Page 257 - Biomedical Engineering and Design Handbook Volume 2, Applications

236 DIAGNOSTIC EQUIPMENT DESIGN

Birdcage wall Local electric fields

x,y
RF electric
z Field

Virtual RF ground region
RF electric
Field
Birdcage wall

FIGURE 8.4 Electric fields inside a low-pass, RF birdcage coil are pre-
sented. Note that electric fields reach their maximum magnitude at the coil and
fall to zero along the coil axis. Capacitors along the coil wall may also give rise
to locally high electric fields. Any conductors should be routed along regions
of low electric field or orthogonal to the electric field. Below is an illustration
of a birdcage coil.

Let a be the radius of the birdcage coil. Assume that (at the moment of time we look) B = B (B =
1
1x
1y
B = 0). Assume conductors of the RF coil lie only parallel to the z direction, then A = A = 0. Let θ
y
1z
x
be the angle between the conductor, the center of the cylinder, and the x axis. Then it is possible to find B 1x
and A (remember that B is constant, independent of z):
z 1
∂ A
B = z → A = B y = B asinθ (8.17)
1
z
1
x 1
z ∂
So, an infinitely long coil with infinite conductors parallel to z, lying on the surface of a cylinder,
will produce a uniform B field, provided current varies with sinθ.
1
Of course, real birdcage coils are not infinitely long. Current is returned through end rings at
the ends of the finite, cylindrical coil. End rings sum (or integrate) current from the straight coil
conductors (which I will call legs). So, if coil leg current varies as sinθ, then current in the end
rings varies as cosθ. Let N be the number of legs in the birdcage coil. Schenck 89,90 showed that
peak end ring current amplitude is a factor 1/[2 sin(π/N)] larger than the peak current in the coil
legs. Let D be the length-to-diameter ratio of the birdcage coil, a be the coil radius, and I be the