American Magnetics AMI Liquid Helium Level Sensors - Manual (Page 5)

Rev. 1 5
AMI
EXCELLENCE IN MAGNETICS AND CRYOGENICS
Region II. The transition region
The normal zone is assumed to propagate at a constant velocity (20 cm/second). The
heat produced in the NbTi filament during the time required for the resistive region to
reach the liquid surface is:
Q
v
= I
2
• R
s
• L
G
• (t
1
– t
0
) / 2
= I
2
• R
s
• L
G
2
/ (2 • v) since (t
1
– t
0
) = L
G
/ v
Region III. The steady state region
After the resistive zone reaches the liquid surface, the filament becomes a simple
resistor with constant resistance. The power produced in this steady state is:
Q
s
= I
2
• R
s
• L
G
• t
EXAMPLES
Let's estimate the loss for an extreme case of a 60 inch (152.4 cm) long sensor in a MRI
system with all of the sensor length above the liquid helium level ( L
G
= active length).
All other cases are better than this and can be easily calculated. The results are:
Q
h
= 0.028 watts • t
Q
v
= 14.86 joules
Q
s
= 3.9 watts • t
Since the heat produced in region III (steady state) is wasted and not required for level
sensing, AMI has developed and patented a sample-and-hold system which reduces the
third term (Q
s
) to zero because it automatically turns the current off when the resistive
zone reaches the liquid helium.
The sample time for this example of a 60 inch sensor is approximately 7.6 seconds. The
total energy input for this sample is thus:
Q
h
= 0.028 watts • t
where t = 7.6 seconds
= 0.21 joules
Q
v
= 14.86 joules
Consequently, total heat input (Q
h
+ Q
v
) is approximately 15.1 joules. The latent heat
of evaporation of liquid helium is approximately 21 joules/gm. So in this case we have
evaporated 0.72 grams of liquid helium (about 5.7 ml) for one sample.