The Lawson criterion used as the measure of the feasibility of controlled thermonuclear reactor is described in this thesis. The Lawson criterion is a minimum condition on the product of ion density, n and confinement time, τ of the energetic ions within a reacting plasma. This criterion is a function of temperature, T and efficiency, η. Assuming an ideal physical system (idealized cycle), the criterion under a single overall efficiency η = 1/3 was established originally by Lawson in 1957. Ten terms, i.e., electron-ion decoupling effect, effect of the ambipolar potential, energy increases due to the kinetic energies of the fusion products and secondary reactions, cyclotron radiation losses, energy losses due to the leaks of the electrons, energy losses due to the leaks of the ions, energy needed to replace fused ions, recovered dumped energy of unreacted fuel ions and electrons and different heating, conversion efficiencies, are omitted from energy balance equation of the Lawson criterion. For successful operation of a thermonuclear reactor, most of the above mentioned effects are not negligible in real physical systems. Including these nonnegligible effects, the Lawson criterion was modified by Bogdan C. Maglich and Robert A. Miller in 1975. It requires that, in addition to the product $n τ, other independent conditions be satisfied. In Magnetic confinement systems with a poor vacuum and an imperfect magnetic field geometry, the plasma energy losses are mainly in the form of radiation emitted by impurities. High-Z impurities make bremsstrahlung, recombination and line radiation losses increase. Including these impurity effects, the modified Lawson criterions is generalized, and is analyzed through the numerical solution of the energy balance equation for the cases of DD-plasma, DD-migma and DD-plasma. We conclude that the minimum conditions are; (1) For the case of DD-migma, 0.5% molybdenum impurity makes $nτ = 6.35 × 10^{15}cm^{-3}ㆍsec$ and ion temperature $T_i=700 kev$. Continuous reaction becomes impossible for molybdenum concentrations greater than 1.0%. (2) For the case of DD-plasma, 0.5% carbon impurity makes $nτ = 2.58 × 10^{17} cm^{-3}ㆍsec$ and $T_i= 60 kev$, and raises the minimum Lawson curve by 22.8. Reaction becomes impossible for 1.0% carbon and other impurities with 0.1% concentrations. (3) For the case of DD-plasma, 0.2% molybdenum impurity makes $nτ = 1.59 × 10^{15} cm^{-3}ㆍsec$ and $T_i= 90 kev$, and increases the minimum Lawson curve by 30.5. Continuous reaction becomes impossible for molybdenum concentrations greater than 0.5%.
