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.