Since time-of-flight energy analysis is based on the time ∆t ≡ t1−t0 over which a particle travels a
distance `, we must produce measurements of both the startt0 and stop t1 times of an interval associated
with a well-understood neutron flight path. As the charged particle beam at the TUNL tandem accelerator can be pulsed, a natural choice is to use the timing of the incident, charged-particle beam pulse ast0 and
the time of interactions in a detector positioned directly in the produced beam ast1. Making use of the fact
that the charged-particle beam producesγ-rays in addition to neutrons, the locations of theγ-ray peaks in collected TOF spectra can provide a convenient mechanism for determination oft0and provide insight into
the timing distribution of the charged-particle beam.
The beam of charged particles from the tandem accelerator can produce γ-rays through interaction with any component along the beam line, not only those in the neutron-production volume4. To provide a
reckoning of t0, aγ-ray population associated with a confidently known production site must be selected:
the distances between the γ-ray production site, the neutron production site, and the detector will factor into the TOF analysis. Examination of the collected TOF data for the CsI[Na] measurements shows three recognizableγ-ray populations in a relatively small region of TOF space; the associated production sites are assumed to be (in order along the direction of the beam): the collimator before the gas cell, the havar foil on the entrance to the gas cell, and the tantalum disk at the end of the gas cell.
Theγ-rays will arrive in this order on the detector and the observed intensities of the populations suggest that the havar foil is the most prominent source ofγs: this is consistent with expectations, as the deuterons incident upon the foil should have lost little energy prior to this interaction and the beam is tuned to maximize flux on the gas cell target whose entrance is subtended by the foil, thereby minimizing the current on the collimator. No significant attenuation of the beam flux is expected through the havar or the deuterium gas, so a large fraction of the deuterons incident upon the havar will also reach the tantalum disk at the end of the gas cell; though the flux on this disk may be nearly equivalent to that on the havar, the considerable deuteron energy loss expected through the foil (and the additional, modest loss through the gas volume) should result in a significantly lower yield of inelasticγ-rays from interaction with the W disk relative to the havar.
4Generally speaking, neutron production is not necessarily restricted to a single volume, either, but the relatively-low proton
and deuteron energies used for these experiments significantly limit the locations of neutron production by virtue of being below threshold for many neutron-production reactions aside from those in the intended production volume.
The region of the TOF spectra with the 3 near-target γ-ray populations is analyzed using the RooFit fitting package [247] in ROOT. The model used for the spectra consists of 3 peak shapes additively combined with a uniform distribution modeling a flat, accidental background; the peak shape used5is that of a Gaussian
with meanµand widthσconvolved with an exponential decay with time constantτ. Using the assumption that each of the γ-ray populations are produced similarly (specifically, that they all are produced in an infinitely thin target and the deuteron transit time over this region is negligibly small), the parameters corresponding to the relative timing features of these peak shapes are common between the three. More explicitly, if the distribution in time for peaki, ini= 1,2,3, is defined by parametersµi, σi,andτi, we fix
σγ =σ1=σ2=σ3, τγ =τ1=τ2=τ3,
only allowing the absolute timing of each pulseµito vary independently. An extended maximum likelihood
(EML) fit is carried out using this model over theγ-ray TOF region, and the means of the Gaussians involved in the peak shapes, µi, are taken to represent the time tγ,i of the γ-ray time of flight. In this fit, count-
rate normalization parameters (i.e., the “extended” component of the EML fit) are allowed to float without constraint and are ultimately immaterial to the result, aside from qualitative interpretation of the relative magnitudes. The shape characteristics of each peak, whose distribution is governed by the parameters σγ
andτγ, are interpreted as a representation of the timing distribution of the deuteron beam itself.
The most intense γ-ray peak, corresponding to production at the havar foil, is selected as a reference; with the location of production thusly identified, the flight path `γ from production site to detection site
can be determined. Writing the mean of the reference peak asµrefand neglecting the transit time ofγ-rays
across the monitor detector, we can express thecharged-particle-beam arrival time,
s0=sref−
`γ
c φcal, sref=µref, (D.1)
where we must be careful to note that we are working in digitized unit space, utilizing the calibration φcal
with units of channel / nanosecond.
The timing distribution of the charged-particle beam is taken into account when fitting neutron timing data.
0 1000 2000 3000 4000 5000 Counts / (1 ns) Full model γ Primary γ Secondary γ Tertiary 0 1000 2000 3000 4000 5000 Counts / (1 ns) 200 210 220 230 240 250 260 270 280 290 300 Time to next BPM (ns) 0 500 1000 1500 2000 2500 3000 3500 4000 Counts / (1 ns) 200 210 220 230 240 250 260 270 280 290 300 Time to next BPM (ns) 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 Counts / (1 ns)
Figure D.2: Clockwise from upper left: middle standoff; close; far; close detuned. The black line in each plot shows the total timing PDF fitted to the data; the green, coarse-dashed line shows the “primary”γ-ray population associated with the Havar foil; and the red-orange, dotted and crimson, fine-dashed lines show populations associated with the tungsten disk at the end of the gas cell and the collimator before the gas cell, respectively. The relative prominence of the collimator population in the close detuned run compared to the close run provided confidence in the identification of the source of beam-correlatedγ-rays along the beam line by intentionally directing more beam current onto near-target apertures (see discussion in Section D.3)