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Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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114 Chapter 4 parallel to perpendicular to the wall, where the analysis above does not apply. However, the magnetic field strength in this region increases rapidly near the magnets and some fraction of the plasma electrons is reflected from the magnetic mirror. This serves to retard the ion flux electrostatically in a manner similar to the ambipolar diffusion case between the cusps described above. Ultimately, the ions are lost at the cusp with the Bohm current to the hybrid area, and it is usually found that the transition to this unimpeded ion flow to the wall occurs over an area that is small compared to the total area between the cusps. The second issue with using Eq. (4.3-17) is that the diffusion thickness l is not known. However, this can be estimated for ring-cusp thrusters using a dipole model for the magnets. Consider the case of two rows of opposite polarity magnets, which is illustrated in part of Fig. 4-10. Each magnet has a dipole strength M per unit length, and the magnets are separated in the x-direction by a distance d. The magnetic field along the line perpendicular to the midline between the magnets is B+(y) = q = q , (4.3-18) r d2 +(y)2 4 where r is the length of the line from the point on the midline to the magnet, q is the number of magnetic dipoles, and is the half height of the magnet. The magnetic field on the centerline between the magnets has only an x-component. The x-component of the field from one magnet (positive polarity) is given by B x+ ( y ) = B + ( y ) c o s = q d2 = q d2 . ( 4 . 3 - 1 9 ) r2 d2 +(y)2 4 The field in the x-direction from both magnets is then Bx(y)= qd qd , (4.3-20) and so the total field on the center line is d2 +(y)2 d2 +(y+)2 44

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