d xp dxβ 1B ⊙ x甘 We can see that the effect is to turn the current and the lorentz force counter clockwise by arc tan B. There is still a forward force(called the"blowing"force), but also now a transverse force, called the"pumping"force, because its main effect is to pump fluid towards the cathode wall, creating a transverse pressure gradient (low pressure at the anode). Basically the axial (or Hall) current does no useful work but it still contributes to the Joule dissipation j /6. Thus, we may want to turn the whole diagram by tan B clockwise and have j flow transversally only and f=jx B point But notice that this implies a forward component of the external field x阝 Hence we have to build the electrode wall in such a way that an axial voltage can be sustained For example, it can be made of independent metallic segments, connected transversally in pairs, and with nsulation between each pair, so that a voltage can also be applied between each segment and its downstream neighbour. Unless a lot of ingenuity is used, this UxBI segmented construction complicates the design and onnections greatly Self-field coaxial construction Leaving aside for the moment the question of how to provide the magnetic field the imple continuous electrode accelerator can be further simplified by wrapping it around"into an annulus thereby eliminating the insulating walls 16.522, Space P pessan Lecture 21 Prof. Manuel martinez Page 10 of 2116.522, Space Propulsion Lecture 21 Prof. Manuel Martinez-Sanchez Page 10 of 21 We can see that the effect is to turn the current and the Lorentz force counter clockwise by arc tanβ . There is still a forward force (called the “blowing” force), but also now a transverse force, called the “pumping” force, because its main effect is to pump fluid towards the cathode wall, creating a transverse pressure gradient (low pressure at the anode). Basically, the axial (or Hall) current does no useful work, but it still contributes to the Joule dissipation 2 j σ . Thus, we may want to turn the whole diagram by tan-1 β clockwise and have j G flow transversally only and f = j × B G GJG point axially. But notice that this implies a forward component of the external field E G : Hence, we have to build the electrode wall in such a way that an axial voltage can be sustained. For example, it can be made of independent metallic segments, connected transversally in pairs, and with insulation between each pair, so that a voltage can also be applied between each segment and its downstream neighbour. Unless a lot of ingenuity is used, this segmented construction complicates the design and connections greatly. Self-field coaxial construction Leaving aside for the moment the question of how to provide the magnetic field, the simple continuous electrode accelerator can be further simplified by “wrapping it around” into an annulus, thereby eliminating the insulating walls: