{'fraction_non_alphanumeric': 0.010966415352981495, 'fraction_numerical': 0.0, 'mean_word_length': 4.983606557377049, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The heating sources of spots on the vacuum arc cathodes

We have considered two stages in the development of a spot on the surface of a vacuum arc cathode: the stage of ignition and the stage of the remaining arc lifetime which consists of arc spot operation until ultimately it is extinguished. A model for the near cathode region of electric arc has been applied to obtain different parameters involved in the cathode spot region during the spot ignition stage. This model is based on the construction of a thin sheath near the cathode wall and electron emission upon the thermo-field theory of electron emission. The model is time-dependent and hence the different parameters of the cathode, plasma and sheath can be derived as a function of time. In particular, we determine the required values of the plasma and sheath parameters for spot ignition on the smooth cathode surface. Based on these calculations and taking into consideration the fluctuation in plasma and sheath parameters, the contribution of different heating mechanisms at the spot initiation stage is evaluated. After spot ignition, some spot parameters such as temperature and mass density of spot material, electron current density and vapour pressure considerably increase. High values of the electron current density and low values of the electrical conductivity of the dense plasma in the spot region significantly increase Joule heating during the evolution stage of spot operation.