Oscillation of the magnetic field and, in some cases, plasma pressure. In tokamaks, Alfvén waves are typically strongly damped (i.e. they would spontaneously decay if externally excited).
Fast Alfvén wave:
The fast Alfvén wave exists over a broad frequency spectrum, from the ion cyclotron range of frequencies (ICRF) where its character is electromagnetic, down to magnetohydrodynamic frequencies. Its velocity is comparable to the Alfvén velocity. The fast Alfvén wave is used routinely for high-power (about 20 megawatts) ICRF heating on JET, as it is efficiently absorbed in the plasma by the mechanism of ion cyclotron resonance.
The velocity of propagation of Alfvén waves in the direction of the magnetic field; it is proportional to the magnetic field strength, and inversely proportional to the square root of the ion density.
The time taken for an Alfvén wave to travel one radian in the toroidal direction. This is a measure of the time-scale on which Alfvénic magnetohydrodynamic effects can occur.
Alfvén gap modes:
The toroidal nature of tokamak plasmas produces gaps in the otherwise continuous spectrum of Alfvén waves, which are populated by discrete, undamped Alfvén gap modes. These modes could be easily destabilised by resonant energy transfer from energetic particles (e.g. alpha particles from fusion reactions). Similar to Toroidal Alfvén Eigenmodes or TAE modes.