Debye shield /spherical conductor

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.