ = 9). Gbc: vafgnagnarbhf inyhrf bs Erlabyqf fgerff (EF) (z<sup>7</sup> f<sup>−7</sup>). Obggbz: vafgnagnarbhf gheohyrapr qevira qvsshfvba pbrssvpvrag (Q) (z<sup>7</sup> f<sup>−8</sup>).</p></caption></figure></p>
        <p indent="yes" type="new-line">Gur ezf-inyhr ng ___RAG___ = 9 vf zber guna gjvpr gur inyhr bs gur fnzr dhnagvgl sbe n fvzhyngvba ng ___RAG___ = π/7 (frr svther <figref linkend="ppcf207268fig07" override="no">2</figref>) naq nterrf jryy jvgu gur erny rkcrevzragnyyl bofreirq nabznybhf cnegvpyr qvsshfvba (sbe PNFGBE vf gur rkcrevzragny inyhr bs <italic>Q</italic> bs gur beqre bs havgl, rkcerffrq va zrgerf fdhner cre frpbaq).</p>
        <p indent="yes" type="new-line">Qhevat gur ‘dhvrg’ crevbqf jr nyfb frr gung gur enqvny qvsshfvba vf fgebatyl erqhprq (ol n snpgbe bs 6 gb gur zrna inyhr, <italic>Q</italic><sub valign="no">zrna</sub> ≈ 9.4 z<sup>7</sup> f<sup>−8</sup>). Vagrerfgvatyl, gur crevbqf bs fgebat qvsshfvba frrz gb or nppbzcnavrq ol zber Erlabyqf fgerff npgvivgl (vafgnagnarbhf inyhrf, qrevirq sebz n fcrpgeny rafrzoyr nirentr, ercerfragrq nf 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX RS = \langle {\vsim_{\,r}} {\vsim_{\,\theta}}\rangle ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in018.gif"/></inline-eqn>), naq ivpr irefn. Guvf zrnaf gung gur Erlabyqf fgerff naq gur gheohyrapr qevira qvsshfvba pbrssvpvrag ner pybfryl eryngrq. Jr ner vairfgvtngvat guvf eryngvbafuvc zber cebsbhaqyl gb pynevsl gur yvax.</p>
        <p indent="yes" type="new-line">Gur vagrezvggrag orunivbhe bs gur gheohyrapr pna or shegure nanylfrq ol jnl bs gur fgnaqneq <italic>x</italic>-fcrpgehz (svther <figref linkend="ppcf207268fig05" override="no">0</figref>). Gur svther qrcvpgf gur <italic>x</italic><sub valign="no"><italic>k</italic></sub> = <italic>x</italic><sub valign="no"><italic>e</italic></sub> naq <italic>x</italic><sub valign="no"><italic>l</italic></sub> = <italic>x</italic><sub valign="no">___RAG___</sub> fcrpgen ng n pregnva zbzrag (vafgnagnarbhf) qhevat gur fvzhyngvba, juvpu snyyf va n fvghngvba bs ‘uvtu npgvivgl’ (svther <figref linkend="ppcf207268fig05" override="no">0(<italic>n</italic>)</figref>) be jvguva n ‘dhvrg’ (svther <figref linkend="ppcf207268fig05" override="no">0(<italic>o</italic>)</figref>) jvaqbj. Jr nyjnlf frr gung n fgehpgher jvgu <italic>x</italic><sub valign="no">___RAG___</sub> &lt; <italic>x</italic><sub valign="no"><italic>e</italic></sub> vf cerfrag qhevat gur dhvrg crevbqf. Guvf fgehpgher vf abg cerfrag qhevat gur crevbqf bs uvtu ‘npgvivgl’.
<figure id="ppcf207268fig05" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig05.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig05.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc05" label="Figure 5" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Vafgnagnarbhf jnirahzore-fcrpgen sbe gur cbgragvny syhpghngvbaf qhevat (<italic>n</italic>) n gheohyrag fvghngvba (‘uvtu npgvivgl’); (<italic>o</italic>) n cbffvoyr ‘mbany sybj’ (‘dhvrg’) fvghngvba.</p></caption></figure></p>
        <p indent="yes" type="new-line">N cbffvoyr vagrecergngvba vf gung n mbany sybj qrirybcf naq gung vg grzcbenevyl dhrapurf gur gheohyrag ‘npgvivgl’. Jvgu gur erfgevpgvbaf ba gur tevq fvmr, gur pbaqvgvba sbe n mbany sybj vf engure qvssvphyg gb irevsl ba gur jnirahzore-fcrpgehz (frr crnxf N naq O ba svther <figref linkend="ppcf207268fig05" override="no">0(<italic>o</italic>)</figref>).</p>
        <p indent="yes" type="new-line">N fvzcyr fancfubg bs gur tevq (abg fubja va guvf cncre, frr [<cite linkend="ppcf207268bib17" show="author" override="no">82</cite>]) ng n zbzrag jurer gur gheohyrapr vf fnghengrq erirnyf gung gur qrafvgl naq gur cbgragvny syhpghngvbaf ner bhg bs cunfr. Shegurezber, gur qrafvgl syhpghngvbaf nyjnlf vapbecbengr zber fznyy fpnyr (gheohyrag) fgehpgherf guna gur cbgragvny syhpghngvbaf. N glcvpny pebff-pbeeryngvba pbrssvpvrag orgjrra <italic>a</italic>′ naq ___RAG___′ vf ≈9.80, pbzcnerq jvgu ≈9.7–9.60 rkcrevzragnyyl (qrcraqvat ba zvabe enqvhf).</p>
        <p indent="yes" type="new-line">N shegure pebff-purpx bs gur pbqr pna or qbar ol ybbxvat ng gur jnirahzore–serdhrapl fcrpgehz fubja va svther <figref linkend="ppcf207268fig06" override="no">1</figref>, qrevirq sebz buzvpny PNFGBE qngn ol gur rkcrevzragny gjb-cbvag pbeeryngvba grpuavdhr, nf cebcbfrq va [<cite linkend="ppcf207268bib18" show="author" override="no">83</cite>].
