Diferenças entre edições de "Electron density and scale lenght"
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(F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column, | (F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column, | ||
| − | \(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), | + | \(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), ''i.e.'', |
\(\partial n_e / \partial r \simeq - n_e/\lambda\). | \(\partial n_e / \partial r \simeq - n_e/\lambda\). | ||
| + | |||
| + | (a) Using \(\vec{E} = -\vec{\nabla}\phi\), find the radial electric field for given \(\lambda\). | ||
| + | |||
| + | (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, | ||
| + | \(v_{t}=\sqrt{2kT_e/m}\) (this means that the finite Larmor radius effects are important if the \(\vec{E}\times\vec{B}\) drift velocity | ||
| + | is of the order of the thermal speed). | ||
Edição atual desde as 15h27min de 4 de abril de 2017
Metadata
- CONTEXTO : Segundo ciclo universitário
- AREA: Física
- DISCIPLINA: Física e Tecnologia dos Plasmas
- ANO: 4
- LINGUA: en
- AUTOR: Vasco Guerra
- MATERIA PRINCIPAL: Debye shielding and fundamental efects
- DESCRICAO:
- DIFICULDADE: *
- TEMPO MEDIO DE RESOLUCAO: 300 [s]
- TEMPO MAXIMO DE RESOLUCAO: 600 [s]
- PALAVRAS CHAVE:
(F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column, \(n_e(r) = n_0\exp(e\phi/kT_e)\). The electron density varies with a scale length \(\lambda\), i.e., \(\partial n_e / \partial r \simeq - n_e/\lambda\).
(a) Using \(\vec{E} = -\vec{\nabla}\phi\), find the radial electric field for given \(\lambda\).
(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, \(v_{t}=\sqrt{2kT_e/m}\) (this means that the finite Larmor radius effects are important if the \(\vec{E}\times\vec{B}\) drift velocity is of the order of the thermal speed).