Simulating magnetic fusion experiments with initial value codes

Fusion laboratory experiments are characterized by large gradients as is needed to confine plasmas hotter than the sun in laboratory devices. These large gradients result in a wide-range of instabilities. In toroidally-confined plasmas these linear instabilities (e.g., $1/1$, TM, ITG) evolve nonlinearly to produce phenomenological events (e.g., sawtooth, MARFE, transport). The phenomenological events are generally of three types: violent relaxation (or transients), coherent saturated steady state, and turbulent steady state. How to formulate the simulation of experiments with an initial value code requires understanding the phenomenological type, and appreciating the subtle implications of the solution technique. These subtle implications are discussed generally, and then specifically in the context of simulating QH-mode, ELM-free regimes.