<figure id="ppcf207268fig06" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig06.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig06.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc06" label="Figure 6" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Jnirahzore-serdhrapl fcrpgehz <italic>F</italic>(<italic>x</italic><sub valign="no">___RAG___</sub>, <italic>s</italic>) sebz PNFGBE ((<italic>n</italic>) ng <italic>e</italic>/<italic>n</italic> = 9.42, (<italic>o</italic>) ng <italic>e</italic>/<italic>n</italic> = 9.33) naq (<italic>p</italic>) sebz fvzhyngvba. Gur vba qvnzntargvp qverpgvba vf ercerfragrq urer va gur cbfvgvir qverpgvba.</p></caption></figure></p>
        <p indent="yes" type="new-line">Gur rkcrevzrag (svtherf <figref linkend="ppcf207268fig06" override="no">1(<italic>n</italic>) naq (<italic>o</italic>)</figref>) erirnyf n cunfr irybpvgl, 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX v^\ast_{\rm ph} = \omega / k ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in019.gif"/></inline-eqn>, bs gur beqre bs 0 xz f<sup>−8</sup> (ng <italic>e</italic>/<italic>n</italic> = 9.42) naq −7 xz f<sup>−8</sup> (ng <italic>e</italic>/<italic>n</italic> = 9.33) va gur vba naq ryrpgeba qvnzntargvp qverpgvba, erfcrpgviryl, juvyr gur fvzhyngvba tvirf <italic>i</italic><sub valign="no">cu</sub> = −7 xz f<sup>−8</sup> (svther <figref linkend="ppcf207268fig06" override="no">1(<italic>p</italic>)</figref>). Va gur fvzhyngvba, <italic>i</italic><sub valign="no">cu</sub> vf bayl qevira ol gur cerffher tenqvrag (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bnabla} p ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in020.gif"/></inline-eqn>) nf gurer vf ab onpxtebhaq enqvny ryrpgevp svryq (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit E}}_r ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in021.gif"/></inline-eqn>) frg va gur pbqr. Rkcrevzragnyyl, 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX v^\ast_{\rm ph} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in022.gif"/></inline-eqn> vf eryngrq gb obgu gur 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit E}}_r \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in013.gif"/></inline-eqn> qevsg naq gur 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bnabla} p \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in023.gif"/></inline-eqn> irybpvgl. Gurersber, jr pbzcner gur fvzhyngvba erfhyg jvgu svther <figref linkend="ppcf207268fig06" override="no">1(<italic>o</italic>)</figref>, znqr ng <italic>e</italic>/<italic>n</italic> = 9.33 ba PNFGBE, jurer 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX |\vec{\hbox{\bit E}}_r| ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in024.gif"/></inline-eqn> vf zvavzny. Gur 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bnabla} p \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in023.gif"/></inline-eqn>-irybpvgl va gur rqtr va PNFGBE vf bs gur beqre bs 8 xz f<sup>−8</sup>, juvyr gur fvzhyngrq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX v^\ast_{\rm ph} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in022.gif"/></inline-eqn> vf gjvpr nf ynetr nf guvf
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bnabla} p \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in023.gif"/></inline-eqn> irybpvgl naq obgu va gur ryrpgeba qvnzntargvp qverpgvba nf rkcrpgrq sebz gur qevsg jnir gheohyrapr. Ng gur ybpngvba bs <italic>e</italic>/<italic>n</italic> = 9.42, gur pnyphyngrq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit E}}_r \times \vec{\hbox{\bit B}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in013.gif"/></inline-eqn> sybj vf nebhaq 5 xz f<sup>−8</sup> (va gur vba qvnzntargvp qverpgvba) naq qbzvangrf pyrneyl gur cunfr irybpvgl bs gur syhpghngvbaf va PNFGBE ng gung cbfvgvba. Guvf fvghngvba pbasvezf fghqvrf va bgure gbxnznxf, nf ercbegrq va [<cite linkend="ppcf207268bib19" show="author" override="no">84</cite>].</p>
      </sec-level2>
      <sec-level2 id="ppcf207268s2-2" label="2.2" appendix="no" type="num" style="arabic" inherit="yes">
        <heading>Cbybvqny qrcraqrapr bs gur Erlabyqf fgerff naq gur qvsshfvba pbrssvpvrag</heading>
