Electron density and scale lenght

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).