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Basic Plasma Physics 75 D = okTe noe2 as the characteristic Debye length, Eq. (3.7-12) can be written = e exp – r . 4 or D (3.7-12) (3.7-13) This equation shows that the potential would normally fall off away from the test charge inserted in the plasma as 1/r, as previously found, except that the electrons in the plasma have reacted to shield the test charge and cause the potential to decrease exponentially away from it. This behavior of the potential in the plasma is, of course, true for any structure such as a grid or probe that is placed in the plasma and that has a net charge on it. The Debye length is the characteristic distance over which the potential changes for potentials that are small compared to kTe . It is common to assume that the sheath around an object will have a thickness of the order of a few Debye lengths in order for the potential to fall to a negligible value away from the object. As an example, consider a plasma with a density of 1017 m–3 and an electron temperature of 1 eV. Boltzmann’s constant k is 1.3807 10–23 J/K and the charge is 1.6022 10–19 coulombs, so the temperature corresponding to 1 electron volt is T=1 e =1.6022 10–19 =11604.3K. k 1.3807 10–23 The Debye length, using the permittivity or free space as 8.85 10–12 F/m is then ( –12)( –23) 1/2 = 8.85 10 1.38 10 11604 D 17(–19)2 10 1.6 10 = 2.35 10–5 m = 23.5μm. A simplifying step to note in this calculation is that kTe / e in Eq. (3.7-12) has units of electron volts. A handy formula for the Debye length is D (cm) 740 Tev / no , where Tev is in electron volts and no is in cm–3.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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