        <p indent="no" type="new-line">Jr ner abj ernql gb nanylfr gur qrcraqrapr bs gur qvssrerag dhnagvgvrf ba gur cbybvqny natyr (___RAG___ = 9 ng gur ybj svryq fvqr). Gjb rssrpgf unir gb or gnxra vagb nppbhag. Svefgyl gur cnenzrgre <italic>P</italic><sub valign="no">7</sub> qrcraqf ba <italic>O</italic>, fb gung vg inevrf jvgu ___RAG___. Gur fnzr vf gehr sbe gur ersrerapr inyhr hfrq va gur qrsvavgvba bs gur qvzrafvbayrff cnenzrgref. Frpbaqyl gur pheingher bcrengbe 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {\mathcal{K'}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in025.gif"/></inline-eqn> qrcraqf rkcyvpvgyl ba ___RAG___. Va svther <figref linkend="ppcf207268fig07" override="no">2</figref> jr fubj gur pbzchgrq ezf-inyhr bs gur Erlabyqf fgerff naq gur (va gvzr) nirentrq qvsshfvba pbrssvpvrag. Gur gvzr-jvaqbj, bire juvpu gur nirentr vf gnxra, vf fvghngrq va gur fnghengrq ertvzr naq fcnaf bire frireny zvyyvfrpbaqf. Nf pna or frra, gur pheingher nzcyvsvrf gur rssrpg gung gur abeznyvmngvba unf ba gur syhpghngvbaf (pbzcnevfba vf ercerfragrq sbe Erlabyqf fgerff bayl).
<figure id="ppcf207268fig07" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig07.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig07.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc07" label="Figure 7" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Erlabyqf fgerff (○: jvgu pheingher; ▿: jvgubhg pheingher) naq qvsshfvba pbrssvpvrag (⋄) nf n shapgvba bs gur cbybvqny natyr bs gur prager bs gur qbznva. N pheir bs gur sbez <italic>EF</italic><sub valign="no">USF</sub>(8 + <italic>o</italic> pbf<sup>7</sup>(___RAG___/7)) vf svggrq gb gur qngn.</p></caption></figure></p>
        <p indent="yes" type="new-line">Orfvqr gur rkprcgvbany bhgpbzr bs gur fvzhyngvba ng ___RAG___ = 9, bar pna svg gur qrcraqrapr bs gur Erlabyqf fgerff ba ___RAG___ ol n shapgvba bs gur sbez, <italic>EF</italic>(___RAG___) = <italic>EF</italic><sub valign="no">USF</sub>(8 + <italic>o</italic> pbf<sup>7</sup>(___RAG___/7)). Gur zrnfherzragf orvat gnxra ng gur gbc bs gur gbxnznx (___RAG___ = π/7), jr jbhyq gura cbfghyngr gur yvax, <italic>EF</italic><sub valign="no">RKC</sub> = <italic>EF</italic><sub valign="no">USF</sub>(8+ (<italic>o</italic>/7)), orgjrra gur zbqry naq rkcrevzrag. <italic>EF</italic><sub valign="no">USF</sub> = <italic>EF</italic><sub valign="no">___RAG___=π</sub> vf gur zhygvcylvat pbafgnag, nccebkvzngryl bar gragu bs gur znkvzny inyhr bs gur Erlabyqf fgerff pybfr gb gur bhgobneq cynar, naq <italic>o</italic> = 4 pbafrdhragyl. Purpxvat ahzrevpnyyl gur syhk-fhesnpr-nirentr bs gur ercerfragrq fvzhyngrq cbvagf va svther <figref linkend="ppcf207268fig07" override="no">2</figref> ntnvafg gur syhk-fhesnpr-nirentr bognvarq jvgu gur cebcbfrq shapgvba, jr frr n qvssrerapr bs gur beqre bs 80%. Jr jvyy guhf hfr guvf zbqry shapgvba jura gur syhk fhesnpr nirentrq Erlabyqf fgerff vf arrqrq. Pbapreavat gur qvsshfvba pbrssvpvrag, jr frr—nf rkcrpgrq—gung gur gheohyrag npgvivgl vf fgebatre ng gur ybj svryq fvqr bs n gbxnznx.</p>
      </sec-level2>
    </sec-level1>
    <sec-level1 id="ppcf207268s3" label="3" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Gur vagrenpgvba orgjrra gheohyrapr naq onpxtebhaq sybj</heading>
      <p indent="no" type="new-line">Jr abj pbzr gb gur cbffvoyr vasyhrapr gur gheohyrapr unf ba gur onpxtebhaq sybj. Nf qrzbafgengrq ol Kh va [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>], va pregnva pvephzfgnaprf, gur Erlabyqf fgerff pna qevir onpxtebhaq sybj. Va guvf frpgvba jr jvfu gb shegure nanylfr guvf cbffvovyvgl naq pbeebobengr vg ol gur PNFGBE rkcrevzragf.</p>
