It is common to regard the alpha rhythm as an idling rhythm, one that takes place when no active work is done. This is taken in contrast to the faster rhythms such as beta and gamma, which are considered to represent a "processing" phase. Thus, the concentration/relaxation cycle is taken to be that characterized by phases of relaxation (alpha) and phases of concentration (beta). The use of alpha enhance protocols, and the use of "squash" protocols, both appeal to the notion of this cycle, and seek to produce either a preponderance of one phase, or the facility to alternate flexibly between phases.
The general observation that alpha amplitude is suppressed during tasks, has caused a view that alpha is solely a 'relaxation" mechanism, and does not participate in information processing. However, it is now evident that the alpha mechanism is not simply a pacing or timekeeping mechanism. Rather, it participates in memory scanning and related mental processing in a profound manner. Contrary to the concept that thinking occurs when alpha is absent, it is more correct to say that alpha activity persists during essentially all mental processing, but that it takes on a character of desynchronization during certain tasks. It is the desynchronization (independence) at a cellular level that produces the amplitude reduction, not any decrease in the "alpha" activity at the individual level.
The mechanism that produces synchronous alpha also operates at the cellular level, as the relaxation of inhibitory fibers whose primary function is to throttle the activity of the active (pyramidal) cells. These are primarily thalamocortical (collateral afferent) and cortico-cortical projections, that hold back the pyramidal cells from firing, despite the considerable excitatory input they may see. These receive information including sensory, body awareness, muscle feedback, and related signals, impinging on a range of primary sensory, secondary sensory, and somatosensory areas.
There is also a mechanism involving the reticulothalamic modulation of thalamocortical activity, via inhibitory projections from the reticular activating system into the thalamus. Training of alpha rhythms also likely affects this mechanism, as part of the brain's overall strategy toward satisfying the training goals.
Timing is what is controlled. At any given time, pyramidal cells are likely to be firing or not firing, as a function of their local population dynamics. But when the firing begins to synchronize, that alone is sufficient to increase the amplitude of the surface waves 2, 3, or more times.
Alpha is always there at a cellular level. However, the memory scanning that it represents is modulated at a unit-cell level, so that the relative timing of neighboring cells is modulated. Desynchronization and synchronization is what is modulated. Thus, the pyramidal cell populations can slide in and out of phase with each other, providing a wide range of surface amplitudes, which we see as EEG.