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56 Chapter 3 = exp(–n x)= exp –x , (3.6-5) o a o where is defined as the mean free path for collisions and describes the distance in which the particle flux would decrease to 1/e of its initial value. The mean free path is given by = 1 , (3.6-6) na which represents the mean distance that a relatively fast-moving particle, such as an electron or ion, will travel in a stationary density of neutral particles. The mean time between collisions for this case is given by the mean free path divided by the charged particle velocity: = 1 . (3.6-7) na v Averaging over all of the Maxwellian velocities of the charged particles, the collision frequency is then = 1 = na v . (3.6-8) In the event that a relatively slowly moving particle, such as a neutral atom, is incident on a density of fast-moving electrons, the mean free path for the neutral particle to experience a collision is given by = vn , (3.6-9) ne ve where vn is the neutral particle velocity and the reaction rate coefficient in the denominator is averaged over all the relevant collision cross sections. Equation (3.6-9) can be used to describe the distance that a neutral gas atom travels in a plasma before ionization occurs, which is sometimes called the penetration distance. Other collisions are also very important in ion and Hall thrusters. The presence of inelastic collisions between electrons and neutrals can result in either ionization or excitation of the neutral particle. The ion production rate per unit volume is given byPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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