# Electron density and scale lenght

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• 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:
(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).