A general method is developed for calculating boundary plasma fluctuations across a magnetic separatrix in a tokamak with a divertor or a limiter. The slab model, which assumes a periodic plasma in the edge reaching the divertor or limiter plate in the scrape-off layer(SOL), should provide a good estimate, if the radial extent of the fluctuation quantities across the separatrix to the edge is small compared to that given by finite particle banana orbit. The Laplace transform is used for solving the initial value problem. The electron temperature gradient(ETG) driven instability is found to grow like t−12e{sup {gamma}mt}.