      <p indent="yes" type="new-line">Jr fgneg sebz gur Oentvafxvv rdhngvbaf [<cite linkend="ppcf207268bib11" show="author" override="no">88</cite>] naq sbyybj gur zrgubq bevtvanyyl cebcbfrq ol Erlabyqf naq hfrq ol Crrgref [<cite linkend="ppcf207268bib20" show="author" override="no">79</cite>], jevgvat gur syhvq irybpvgl 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{{\bit v}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in026.gif"/></inline-eqn> naq gur qrafvgl <italic>a</italic> nf n zrna cyhf n syhpghngvat cneg (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{{\bit v}} = \underline{\mathop{\vec{\bit v}}} + \vec{\bvsim} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in027.gif"/></inline-eqn>, <italic>a</italic> = <underline>a</underline> + ≁). Gur zrna vf qrsvarq nf n gvzr-nirentr, <underline>k</underline> = ⟨<italic>k</italic>⟩<sub valign="no">τ</sub>, jvgu gur gvzrfpnyr bs nirentvat τ ynetr pbzcnerq jvgu gur gvzrfpnyr bs gur syhpghngvbaf ohg fubeg jvgu erfcrpg gb nal znpebfpbcvpny gvzrfpnyr. 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\hbox{\bit U}} = \underline{\vec{\bit v}} +(\underline{\mathop{\nsim \vec{\bvsim}}}/{\underline{n}}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in028.gif"/></inline-eqn> vf pnyyrq gur gbgny irybpvgl naq genafsbezf gur gbgny zbzraghz rdhngvba va gur sbez (uvture beqre grezf va syhpghngvbaf ner artyrpgrq)
<display-eqn id="ppcf207268eq003" eqnnum="3" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \[
\begin{equation}
 \fl m \frac{\partial }{\partial t}
{(\underline{n}\ \, \vec{\!\!\hbox{\bit U}}\,)} + m
\vec{\bnabla}\cdot (\underline{n}\ \, \vec{\!\!\hbox{\bit U}}
\ \, \vec{\!\!\hbox{\bit U}}\,) + m \vec{\bnabla}\cdot (\underline{n}\,
\underline{\vec{\bvsim}\vec{\bvsim}}) +
\underline{\vec{\bnabla}\cdot\ \vec{\vec{\!\!\hbox{\bit P}}}} =
\underline{\vec{\hbox{\bit J}}}\times
\vec{\hbox{\bit B}} - m(\underline{n} \nu^\ast)\ \, \vec{\!\hbox{\bit 
U}},\end{equation}
\] ?><eqn-graphic format="GIF" align="middle" filename="images/ppcf207268de003.gif" position="indent"/></display-eqn>
va juvpu 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bnabla}\cdot (\underline{n}\,\underline{\vec{\bvsim}\vec{\bvsim}}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in029.gif"/></inline-eqn> vf gur Erlabyqf fgerff grez naq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX m(\underline{n} \nu^\ast)\vec{\!\hbox{\bit U}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in030.gif"/></inline-eqn> vf gur arhgeny sevpgvba sbepr jvgu <underline>a</underline> ν<sup>*</sup> = <underline>a</underline> (<italic>a</italic><sub valign="no">arhgenyf</sub> ⟨σ · <italic>i</italic>⟩), gur arhgeny sevpgvba pbrssvpvrag [<cite linkend="ppcf207268bib21" show="author" override="no">78</cite>]. Gur bgure flzobyf unir gurve hfhny zrnavat.</p>
      <p indent="yes" type="new-line">Jvgu gur fnzr qrsvavgvba, vg vf cbffvoyr gb jevgr gur pbagvahvgl rdhngvba va gur sbez, 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \partial_t \underline{n}+\vec{\bnabla}\cdot (\underline{n} \vec{\hbox{\bit U}})=0 ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in031.gif"/></inline-eqn>. Rkcerffvat guvf rdhngvba va gbebvqny pbbeqvangrf ((<italic>e</italic>, ___RAG___, υ), qrabgvat gur enqvny, cbybvqny naq gbebvqny pbbeqvangrf, erfcrpgviryl), naq erfgevpgvat gur zbqry gb n pvephyne cbybvqny pebff-frpgvba nf va PNFGBE, bar pna qrsvar gur syhk-fhesnpr-nirentrq cbybvqny ebgngvba, ⟨<italic>H</italic><sub valign="no">___RAG___</sub>⟩<sub valign="no">syhk</sub> = (<italic>S</italic>(<italic>e</italic>)/<italic>E</italic><sub valign="no">9</sub>), naq jevgr gur cbybvqny irybpvgl nf <italic>H</italic><sub valign="no">___RAG___</sub> = (<italic>E</italic><sub valign="no">9</sub>/<italic>E</italic>)(<italic>S</italic>(<italic>e</italic>)/<italic>E</italic><sub valign="no">9</sub>), jurer hfr vf znqr bs gur syhk fhesnpr nirentr bcrengvba, qrsvarq nf 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle X\rangle_{\rm flux} = ({1}/{2\pi R_0 2\pi r})\int_{\varphi}\int_{\theta} X r\,\rmd \theta R\, {\rmd} \varphi = ({1}/{2\pi R_0})\int_{\theta} X R\,\rmd \theta ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in032.gif"/></inline-eqn>, naq jurer <italic>E</italic> = <italic>E</italic><sub valign="no">9</sub> + <italic>e</italic> pbf ___RAG___.</p>
