1. a) Plasma discharges are an important tool in industry and manufacturing for materials processing applications. In one or two sentences, say what you understand by the term "plasma". ii) What are the main differences between non-equilibrium and equilibrium plasmas? Give one technological application for each. b) In the theory of the electrical breakdown of gases in a discharge tube, Townsend's first coefficient a is often used and can be written as = ex 2 y' Describe in words the meaning of each of the individual terms in this equation. In addition, discuss the physical meaning of the terms 1/2 and exp{-V'/E2} in relation to processes occurring in the tube. c) By considering the charged particle fluxes at the electrodes and the secondary electron yield y, show that the condition for plasma self- sustainment in a tube of length d is ad = ln 1+- = In (1 + / -) d) i) Using the definition of a in part b) above and the self-sustainment condition in part c) above, derive the Paschen Law for electrical breakdown. Define all the symbols used. ii) Draw and label a typical Paschen curve and explain the reasons why the breakdown voltage increases on each side of the Paschen minimum.