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Calculation of charge‐state ratios for satellite Tori
Author(s) -
Summers Danny,
Siscoe George L.
Publication year - 1985
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/gl012i011p00753
Subject(s) - torus , ion , ionization , physics , atomic physics , diffusion , residence time (fluid dynamics) , mathematics , quantum mechanics , geometry , geotechnical engineering , engineering
We model the diffusion of ions in a satellite plasma torus by means of a symmetric one dimensional random walk in which the particle source is at O, the particle sink is at N (an integer ⩾ 2), and the scale size of the diffusion cell is unity. We obtain the probability distribution function of the number of steps to exit for an ion or, equivalently, the probability distribution of ion residence times. This distribution is used in a model incorporating ionization by electron impact to derive steady state expressions for the ratio of the numbers of doubly to singly ionized ions, and the total number of ions in the torus. These expressions involve the diffusion time scale τ s , the ionization time scale τ i , and N. We compare the result for the charge‐state ratio with its corresponding value based on the assumption that all ions reside in the torus for the mean residence time, the latter being the standard assumption. Typically, we find that for given values of τ s , τ i and N our result is twice that obtained with the standard assumption. We apply the results to the torus of the Jovian satellite Io to predict mean residence times for sulphur and oxygen ions. A factor of two reduction in the time required to produce the observed charge state partitioning gives residence time estimates closer to those found by considering power requirements.