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n_TOF EAR-1 Neutron Flux TOF to energy conversion

n_TOF EAR-1 Neutron Flux TOF to energy conversion. Group discussion. n_TOF Analysis Group Meeting CERN, October 4-5, 2011. The problem…. How do we reconstruct the neutron energy from the measured time-of-flight? Protons hit the lead target

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n_TOF EAR-1 Neutron Flux TOF to energy conversion

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  1. n_TOF EAR-1 Neutron FluxTOF to energy conversion Group discussion n_TOF Analysis Group Meeting CERN, October 4-5, 2011

  2. The problem… • How do we reconstruct the neutron energy from the measured time-of-flight? • Protons hit the lead target • Neutrons enter the tubeafter following an unknownpath inside the target andother materials during anunknown time interval • Different (equivalent) approaches to the problem… EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  3. The moderation length • Moderation length evaluated as:v: velocity, tmod: moderation time • The moderation time is an experimental unknown, but it is known in the simulations • We can therefore study the behaviour of λ over the fullenergy range EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  4. The moderation length • The λ(E) distribution • Taking the maximum for each energy: • We could also use the mean value DISCUSS EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  5. The equivalent “t0 offset” • “Time-energy relation of the n_TOF neutron beam: energy standards revisited” • Summary follows… EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  6. The equivalent “t0 offset” • The neutron energy can be given as:The effective flight path L can be expressed as:where L0 is the geometrical length (plus the energy independent term of the moderation length) • The moderation length λ is extracted from simulations EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  7. The equivalent “t0 offset” • A fit is performed between 1eV-105eV following E-½ • The moderation process canequivalently be treated in termsof a time offset. Given eqs. (1) and (2): EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V. EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  8. The equivalent “t0 offset” • Comparing equations (2) and(3), the “t0 offset” is found tobe approximately -73ns. • An increase in the flight lengthcorresponds to a negative t0 • In reality, it is also t0= t0(E),but it is not consideredimportant WHY? EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  9. Extracting correct energy from λ(E) • Starting again from eq. (1):The effective flight path L can be expressed as:where Lgeom is the geometrical length, thus giving a new estimate for the energy:In general: • The correct energy can be determined iteratively, based on the λ(E) relation extracted from the simulations • Very quick convergence (2-3 Newton-Raphson iterations) EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  10. Open questions • Can we agree on a common approach to the problem? • Do we need to? • Perhaps different measurements, e.g. capture (up to 100s keV) and fission (up to MeV region) can adopt the most convenient approach • t0 offset for capture • Iteration based on simulated λ(Ε) distribution for fission • How was past analysis performed? • Other? EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  11. n_TOF line EAR 1 Lgeom ≈ 185m λ(E) t0 EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  12. The end EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

  13. Simulations: energy reconstruction • Proton hits the target (t = 0) • Neutron enters the beam tube after a time interval dependent on energy, flight-path, etc. • This time is given by the simulation • Given the real energy at that point, the time-of-flight to the EAR is (1): •  the measured TOF will be the “moderation” time + the real time-of-flight (2) • The measured energy can then be calculated as (3): • Simulations provide the real neutron energy • How is the measured energy reconstructed? EAR-1 Neutron Flux : TOF to energy conversion n_TOF Analysis Group Meeting – CERN, October 4-5, 2011 | A.T. | C.G. | N.C. | M.B. | V.V.

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