B Cathode Dection B The magnetic field is now azimuthal, with circular lines of force. The lower part of this diagram is seen to be equivalent to that for the simple linear channel( with the Hall effect included). The insulating sidewalls have been replaced by the annular plasma itself; of course an insulating backwall is still required It can be seen that the current will(because of the skewness due to the Hall effect tend to concentrate near the anode downstream edge and near the cathode roo Also, the pumping force will now tend to produce a highly concentrated jet of plasma; in fact, a highly luminous central core is usually observed in MPD plumes, extending from immediately downstream of the cathode for sometimes several cathode lengths Turning now to the question of the magnetic field, notice that the azimuthal b can be provided by the plasma current flowing in the meridional plane. This can be seen from Ampere's law, written in cylindrical coordinates 1aB.aB=2B(rB、=0) Ho]r ab =1(B.1B1(B,) 冲r冲 The direction of B is also that required for acceleration this can be seen either fror the equations or from the right hand rule applied to a number of representative j vectors, or from the known fact that parallel wires carrying current in the same direction attract each other 16.522, Space P pessan Lecture 21 Prof. Manuel martinez Page 11 of 2116.522, Space Propulsion Lecture 21 Prof. Manuel Martinez-Sanchez Page 11 of 21 The magnetic field is now azimuthal, with circular lines of force. The lower part of this diagram is seen to be equivalent to that for the simple linear channel (with the Hall effect included). The insulating sidewalls have been replaced by the annular plasma itself; of course, an insulating backwall is still required. It can be seen that the current will (because of the skewness due to the Hall effect) tend to concentrate near the anode downstream edge and near the cathode root. Also, the pumping force will now tend to produce a highly concentrated jet of plasma; in fact, a highly luminous central core is usually observed in MPD plumes, extending from immediately downstream of the cathode for sometimes several cathode lengths. Turning now to the question of the magnetic field, notice that the azimuthal B JG can be provided by the plasma current flowing in the meridional plane. This can be seen from Ampere’s law, written in cylindrical coordinates: x 0 r 1 B B B j= - = r xx φ φ ∂ ∂ ∂ µ ∂φ ∂ ∂ (for Bx=0) (22) ( ) ( ) r 0 x 1 11 rB rB B j= - = r r rr φ φ ∂ ∂ ∂ µ ∂φ ∂φ ∂ (for Br=0) (23) The direction of B JG is also that required for acceleration. This can be seen either from the equations, or from the right hand rule applied to a number of representative j G vectors, or from the known fact that parallel wires carrying current in the same direction ATTRACT each other