16.522, Space Propulsion Prof. manuel martinez-sanchez Lecture 22: A Simple Model For MPD Performance-onset It is well known that rapidly pulsed current tends to concentrate near the surface of copper conductors forming a skin". A similar effect occurs when current flows near the entrance and exit of the channel. The reason is the appearance of a strong through a highly conductive and rapidly moving plasma: current tends to concentrat back EMF which tends to block current over most of the channels length this is most easily seen if we" unwrap"the annular chamber of an MPd thruster into a ectangular 1-D channel B=0 了 H Amperes law j=-V×B (1) In our case and calling dB Ohms law(ignoring Hall effect)is j=G(E+uxB Pro f a spa m artie ssn Lecture 22 1 of 816.522, Space Propulsion Lecture 22 Prof. Manuel Martinez-Sanchez Page 1 of 8 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 22: A Simple Model For MPD Performance-onset It is well known that rapidly pulsed current tends to concentrate near the surface of copper conductors forming a “skin”. A similar effect occurs when current flows through a highly conductive and rapidly moving plasma: current tends to concentrate near the entrance and exit of the channel. The reason is the appearance of a strong back EMF which tends to block current over most of the channel’s length. This is most easily seen if we “unwrap” the annular chamber of an MPD thruster into a rectangular 1-D channel. Ampère’s law: 0 1 j= B ∇ µ × G JG (1) In our case = l,x x ∂ ∇ ∂ G so y z 0 1 dB j j=+ dx ≡ µ and calling B -By ≡ , 0 1 dB j=- µ dx (2) Ohm’s law (ignoring Hall effect) is j = E + u × B σ ( ) G GGJG (3)