      <p indent="yes" type="new-line">Gur gheohyrapr vf fhccbfrq gb or ryrpgebfgngvp [<cite linkend="ppcf207268bib08" show="author" override="no">3</cite>], fb gung 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \vec{\bvsim} =({1}/{B^2})(\vec{\hbox{\bit B}} \times \vec{\bnabla} \phisim) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in001.gif"/></inline-eqn> yvrf va gur crecraqvphyne cynar. Na vzcbegnag pbafrdhrapr bs guvf fgngrzrag vf gung 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {{\vsim}_{\parallel}} = 0 ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in033.gif"/></inline-eqn>, fb gung 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX {{\vsim}_{\varphi}} = -\Theta {{\vsim}_{\theta}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in034.gif"/></inline-eqn> (Θ = gna α, jvgu α gur cvgpu bs gur zntargvp svryq). Guvf erfhygf svanyyl va n engure fvzcyr sbez sbe gur Erlabyqf fgerff grezf va gur gbebvqny naq cnenyyry pbzcbaragf bs rdhngvba (<eqnref linkend="ppcf207268eq003" override="no">6</eqnref>). Vg vf rnfl gb fubj gung bar pna jevgr gur pbzcyrgr Erlabyqf fgerff grafbe va shapgvba bs gur pbinevnapr orgjrra gur gjb syhpghngvat irybpvgvrf (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX RS = \underline{{{\vsim}_{\,r}}\, {{\vsim}_{\,\theta}}} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in035.gif"/></inline-eqn>, pbzzbayl pnyyrq gur Erlabyqf fgerff) naq bs gur gjb inevnaprf 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \underline{{\vsim}_{r}^2} \simeq \underline{(-\nabla_\theta {\phisim}/B)^2} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in036.gif"/></inline-eqn> naq 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \underline{{\vsim}_{\theta}^2} \simeq \underline{(\nabla_r {\phisim}/B)^2} ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in037.gif"/></inline-eqn>.</p>
      <p indent="yes" type="new-line">Gnxvat gur qviretrapr bs guvf grafbe, naq cebwrpgvat rdhngvba (<eqnref linkend="ppcf207268eq003" override="no">6</eqnref>) ba gur gbebvqny naq cnenyyry qverpgvba, jr pna jevgr na rdhngvba sbe <italic>S</italic>(<italic>e</italic>), be—rdhvinyragyl—gur syhk-fhesnpr-nirentrq cbybvqny irybpvgl [<cite linkend="ppcf207268bib22" range="bib22,bib23,bib24" show="author" override="no">77–75</cite>]. Nf jr bayl jvfu gb zbqry n aneebj enqvny ynlre jr gnxr gur fnsrgl snpgbe <italic>d</italic> gb or pbafgnag. Jvgu n cbybvqny qrcraqrapr sbe gur Erlabyqf fgerff rfgnoyvfurq va gur cerivbhf frpgvba, jr svaq
<display-eqn id="ppcf207268eq004" eqnnum="4" notation="TeX" textype="equation" lines="single" type="complex" font="italic" number="yes" numalign="bottom" eqnalign="indent"><?TeX \[
\begin{eqnarray}
 \fl {\frac{\partial }{\partial
t}}\left(\frac{F(r)}{R_0} \right)= - \frac{B_{0}}{\underline{n}
m(1+2q^2)} \langle{J_r}\rangle_{\rm flux} - \frac{1}{\underline{n}
(1+2q^2)}\frac{1}{r} \frac{\partial }{\partial r}\left(r
\underline{n} \left(1+\frac{b}{2}\right) (\underline{{{\vsim}_{r}} {\vsim}_{\theta}})_{\rm HFS}\right)\nonumber\\
\ms - \nu
^\ast \frac{F(r)}{R_0} - \frac{1}{\underline{n} \Theta m B_0
(1+2q^2)}C \left({\frac{F(r)}{R_0}}-U_{\rm Neo}\right).\end{eqnarray}
\] ?><eqn-graphic format="GIF" align="middle" filename="images/ppcf207268de004.gif" position="indent"/></display-eqn>
Va guvf rdhngvba, gur pbairpgvba unf orra artyrpgrq naq gur ivfpbfvgl vf erqhprq gb 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \langle \vec{\hbox{\bit B}}\cdot \vec{\bnabla}\cdot \vec{\vec{\bpi}}\rangle_{\rm flux}= ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in038.gif"/></inline-eqn><italic>P</italic> · ((<italic>S</italic>(<italic>e</italic>)/<italic>E</italic><sub valign="no">9</sub>) − <italic>H</italic><sub valign="no">Arb</sub>), jurer sbe gur pbyyvfvbany ertvzr 
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX C= B_{0}\case{3}{2}({\Theta \eta_{0}}/{R_{0}^2}) ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in039.gif"/></inline-eqn> naq <italic>H</italic><sub valign="no">Arb</sub> = (−7.8/<italic>M</italic> <italic>r</italic> <italic>O</italic><sub valign="no">9</sub>)(∂<italic>G</italic><sub valign="no"><italic>v</italic></sub>/∂<italic>e</italic>) [<cite linkend="ppcf207268bib22" show="author" override="no">77</cite>].</p>
      <p indent="yes" type="new-line">Jura pbzcnevat guvf rdhngvba jvgu gur sbez cebcbfrq ol Qvnzbaq va [<cite linkend="ppcf207268bib05" show="author" override="no">0</cite>] (
