Difference between revisions of "Neutron Polarimeter"
Jump to navigation
Jump to search
Line 73: | Line 73: | ||
The neutron's kinetic energy as function of the neutron's time of flight is: | The neutron's kinetic energy as function of the neutron's time of flight is: | ||
− | <math>T_n = m_n (\gamma - 1) = m_n\left[ \frac{1}{\sqrt{1-\left(\frac{ | + | <math>T_n = m_n (\gamma - 1) = m_n\left[ \frac{1}{\sqrt{1-\left(\frac{s}{c\ t}\right)^2}} - 1 \right]</math> |
And it follows, that neutron's kinetic energy error as function of the neutron's time of flight error is: | And it follows, that neutron's kinetic energy error as function of the neutron's time of flight error is: | ||
Line 81: | Line 81: | ||
Also we need the neutron time of flight as function of neutron kinetic energy: | Also we need the neutron time of flight as function of neutron kinetic energy: | ||
− | <math>t:=\frac{ | + | <math>t:=\frac{s}{c\ \beta_n} = \frac{s}{c\ (p_n/E_n)} = |
− | \frac{ | + | \frac{s\ (T_n + m_n)}{c\sqrt{T^2+2m_nT_n}} = 23\ ns</math> |
Revision as of 04:43, 17 June 2010
Analysis of energy dependence
four-vectors algebra
writing four-vectors:
Doing four-vector algebra:
Detector is located at
, so
and visa versa
how it looks
low energy approximation
As we can see from Fig.2 for low energy neutrons (0-21 MeV)
energy dependence of incident photons is linear
Find that dependence. We have:
So, the equation of the line is:
Finally for low energy neutrons (0-21 MeV):
example of error calculation
example 1
Say, we have, 10 MeV neutron with uncertainty 1 MeV, the corresponding uncertainly for photons energy is:
example 2
Say, we have, neutron with time of flight uncertainly is 1 ns
The neutron's kinetic energy as function of the neutron's time of flight is:
And it follows, that neutron's kinetic energy error as function of the neutron's time of flight error is:
Also we need the neutron time of flight as function of neutron kinetic energy:
Say, we have 10 MeV neutron, 1 m away detector, and neutron time of flight error is 1 ns
Using formulas above:
absolute neutron kinetic energy error relative neutron kinetic energy error
absolute photon energy error relative photon energy error
Some other calculations for different detector distance and neutron kinetic energy are:
detector distance | neutron energy | time of flight uncertainty | neutron | neutron time of fligh | neutron absolute error | neutron relative error | photon absolute error | photon relatibe error |
1 m | 20 MeV | 1 ns | 4.79 cm | 75 cm | 7.49 cm |