Diode constant of cylindrical diode¶

In a cylindrical diode, the cathode is located in the center, and the anode is located around it in the form of a cylinder. The radius of the anode is usually much larger than the radius of the cathode. The diode constant depends on the radii and on the area of the anode.

Notation:

\(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.
\(e\) (e) is elementary_charge.
\(m_\text{e}\) (m_e) is electron_rest_mass.

diode_constant¶: diode_constant.

Symbol:: g
Latex:: \(g\)
Dimension:: current/voltage**(3/2)

anode_area¶: area of the anode.

Symbol:: A_a
Latex:: \(A_\text{a}\)
Dimension:: area

anode_radius¶: radius of the anode.

Symbol:: r_a
Latex:: \(r_\text{a}\)
Dimension:: length

cathode_radius¶: radius of the cathode.

Symbol:: r_c
Latex:: \(r_\text{c}\)
Dimension:: length

law¶

g = 4 * epsilon_0 / 9 * sqrt(2 * e / m_e) * A_a / (r_a^2 * (1 - r_c / r_a)^2)

Latex:: \[g = \frac{\frac{4 \varepsilon_0}{9} \sqrt{\frac{2 e}{m_\text{e}}} A_\text{a}}{r_\text{a}^{2} \left(1 - \frac{r_\text{c}}{r_\text{a}}\right)^{2}}\]