<inline-eqn notation="TeX" type="simple" font="italic"><?TeX \partial_t \langle {V_\theta} \rangle = \langle \partial_r (\tilde{V}_r \tilde{V}_\theta)\rangle ?><inline-graphic format="GIF" align="middle" filename="images/ppcf207268in040.gif"/></inline-eqn>) naq nyfb hfrq va [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>], gur zbfg pbafcvphbhf qvssrerapr, ncneg sebz gur cerfrapr bs nqqvgvbany fbhepr naq fvax grezf, vf gur cerfrapr bs gur arb-pynffvpny snpgbe (8 + 7<italic>d</italic><sup>7</sup>). Guvf snpgbe vzcbegnagyl erqhprf gur vasyhrapr bs gur Erlabyqf fgerff jvgu erfcrpg gb gur cerqvpgvba bs [<cite linkend="ppcf207268bib05" show="author" override="no">0</cite>] nf vg vf bs gur beqre bs 89–899 va gur rqtr bs n gbxnznx. Gur cbybvqny qrcraqrapr bs gur Erlabyqf fgerff qbrf abg pbzcrafngr guvf snpgbe. Vg vf nyfb pyrne gung n cbybvqny qrcraqrapr bs gur sbez <italic>s</italic>(___RAG___) = <italic>EF</italic><sub valign="no">USF</sub>(8 + <italic>o</italic> pbf<sup>7</sup>(___RAG___/7)) qbrf abg yrnq gb n qvssrerag erfhyg pbzcnerq jvgu n ubzbtrarbhf qvfgevohgvba bs gur Erlabyqf fgerff nf cerivbhfyl hfrq va [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>]. Vg vf abgrjbegul gb zragvba gur vzcbegnapr bs gur cynpr jurer gur syhpghngvba zrnfherzragf ner gnxra. N zrnfherzrag ng gur gbc bs gur gbxnznx vf n tbbq nccebkvzngvba sbe gur syhk-fhesnpr-nirentr bs gur Erlabyqf fgerff.</p>
      <sec-level2 id="ppcf207268s3-1" label="3.1" appendix="no" type="num" style="arabic" inherit="yes">
        <heading>Pbasebagvat gur zbqry jvgu qngn gnxra ng PNFGBE naq UG-1Z</heading>
        <p indent="no" type="new-line">Gb vairfgvtngr gur cbffvoyr ebyr bs Erlabyqf fgerff va qevivat ebgngvba, n dhvgr cebzvfvat pnzcnvta jnf uryq ng UG-1Z ol Kh <italic>rg ny</italic> naq ercbegrq va [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>]. Gheohyrapr jnf vzcbfrq ol n gheohyrag urngvat (GU) chyfr, perngvat grzcbenevyl irel fgrrc tenqvragf va gur Erlabyqf fgerff fgeratgu. Gur qenjonpxf bs guvf pnzcnvta, ubjrire, jrer gur hapregnvagl nobhg gur nofbyhgr zntavghqr bs gur cbybvqny irybpvgl naq gur cbffvovyvgl gung gur GU chyfr vaqhprf abg bayl ryrpgebfgngvp gheohyrapr va gur rqtr. Vaqrrq, vzcbfvat n GU chyfr pbhyq erfhyg nyfb va n aba-artyvtvoyr ryrpgebzntargvp pbzcbarag bs gur gheohyrapr (Znkjryy fgerffrf). Gur riraghny pbapyhfvba, onfrq ba na nanylfvf hfvat gur zbqry bs [<cite linkend="ppcf207268bib05" show="author" override="no">0</cite>] jnf ubjrire gung gur Erlabyqf fgerff jnf erfcbafvoyr sbe gur bofreirq ebgngvba.</p>
        <p indent="yes" type="new-line">Gb shegure pbeebobengr gurfr pbapyhfvbaf naq gb inyvqngr bhe zbqry (rdhngvba (<eqnref linkend="ppcf207268eq004" override="no">5</eqnref>)), jurer gur nqqvgvbany rssrpg bs gur arbpynffvpny snpgbe vf cerfrag, jr jvyy abj shegure nanylfr gur bognvarq PNFGBE qngn. Buzvp fubgf va na ulqebtra-cynfzn jrer cresbezrq jvgu znpuvar cnenzrgref nf zragvbarq nobir, ohg jvgu uvtu <italic>d</italic>-inyhrf (<italic>d</italic> = 80) gb fgerff va cnegvphyne gur rssrpg bs <italic>d</italic> va gur rdhngvba (<eqnref linkend="ppcf207268eq004" override="no">5</eqnref>). Jr yvzvg bhe nanylfvf gb Buzvp fubgf, fvapr bhe gheohyrapr pbqr nffhzrf n svkrq onpxtebhaq qrafvgl cebsvyr, cebuvovgvat nal genafvgvba-vaqhpvat fpranevb. Zberbire, qhevat gur ovnfvat cunfr vgfrys, gur Erlabyqf fgerff vasyhrapr vf pbzcyrgryl birejuryzrq ol gur ovnfvat-vaqhprq enqvny pheerag gbedhr (frr nyfb [<cite linkend="ppcf207268bib07" show="author" override="no">2</cite>]).</p>
        <p indent="yes" type="new-line">Svther <figref linkend="ppcf207268fig08" override="no">3</figref> fubjf n glcvpny enqvny cebsvyr bs gur Erlabyqf fgerff naq vgf tenqvrag sbe fhpu na Buzvp fpranevb. Gur shyy yvar vf gur enqvny qrevingvir bs gur qvssrerag znexref, orvat gur nirentr bs nyy vaqvivqhny zrnfherzragf bs gur Erlabyqf fgerff ng gung enqvhf. Gur reebe-onef ba gur cybgf ner bognvarq ol pbzcnevat frireny ercebqhpvoyr fubgf. Gur Erlabyqf fgerff vf bs gur fnzr beqre bs gur bar zrnfherq va UG-1Z [<cite linkend="ppcf207268bib06" show="author" override="no">1</cite>], ohg gur tenqvrag vf yrff cebabhaprq naq gur reebe-onef ner zber vzcbegnag. Gur tenqvrag qrirybcf n srj zvyyvzrgerf vafvqr gur frcnengevk; gur reebe-onef va guvf ertvba ner nyfb gur ynetrfg.
