the electron-suppressor can be written in the form where is elementary charge, is the ion charge state, and is the one-dimensional ion velocity distribution function. Therefore, the ion current at the ion-decelerating voltage of the Faraday cup can be calculated by integrating Eq. () after substituting Eq. (), where the lower integration limit is defined from the equation where is the velocity of the ion stopped by the decelerating potential , and is the ion mass. Thus Eq. () represents the I-V characteristic of the Faraday cup. Differentiating Eq. () with respect to , one can obtain the relation where the value is an invariable constant for each measurement. Therefore, the average velocity of ions arriving into the Faraday cup and their average energy can be calculated (under the assumption that we operate with a single type of ion) by the expressions where is the ion mass in atomic units. The ion concentration in the ion flow at the Faraday cup vicinity can be calculated by the formula which follows from Eq. () at , and from the conventional condition for distribution function normalizing Fig. 2 illustrates the I-V characteristic and its first derivative of the Faraday cup with installed at output of the Inductively coupled plasma source powered with RF 13.56 MHz and operating at 6 mTorr of H2. The value of the electron-suppressor voltage (accelerating the ions) was set experimentally at , near the point of suppression of the secondary electron emission from the inner surface of the Faraday cup. Error sources The counting of charges collected per unit time is impacted by two error sources: 1) the emission of low-energy secondary electrons from the surface struck by the incident charge and 2) backscattering (~180 degree scattering) of the incident particle, which causes it to leave the collecting surface, at least temporarily. Especially with electrons, it is fundamentally impossible to distinguish between a fresh new incident electron and one that has been backscattered or even a fast secondary electron. See also Nanocoulombmeter Electron multiplier Microchannel plate detector Daly detector Faraday cup electrometer Faraday cage Faraday constant SWEAP References External links Detecting Ions in Mass Spectrometers with the Faraday Cup By Kenneth L. Busch Mass spectrometry Measuring instruments Plasma physics Plasma diagnostics