4 25 pts Solve 1 D Poisson equation considered in class (see lecture notes for Section 3 Plasma Fundamentals, slide 15) for the perfectly transparent grid inserted into infinite plasma volume with uniform density no The grid is placed at x 0 and carries negative potential (x 0) 0 Assume condition 1 is satisfied and use Taylor series expansion of the exponential term in the right hand side of Poisson equation Sheath Analytical derivation (1D case) Uniform plama he ni Problem formulation Consider perfectly transparent grid at potential inside infinite volume of uniform plasma with number density n ( is negative with respect to plasma) electric potential h umber Mensity grid(mesh) AAE 534 Electric Propulsion he hiano e(n n ) Poisson's equation dielectr n n permittivity of vacuum E 8 85 10 12 m cxp (g) 1 n no exp (eo KT) Boltzmann distribution 60 exp( x AD) EKT 1 2 AD ne en In HW 2 le 1 for x 1 ex x 2D Debye layer (sheath radius) thickness 15

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Question: 4. [25 pts] Solve 1-D Poisson equation considered in class (see lecture notes for Section 3: Plasma Fundamentals, slide 15) for the perfectly transparent

4. [25 pts] Solve 1-D Poisson equation considered in class (see lecture notes for Section 3: Plasma Fundamentals, slide 15) for the perfectly transparent

4. [25 pts] Solve 1-D Poisson equation considered in class (see lecture notes for Section 3: Plasma Fundamentals, slide 15) for the perfectly transparent grid inserted into infinite plasma volume with uniform density no. The grid is placed at x = 0 and carries negative potential (x = 0) = 0. Assume condition <

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