Helical winding of current-carrying wire that produces a magnetic field along the axis of the helix.

A coil of wire wound in the form of a long cylinder. When a current is passed through the coil, the magnetic field within the coil is relatively uniform. Solenoid RF coils are commonly used when the static magnetic field is perpendicular to the long axis of the body.
The reason against a solenoidal coil is that the signal is missed when the axis of the solenoidal coil is coaxial with the horizontal magnetic field Bo. If the coil's axis can be put near a right angle (60° to 90°) with the principal field, so the loss in the signal is greatly dismissed, and good SNR can be achieved.
The two forms are single turn solenoid and multiple turn solenoids.

The multi turn solenoid is a volume coil that typically operates as the transmitter and receiver of RF energy. Multi turn solenoids can be wrapped, but the uniformity of the field suffers.

Single turn solenoid is a transmit and receive RF imaging coil that, in general, has a cylindrical shape. The solenoidal configuration of this coil is a further developed planar surface coil. While surface coils have a strong coupling and high signal to noise ratio to nearby signals they have a marked loss of signal beyond one radius from the center of the coil. With a solenoidal coil design the imaging object lies within one radius from the coil center, which improved imaging (of extremities, such as wrist or knee).

See also Radio Frequency Coil and Imaging of the Extremities.

A coil is a large inductor with a considerable dimension and a defined wavelength, commonly used in configurations for MR imaging. The frequency of the radio frequency coil is defined by the Larmor relationship.
The MRI image quality depends on the signal to noise ratio (SNR) of the acquired signal from the patient. Several MR imaging coils are necessary to handle the diversity of applications. Large coils have a large measurement field, but low signal intensity and vice versa (see also coil diameter). The closer the coil to the object, the stronger the signal - the smaller the volume, the higher the SNR. SNR is very important in obtaining clear images of the human body. The shape of the coil depends on the image sampling. The best available homogeneity can be reached by choice of the appropriate coil type and correct coil positioning. Orientation is critical to the sensitivity of the RF coil and therefore the coil should be perpendicular to the static magnetic field.

RF coils can be differentiated by there function into three general categories:
The RF signal is in the range of 10 to 100 MHz. During a typical set of clinical image measurements, the entire frequency spectrum of interest is of the order 10 kHz, which is an extremely narrow band, considering that the center frequency is about 100 MHz. This allows the use of single-frequency matching techniques for coils because their inherent bandwidth always exceeds the image bandwidth. The multi turn solenoid, bird cage coil, single turn solenoid, and saddle coil are typically operated as the transmitter and receiver of RF energy. The surface and phased array coils are typically operated as a receive only coil.

See also the related poll result: '3rd party coils are better than the original manufacturer coils'