16.522, Space Propulsion Prof. Manuel martinez-Sanchez Lecture 21: Electrostatic versus Electromagnetic Thrusters Ion Engine and Colloid Thrusters are Electrostatic devices, because the electrostatic orces that accelerate the ions (or droplets) are also directly felt by some electrode, and this is how the structure receives thrust. We could manipulate the expression for thrust density in an ion engine to Fa2E0Ea, where E,=3 d was the field on the surface of the extractor electrode. This is the electrostatic pressure Since E0=8.85×1012F/ m and ea is rarely more than2,000mm=2×10°Vm, we are limited to electrostatic pressure of about 20 N/m2(and due to various inefficiencies more like 1-2 N/m) Hall thrusters occupy an intermediate position, and point the way to a higher thrust density Ions accelerate electrostatically but electrons, which see the same(and opposite) electrostatic force, because the plasma is quasineutral (ne=ni),are essentially stopped(axially) by an interposed magnetic field. Of course, the force is he azimuthal Hall current they carry). In the end, then, the structure is pushed s of mutual, and so the electrons exert this force on the magnetic assembly(by means of magnetically. To be more precise, we should say that most of the force is magnetically transmitted. There is still an electrostatic field in the plasma, and so there will be some electrostatic pressure =EoE acting on various surfaces. But because we made the plasma quasineutral these fields are much weaker than they are between the grids of an ion engine and it is a good thing we have the magnetic mechanism available. In fact, the thrust density of Hall thrusters is about 10 times higher than that of ion engines despite the weak electrostatic fields More generally, we can ask how much stronger can the force per unit area on some structure be when it is transmitted magnetically as compared to electrostatically. As we will see in detail, the counterpart to the "electrostatic pressure"is the"magnetic H,Where b is the field strength and Ho=1. 256X10-Hy/m is the permeability of vacuum. Without recourse to superconductive structures, B can easily be of the order of 0.1 Tesla (either using coils or permanent magnets),so 2u. =8,000N/m, or 400 times the maximum practical electrostatic pressure Thrusters that exploit these magnetic forces are called Electromagnetic"(although they should be called" Magnetic"by rights). The magnetic field can be external, i.e supplied by coils and not greatly modified by plasma currents or it may be self induced, when plasma currents became large enough. They can also be steady(or at least slowly varying compared to plasma flow time), or they can be varying very ast, so as to set up strong induced electromotive forces(transformer effect). A few examples are: Magneto Plasma Dynamic(MPD thrusters The most powerful type, with self-induced, magnetic fields, operates in steady(or quasi-steady fashion, and can generate multi-Newton thrust 16.522, Space P pessan Lecture 21 Prof. Manuel martinez Page 1 of 2116.522, Space Propulsion Lecture 21 Prof. Manuel Martinez-Sanchez Page 1 of 21 16.522, Space Propulsion Prof. Manuel Martinez-Sanchez Lecture 21: Electrostatic versus Electromagnetic Thrusters Ion Engine and Colloid Thrusters are Electrostatic devices, because the electrostatic forces that accelerate the ions (or droplets) are also directly felt by some electrode, and this is how the structure receives thrust. We could manipulate the expression for thrust density in an ion engine to 2 A 0a 1 F= E 2 ε , where a 4 V E = 3 d was the field on the surface of the extractor electrode. This is the electrostatic pressure. Since -12 ε0 = 8.85 × 10 F/m and Ea is rarely more than 6 2,000 V/mm = 2 ×10 V/m, we are limited to electrostatic pressure of about 20 N/m2 (and due to various inefficiencies more like 1-2 N/m2 ). Hall thrusters occupy an intermediate position, and point the way to a higher thrust density. Ions accelerate electrostatically, but electrons, which see the same (and opposite) electrostatic force, because the plasma is quasineutral (ne=ni), are essentially stopped (axially) by an interposed magnetic field. Of course, the force is mutual, and so the electrons exert this force on the magnetic assembly (by means of the azimuthal Hall current they carry). In the end, then ,the structure is pushed magnetically. To be more precise, we should say that most of the force is magnetically transmitted. There is still an electrostatic field in the plasma, and so there will be some electrostatic pressure 2 0 n 1 E 2 ε acting on various surfaces. But because we made the plasma quasineutral, these fields are much weaker than they are between the grids of an ion engine, and it is a good thing we have the magnetic mechanism available. In fact, the thrust density of Hall thrusters is about 10 times higher than that of ion engines, despite the weak electrostatic fields. More generally, we can ask how much stronger can the force per unit area on some structure be when it is transmitted magnetically as compared to electrostatically. As we will see in detail, the counterpart to the “electrostatic pressure” is the “magnetic pressure”, 2 0 B 2µ , where B is the field strength and -6 µ0 = 1.256x10 Hy/m is the permeability of vacuum. Without recourse to superconductive structures, B can easily be of the order of 0.1 Tesla (either using coils or permanent magnets), so 2 2 0 B 8,000 N/m 2µ  , or 400 times the maximum practical electrostatic pressure. Thrusters that exploit these magnetic forces are called “Electromagnetic” (although they should be called “Magnetic” by rights). The magnetic field can be external, i.e., supplied by coils and not greatly modified by plasma currents, or it may be self￾induced, when plasma currents became large enough. They can also be steady (or at least slowly varying compared to plasma flow time), or they can be varying very fast, so as to set up strong induced electromotive forces (transformer effect). A few examples are: - Magneto Plasma Dynamic (MPD) thrusters The most powerful type, with self-induced ,magnetic fields, operates in steady (or quasi-steady) fashion, and can generate multi-Newton thrust