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Basic Plasma Physics 47 Fp =– p=– (nkT), (3.5-2) nn where the pressure is given by P = nkT and should be written more rigorously as a stress tensor since it can, in general, be anisotropic. For plasmas with temperatures that are generally spatially constant, the force due to the pressure gradient is usually written simply as Fp = –kT n . (3.5-3) n Finally, collisions transfer momentum between the different charged particles, and also between the charged particles and the neutral gas. The force due to collisions is Fc =–m ab(va –vb), (3.5-4) a,b where vab is the collision frequency between species a and b. Using these three force terms, the fluid momentum equation for each species is mndv =mn v+(v )v =qn(E+v B)– p–mn (v–v ), (3.5-5) dt t o where the convective derivative has been written explicitly and the collision term must be summed over all collisions. Utilizing conservation of momentum, it is possible to evaluate how the electron fluid behaves in the plasma. For example, in one dimension and in the absence of magnetic fields and collisions with other species, the fluid equation of motion for electrons can be written as mn vz+(v )v =qnE – p, (3.5-6) e t z ez z where vz is the electron velocity in the z-direction and p represents the electron pressure term. Neglecting the convective derivative, assuming that the velocity is spatially uniform, and using Eq. (3.5-3) gives m vz = –eEz – kTe ne . (3.5-7) t ne zPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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