ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: is submitted to the electric field of a single proton. The calculation of this electric field requires knowing the distance between the electron and the proton, which can be taken as the mean distance between particles, which is the −1/3 power of their density, which is roughly the same for electrons and protons. This electric field derives from a potential, as does the gravitation field. Thus, there is also an escape velocity, as there is for gravitation. The escape velocity for freeing the electron from the corresponding single proton is then where q is the elementary charge, m e is the electron mass, and n the density, which is nearly the same for electrons and protons. In the solar interior conditions given by Allen (1973) , we then obtain that this escape velocity is nevertheless six times lower than the quadratic average thermal velocity for electrons, which then also escape from the protons, at least initially. As the escape velocity is obtained by equating the particle kinetic and potential energies, the total escape velocity from gravity and proton for an electron is and we obtain that for electrons it is 5.5 times lower than the quadratic average thermal velocity at 0.5 R ⊙ . The electrons then initially escape from gravity and protons. 6.4. Escape velocity from several protons As the electron cloud is free at the beginning, in a first approximation it begins to expand. The result is a decrease in the electron density, while the proton density remains unchanged. As a consequence, the number of electrons and protons is not yet the same in a given volume. As a result, an escaping electron is now submitted to the attraction of more than one mean proton, depending on the density ratio. If we denote as ρ this density ratio where n e and n p are the electron and proton density, respectively, the total escape velocity of the electron submitted to ρ > 1 protons and to gravity becomes because the mean distance between the electron and the other particles is . If we denote as x the ratio between the electron escape and thermal velocities we obtain from the preceding equations which permits us to compute the proton-to-electron density ratio ρ from the desired velocity ratio x . The electron escaping will certainly be suppressed when x = 3, which means that the escape velocity will be at least three standard deviations higher than the thermal velocity for each velocity component. In this case, ρ is found to be 6 × 10 3 at 0.5 R ⊙ in the Allen (1973) conditions. This corresponds to a mean distance between electrons 18 times larger than that between protons. These quantities are found to be quite constant along the solar radius. 6.5. Spreading time One important question is where exactly do the initially free electrons escape, and the answer is to the distance where the electron cloud density is divided by the ratio ρ defined above. We propose that the density scale height is the typical dimension of the cloud. We denote as h this density scale