Debye shield /spherical conductor

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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: Debye shield /spherical conductor
  • DIFICULDADE: *
  • TEMPO MEDIO DE RESOLUCAO: 300 [s]
  • TEMPO MAXIMO DE RESOLUCAO: 600 [s]
  • PALAVRAS CHAVE:

(F. F. Chen \(\sim\) 1.10) A spherical conductor of radius \(R\) is immersed in a plasma and charged to a potential \(\phi_0\). The electrons remain Maxwellian and move to form a Debye shield, but the ions are stationary during the time frame of the experiment. Assuming \(e\phi_0\ll k T_e\):

(a) derive an expression for the potential as a function of \(r\);

(b) calculate the charge in the sphere;

(c) calculate the sphere capacity for \(R=10\) cm, \(T_e=1\) keV and \(n_0=10^{14}\) and \(10^6\) cm\(^{-3}\), and show that for high electron densities the plasma behaves as a dielectric.