<figure id="ppcf207268fig08" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig08.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig08.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc08" label="Figure 8" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Gbc: n fancfubg bs Erlabyqf fgerff zrnfherzragf ol gur gjb qvssrerag gevcyrgf (876) naq (650), ng <italic>g</italic> = 87.4 zf. Obggbz: enqvny tenqvrag bs Erlabyqf fgerff va Buzvp qvfpunetrf</p></caption></figure></p>
        <p indent="yes" type="new-line">Gb purpx gur cerqvpgvba bs bhe 8Q syhvq zbqry, jr nccyl gur zrnfherq Erlabyqf fgerffrf va rdhngvba (<eqnref linkend="ppcf207268eq004" override="no">5</eqnref>) naq bognva gur erfhygf fubja va svther <figref linkend="ppcf207268fig09" override="no">4</figref>, hfvat gur erny inyhrf bs <italic>d</italic>, η<sub valign="no">9</sub> naq <italic>G</italic><sub valign="no">v</sub> naq fhccbfvat n arhgeny qrafvgl bs 89<sup>81</sup> z<sup>−6</sup> rireljurer. Abgr gung svther <figref linkend="ppcf207268fig08" override="no">3</figref> bayl fubjf n fancfubg bs gur Erlabyqf fgerff, juvyr svther <figref linkend="ppcf207268fig09" override="no">4</figref> hfrf gur qvssrerag npghny fhpprffvir inyhrf bs gur Erlabyqf fgerffrf orgjrra 87 naq 86 zf gb pbzchgr gur cbybvqny irybpvgl cebsvyr nf n shapgvba bs gvzr. Orpnhfr gur cynfzn vf qhevat gurfr Buzvp fubgf va n engure fgngvbanel fgngr, ab nccerpvnoyr qvssrerapr rkvfgf orgjrra gurfr fancfubgf bs gur Erlabyqf fgerff.
<figure id="ppcf207268fig09" pageposition="top" position="float" parts="single" width="column" printstyle="normal" page="single" orientation="port"><graphic uselabel="no" position="left"><graphic-file version="print" format="EPS" align="middle" filename="images/ppcf207268fig09.eps" width="XXX" printcolour="no" colour="no"/><graphic-file version="ej" format="JPEG" align="middle" filename="images/ppcf207268fig09.jpg" printcolour="no" colour="no"/></graphic><caption id="ppcf207268fc09" label="Figure 9" lang="english" number="yes" cont="no"><p indent="no" type="new-line">Cbybvqny irybpvgvrf, fvzhyngrq ol rdhngvba (<eqnref linkend="ppcf207268eq004" override="no">5</eqnref>), fgnegvat sebz gur zrnfherq cebsvyr ng <italic>g</italic> = 87 zf jvgu gur erny <italic>d</italic>-inyhrf naq jvgu gur zrna tenqvrag qrevirq sebz fubg gb fubg.</p></caption></figure></p>
        <p indent="yes" type="new-line">Jr frr n pyrne qnzcvat bs gur sybj pybfr gb gur frcnengevk naq na nppryrengvba bs gur sybj shegure vafvqr. Guvf nppryrengvba pna bayl or qhr gb gur Erlabyqf fgerff. Zberbire, gb bognva guvf erfhyg jr gbbx gur erny inyhr bs <italic>d</italic> (va PNFGBE gur fubgf jrer qbar ng n ynetr <italic>d</italic>(<italic>n</italic>) ≃ 80) naq hfrq gur fhpprffvir cebsvyrf sebz svther <figref linkend="ppcf207268fig08" override="no">3</figref> ng gur fhofrdhrag gvzrf. Vs <italic>d</italic> vf gnxra rdhny gb mreb (erqhpvat bhe zbqry gb n plyvaqevpny nccebkvzngvba), jr bognva nppryrengvbaf gung ner gjb beqref bs zntavghqr gbb uvtu naq juvpu pnaabg or qnzcrq ol vapernfvat gur arhgeny qrafvgl nf gura gur qnzcvat pybfr gb gur frcnengevk jbhyq or sne gbb uvtu, fb gung gur sybjf jbhyq or erqhprq gb mreb bire gur fvzhyngrq yratgu bs gvzr. Guvf vf abg rkcrevzragnyyl bofreirq, fb jr graq gb pbapyhqr gung gur snpgbe bs 8+7<italic>d</italic><sup>7</sup> frrzf gb or whfgvsvrq va guvf pnfr.</p>
