index

Experimental data fit of the VA characteristics is based on 4 parameter \(a=(a_1,a_2,a_3,a_4)\) formula (see Aazoz@AIP, 2009):

\[I(a,V_{bias})=\exp[a_1 \tanh{(V_{bias}+a_2)/a_3}]+a_4\]

where \(I\) is the probe current measured on the resistor \(R\) and performed via function matlab function nlinfit, see code, part "Perform fit" originally created by Aazoz@matlab, 2008

and output parameters are calculated as follows (see code and Crowley et al@IAEA TM, 2005):

Ion saturation current: \(I_{is}=I(a,2*min(V_{bias}))\)
Electron saturation current: \(I_{es}=I(a,3*max(V_{bias}))\)
Plasma potential: \(V_p=a_3*\text{atanh}(((\sqrt{1+a_1^2})-1)/a_1)-a_2\);
Floating potential \(V_{fl}\) from the condition \(I(a, V_{fl})=0\)
Electron energy distribution function (EEDF): \(N(\epsilon)=\frac{2}{Ae}\sqrt{\frac{2m\epsilon}{e}}\frac{d^2I}{dV^2}\)
Electron energy distribution function (EEPF): \(P(\epsilon)=\frac{2}{Ae}\sqrt{\frac{2m}{e}}\frac{d^2I}{dV^2}\)
Electron density \[n_e=\int_0^\infty{P(\epsilon)d\epsilon}\]
Ion density \(n_i=\frac{|I_{is}|}{0.52*A*e^{2/3}}\sqrt{\frac{M_i}{T_e}}\)
Electron temperature \[T_e=\frac{2}{3}<\epsilon>=\frac{2}{3n_e}\int_0^\infty{\epsilon P(\epsilon)d\epsilon}\]

where \(M_i\) is ion mass, \(A\) is probe effective area, \(e\) and \(m\) are the electron charge and mass.