A physical model for the space and time evolution of the primary parameters of ordinary and burning tokamak plasmas is described by employing a fluid plasma treatment coupled to a magnetohydrodynamic equilibrium description, the solution to the appropriate Maxwell equations, and the solution of the linear transport equation describing neutral atom transport in plasmas. The specific problems of plasma heating by ion cyclotron radiofrequency (ICRF) waves and neutral atom transport in the plasma edge and in complicated geometrical components such as divertor channels or pumped limiter structures are analyzed. A theoretical, one-dimensional slab model of ICRF heating at ω = 2ωcD is developed and applied to determine the space-time response of tokamak plasmas. Generally, strong single-pass absorption is found for high-density, high ⟨Β⟩ plasmas using a low k11 spectrum (0.05 to 0.1 cm−1) although for ⟨Β⟩ > 1%, electron Landau damping becomes important. Deterministic and Monte Carlo methods to solve the neutral atom transport problem are described. Specific application to determine the spectrum of neutral atoms emerging from the duct of a pump limiter shows it to be hard (mean energy > 20 eV), indicating very incomplete energy thermalization. Uncertainties are identified in the overall problem of dynamic burning plasma analysis caused by the complexity of the problem itself and by uncertainties in fundamental areas such as plasma transport coefficients, stability, and plasma edge physics.