E×B E Figure 2 B The ions have no such azimuthal drift (or have a very small one because their Gyro radius is larger than the device's length), and so a net azimuthal current density arises, called a hall current E -en Given a current JHall in a plasma, the magnetic (Lorentz) force density on it is f=jHall xb )and an equal and opposite force is exerted by the plasma currents on the magnetic structure). We then have -en and using Eg.(2), = +en E i. e. the same as the forward electrostatic force on the ions as it should be. The important point is that the structure is not electrostatically acted on(electric fields and electric pressures are too weak here), but magnetically through the Hall current hence the name the device is a hall thruster but an electrostatic accelerator a duality which has led to some confusion 3. Thrust Capability Unlike the case of a gridded ion engine, there is not a clear-cut upper limit to the obtainable thrust density in a Hall thruster. In principle increasing the mass flow rate through a given engine would increase thrust by the same factor, provided the same degree of ionization can be maintained the voltage is presumed to be kept the same, since this controls specific impulse fairly directly. The ion beam current and the electron current leaking into the accelerating channel would increase as the mass Prof. Manuel martinez-Sanchez Page 4 of 7( ) −e/ [ e ] G B G υ G (2) E + × = 0 or G υ e = − Drift G B G E × B2 (3) ⎛ ⎜υ = − Ex ⎟ ⎞ e ϑ (4) ⎝ B ⎠ r The ions have no such azimuthal drift (or have a very small one, because their Gyro radius is larger than the device’s length), and so a net azimuthal current density arises, called a Hall current: G G j = −ene Drift υ G B G E × = en (5) e B2 Given a current Hall in a plasma, the magnetic (Lorentz) force density on it is = Hall × G j G B ) and an equal and opposite force is exerted by the plasma currents on G j G f the magnetic structure). We then have e e × Drift G υ G f = −en G B and using Eq. (2), G E G f = +ene (6) i.e., the same as the forward electrostatic force on the ions, as it should be. The important point is that the structure is not electrostatically acted on (electric fields and electric pressures are too weak here), but magnetically, through the Hall current - hence the name. The device is a Hall thruster, but an electrostatic accelerator, a duality which has led to some confusion. 3. Thrust Capability Unlike the case of a gridded ion engine, there is not a clear-cut upper limit to the obtainable thrust density in a Hall thruster. In principle, increasing the mass flow rate through a given engine would increase thrust by the same factor, provided the same degree of ionization can be maintained. The voltage is presumed to be kept the same, since this controls specific impulse fairly directly. The ion beam current and the electron current leaking into the accelerating channel would increase as the mass 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 17 Page 4 of 7