flow rate, so that the energetic ability of these electrons to ionize the increased neutral flow would be maintained Since no space change develops these increases in flow, current and power could go on indefinitely The above reasoning has ignored the various effects of collisions (a)As far as the electrons, as the flow rate, and hence the gas density increases, so does the scattering collision frequency ve=ny C Qen (ny=heavy particle density, mean electron speed, QeH=mean scattering cross-section). When this frequency becomes comparable to the gyro or cyclotron frequency o el the electrons can no longer maintain pure azimuthal drift because each collision will allow the electric field to nudge them in the direction of the anode by about one Larmor radius v/o correspondingly to a velocity u=e /B, which is the azimuthal drift velocity. Thus, electrons are now able to cross the magnetic barrier at a velocity E Dx B which increases with be, hence with nH and ultimately with nY. The electron density n, in the acceleration region is governed by the flow of ions from the upstream ionization region as shown in the schematic, and increases generally in the same proportion as mr or I. This means that the electron"leakage "current E (8) will increase faster than IB, due to the ny factor in Ue. As will be discussed later, one of the factors determining the overall efficiency n of the device and from the schematic, ignoring wall losses, 18=1,-leak,so I 1+L,/I 22, Space Propulsion re 17 5 of 7x flow rate, so that the energetic ability of these electrons to ionize the increased neutral flow would be maintained. Since no space change develops these increases in flow, current and power could go on indefinitely. The above reasoning has ignored the various effects of collisions: (a) As far as the electrons, as the flow rate, and hence the gas density increases, so does the scattering collision frequency υe = nHceQEH (nH =heavy particle density, frequency becomes comparable to the gyro or cyclotron frequency ω ce = 8 π kTe me mean electron speed, QeH =mean scattering cross-section). When this eB c = the me electrons can no longer maintain pure azimuthal drift, because each collision will allow the electric field to nudge them in the direction of the anode by about one Larmor radius V / ω correspondingly to a velocity υ = Ex / B, which is the azimuthal c drift velocity. Thus, electrons are now able to cross the magnetic barrier at a velocity Ex e V υ ≅ (7) B ω c which increases with υ , hence with nH and ultimately with mÝ. The electron density e n in the acceleration region is governed by the flow of ions from the upstream e ionization region, as shown in the schematic, and increases generally in the same proportion as mÝ or IB . This means that the electron “leakage” current Ex e υ Ileak = ene B ω (8) c will increase faster than IB , due to the nH factor in υ . As will be discussed later, e one of the factors determining the overall efficiency η of the device η = IB a Ia and from the schematic, ignoring wall losses, IB = I − Ileak a , so 1 η =1 − Ileak a = I 1 + Ileak / I a B 16.522, Space Propulsion Lecture 17 Prof. Manuel Martinez-Sanchez Page 5 of 7