The quality factor (Q) applies to any resonant circuit component; most often the quality factor of the coil determines the overall Q of the circuit.
Inversely related to the fraction of the energy in an oscillating system lost in one oscillation cycle. Q is inversely related to the range of frequency over which the system will exhibit resonance.
In a parallel tuned circuit (such as used in a MR coil), the quality factor is defined as:
Q = vL/R
where L is the coil inductance, R is the circuit resistance, and v is the angular frequency. Increasing quality factor results in improving the signal to noise ratio SNR by a factor √Q and also produces a sharper frequency response (decreased band width). The Q of a coil will depend on the circumstances under which it is measured, e.g. whether it is 'unloaded' (no patient) or 'loaded' (patient).

See Digitization Noise Artifact.

Quenching is the cryogen boil off (liquid helium) which is used to cool the superconducting magnet coils of high field MRI systems. This results in a loss of superconductivity in the magnet, in a rapid increase in the resistivity of the magnet, which generates heat that results in further evaporation of the cryogen.

A quench can cause total magnet failure and should be avoided.

A quench is the rapid helium evaporation and the loss of superconductivity of the current-carrying coil that may occur unexpectedly, or from pressing the emergency button in a superconducting magnet. As the superconductive magnet becomes resistive, heat will be released that can result in boiling of liquid helium in the cryostat. This may present a hazard if not properly planned for.
The evaporated coolant requires emergency venting systems to protect patients and operators. Quenching can cause total magnet failure and cannot be stopped. MRI systems are designed such that all of the escaping cryogenic gas is directed out of the building (quench pipe through the roof or the wall). In the event of a burst of the tank (possible in the case of an accident) or a blockage of the pipes, the helium gas will be forced into the scanner room, giving rise to a large white cloud of chilled gas. Under such circumstances it is essential that the scanner room is evacuated, also caused by the displacement of oxygen, which under extreme conditions could lead to asphyxiation. The force of quenching can be strong enough to destroy the walls of the scanner room or the MRI equipment.