http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?action=history&feed=atom&title=Electron_density_and_scale_lenght 2026-07-01T10:48:27Z Histórico de edições para esta página nesta wiki MediaWiki 1.35.2 http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Electron_density_and_scale_lenght&diff=2955&oldid=prev 2017-04-04T14:27:33Z

<p></p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="pt"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Revisão anterior</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revisão das 14h27min de 4 de abril de 2017</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l18" >Linha 18:</td> <td colspan="2" class="diff-lineno">Linha 18:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column,  </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column,  </div></td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>\(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), <del class="diffchange diffchange-inline">\textit{</del>i.e.<del class="diffchange diffchange-inline">}</del>,</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>\(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), <ins class="diffchange diffchange-inline">''</ins>i.e.<ins class="diffchange diffchange-inline">''</ins>,</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\(\partial n_e / \partial r \simeq - n_e/\lambda\).</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>\(\partial n_e / \partial r \simeq - n_e/\lambda\).</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">(a) Using \(\vec{E} = -\vec{\nabla}\phi\), find the radial electric field for given \(\lambda\).</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">(b) For electrons, show that  \(r_L = 2\lambda\) when the \(\vec{E}\times\vec{B}\) drift velocity, \(v_E\), is equal to the thermal speed, </ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">\(v_{t}=\sqrt{2kT_e/m}\) (this means that the finite Larmor radius effects are important if the \(\vec{E}\times\vec{B}\) drift velocity</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">is of the order of the thermal speed).</ins></div></td></tr> </table>

Ist426982 http://www.mysolutions.tecnico.ulisboa.pt//wiki/index.php?title=Electron_density_and_scale_lenght&diff=2954&oldid=prev 2017-04-04T14:02:34Z

<p>Criou a página com &quot;&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt; &#039;&#039;&#039;Metadata&#039;&#039;&#039; &lt;div class=&quot;mw-collapsible-content&quot;&gt; *CONTEXTO : Segundo ciclo universitário *AREA:...&quot;</p> <p><b>Página nova</b></p><div>&lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot; style=&quot;width:420px&quot;&gt;<br /> '''Metadata'''<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *CONTEXTO : Segundo ciclo universitário<br /> *AREA: Física<br /> *DISCIPLINA: Física e Tecnologia dos Plasmas<br /> *ANO: 4<br /> *LINGUA: en<br /> *AUTOR: Vasco Guerra<br /> *MATERIA PRINCIPAL: Debye shielding and fundamental efects<br /> *DESCRICAO: <br /> *DIFICULDADE: *<br /> *TEMPO MEDIO DE RESOLUCAO: 300 [s]<br /> *TEMPO MAXIMO DE RESOLUCAO: 600 [s]<br /> *PALAVRAS CHAVE: <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> (F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column, <br /> \(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), \textit{i.e.},<br /> \(\partial n_e / \partial r \simeq - n_e/\lambda\).</div>

Ist426982