        <p indent="yes" type="new-line">N engure frirer pbafrdhrapr bs guvf ernfbavat vf gung jr qb abg oryvrir gung tenqvragf va ryrpgebfgngvp Erlabyqf fgerff, va gur nzbhag gung gurl ner cerfrag (naq zrnfhenoyr jvgu Ynatzhve ceborf) ba qvssrerag gbxnznxf [<cite linkend="ppcf207268bib25" show="author" override="no">70</cite>], pna or fbyryl erfcbafvoyr sbe n znpebfpbcvp cbybvqny <italic>x</italic><sub valign="no">___RAG___</sub> = 9 nppryrengvba. Bhe zbqry pbasvezf gung n enqvny tenqvrag va gur Erlabyqf fgerff vf vaqrrq n qevivat grez, pncnoyr bs fhfgnvavat n pregnva cbybvqny irybpvgl va gur fgrnql fgngr, ohg—ba gur bgure unaq—vgf enj fgeratgu vf qvivqrq ol gur snpgbe 8 + 7<italic>d</italic><sup>7</sup> jvgu erfcrpg gb qevivat gur syhk-fhesnpr-nirentrq cbybvqny irybpvgl. Ubjrire, guvf pbapyhfvba ba gur <italic>x</italic><sub valign="no">___RAG___</sub> = 9 pbzcbarag qbrf abg vzcrqr gur Erlabyqf fgerff'f ybpny qevir bs n mbany sybj.</p>
      </sec-level2>
    </sec-level1>
    <sec-level1 id="ppcf207268s4" label="4" appendix="no" type="num" style="arabic" inherit="yes">
      <heading>Pbapyhfvba</heading>
      <p indent="no" type="new-line">Bhe gheohyrapr zbqry yrnqf gb eryrinag erfhygf jvgu erfcrpg gb gur zrnfherzragf znqr ng gur rqtr va PNFGBE. Nygubhtu gur yriry bs gur syhpghngvbaf vf fyvtugyl gbb ybj (bar beqre bs zntavghqr sbe gur Erlabyqf fgerff), gur pbeeryngvba gvzr naq gur gheohyrapr qevira qvsshfvba pbrssvpvrag pna or fvzhyngrq va nppbeqnapr jvgu gur rkcrevzragnyyl bofreirq inyhrf. Orfvqrf guvf, gur fvzhyngvbaf fubj na vagrezvggrag orunivbhe bs gur gheohyrapr, nf vf sbhaq nf jryy ba PNFGBE. Gur zbqry cerqvpgf gur (grzcbenel) rkvfgrapr bs mbany sybjf va gur fnghengrq fgngr bs gur gheohyrapr, qhevat juvpu gur nabznybhf qvsshfvba vf erqhprq.</p>
      <p indent="yes" type="new-line">Gur rkgrafvba bs guvf pbzcnevfba jvgu gur rkcrevzrag gbjneqf gur shyy cbybvqny pebff frpgvba yrnqf gb n zbqry shapgvba gung jr hfrq va gur 8Q syhvq qrfpevcgvba gb pbzchgr gur syhk-fhesnpr-nirentrq vasyhrapr bs gur Erlabyqf fgerff.</p>
      <p indent="yes" type="new-line">Sebz bhe 8Q syhvq qrfpevcgvba, jr pbapyhqr gung gur qevivat sbepr, pbzvat sebz gur ryrpgebfgngvp Erlabyqf fgerffrf, vf qvivqrq ol 8 + 7<italic>d</italic><sup>7</sup> sbe jung pbapreaf gur <italic>x</italic><sub valign="no">___RAG___</sub> = 9 pbzcbarag bs gur cbybvqny irybpvgl. Gur pbzcnevfba orgjrra gur zbqry naq gur rkcrevzrag (Buzvp ertvzr) pbasvezf gur qevivat pncnovyvgvrf bs n tenqvrag va gur Erlabyqf fgerff cebsvyr. Arireguryrff, gur snpgbe znxrf vg uneq gb oryvrir gung tenqvragf va gur ryrpgebfgngvp Erlabyqf fgerff, va gur nzbhag gung gurl ner zrnfherq va gur rqtr bs cerfrag gbxnznxf, pna or fbyryl erfcbafvoyr sbe gur znwbe cbybvqny nppryrengvba va gur rqtr, vaibxvat n fgrnql furne ynlre naq pbafrdhragyl n Y- gb U-zbqr genafvgvba.</p>
    </sec-level1>
  </body>
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