xB Cathode d Front View Side View(through insulating wall) a plasma is flowing in the channel at velocity u, and an external electric field is applied Ignoring for now the hall effect if this e field is larger in magnitude than uB (the induced Faraday field), a current j will flow. given by j=oE=o(E+ux B)in the direction of E he Lorentz force f=jx B is then in the forward direction as indicated and we have an accelerator E On the other hand if e<ub the current j flows in the direction opposite to E. Externally, positive X current flows into the(+)pole of our "battery"and could be used to recharge it; we have now an MHD generator, and the battery would probably be replaced by a passive load The Lorentz force now points backwards, so that the fluid has to be forced to flow by an external pressure gradient (like in a turbine ). Effect of the hall parameter In a moderate pressure plasma B can easily exceed unity. If the construction is the same as before, Ohm's law can be represented graphically as shown below: 16.522, Space P pessan Lecture 21 Prof. Manuel martinez Page 9 of 2116.522, Space Propulsion Lecture 21 Prof. Manuel Martinez-Sanchez Page 9 of 21 A plasma is flowing in the channel at velocity u G , and an external electric field is applied. Ignoring for now the Hall effect, if this E G field is larger in magnitude than uB (the induced Faraday field), a current j G will flow, given by j = E' = E + u × B σ σ ( ) G JJG GGJG in the direction of E G . The Lorentz force f = j × B G G JG is then in the forward direction, as indicated, and we have an accelerator. On the other hand, if E<uB, the current j G flows in the direction opposite to E G . Externally, positive current flows into the (+) pole of our “battery” and could be used to recharge it; we have now an MHD generator, and the battery would probably be replaced by a passive load. The Lorentz force now points backwards, so that the fluid has to be forced to flow by an external pressure gradient (like in a turbine). Effect of the Hall Parameter In a moderate pressure plasma β can easily exceed unity. If the construction is the same as before, Ohm’s law can be represented graphically as shown below: