nuclear engineering

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Models for Dead Time Behaviorchapter 4

• Presentation by
• Ali Asghar Adibi
• Guide master
• Dr.soltani
• Autumn 92

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Models for Dead Time Behavior
Paralyzable
Models for Dead Time Behavior
Non-Paralyzable
True Event
True Event
True Event
A fixed time t is assumed to follow each true
event that occurs during the "live period" of the
detector.
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Point The detailed behavior of a specific
counting system may depend on the physical
processes taking place in the detector itself or
on delays introduced by the pulse processing and
recording electronics.
True events that occur during the dead period are
lost and assumed to have no effect whatsoever on
the behavior of the detector
True events
The same dead time T is assumed to follow each
true interaction that occurs during the live
period of the detector
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n true interaction rate m recorded count
rate t system dead time
P(T) dT is the probability of observing an
interval whose length lies within dT about T.
In the nonparalyzable case the rate at which
true events are lost is simply nmT. But because n
- m is another expression for the rate of losses
In the paralyzable case we note that rate m is
identical to the rate of occurrences of time
intervals between true events which exceed T.
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Non-Paralyzable
Paralyzable
M .88 1.58 2 2.144 2.6 3.33 3.65 3.75 3.77 3.78 3.79
N 1 2 3 4 5 6 7 7.5 8 9 10








M .85 1.53 2 2.34 2.57 2.7 2.75 2.76 2.73 2.6 2.3
N 1 2 3 4 5 6 7 7.5 8 9 10
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For low rates (n ltlt I/T) the following
approximations can be written
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Methods of Dead Time Measurement

• the dead time will not be known or may vary with
  operating conditions and must therefore be
  measured directly
• Common measurement techniques
• observed rate varies nonlinearly with the true
  rate
• 1. two-source method
• The method is based on observing the counting
  rate from two sources individually and
  combination
• N1 counting rates source 1
• N2 counting rates source 2
• M1 observed rates source 1
• M2 observed rates source 2
• N12 counting rates combined sources
• Nb counting rate background
• Mb observed rates background
• M12 observed rates combined sources

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Methods of Dead Time Measurement

• 2. Decaying source method
• N0 is the true rate at the beginning of the
  measurement
• ? is the decay constant

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Dead Time Losses from Pulsed Sources
1. If t is much smaller than T the fact that the
source is pulsed has little effect, and the
results given earlier in this section for
steady-state sources may be applied with
reasonable accuracy.
2. If t is less than T but not by a large factor,
only a small number of counts may be registered
by the detector during a single pulse. This is
the most complicated circumstance and is beyond
the scope of the present discussion
3. If t is larger than T but less than the "off"
time between pulses (given by l/f - T), the
following analysis applies. Note that under these
conditions, we can have a maximum of only one
detector count per source pulse. Also, the
detector will be fully recovered at the start of
each pulse.

• There are many applications in which the source
  of radiation is not continuous but instead
  consists of short pulses repeated at a constant
  frequency
• electron linear accelerators used to generate
  high-energy X-rays can be operated to produce
  pulses of a few microsecond width with a
  repetition frequency of several kilohertz

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This result can be viewed as predicting an
effective dead time value of 1/2f in this
low-loss limit. Since this value is now one-half
the source pulsing period, it can be many times
larger than the actual physical dead time of the
detector system.

• t dead time of the detector system
• m observed counting rate
• n true counting rate (if T were 0)
• T source pulse length
• f source pulse frequency

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