3.2.1 Introduction
A measure of the Ps beam energy distribution may be ascertained by converting the time-of-flight spectrum from the MCA (see section 2.7.1). In order to calibrate the MCA, the time-per-channel, tch, is measured as described below. From this and measurements of the positron time-of-flight peak channel versus positron energy, the sum of the magnitude of the workfunction and contact potential of the remoderator, \ W\ + C, may be ascertained.
3.2.2 Time-per-channel, tch
To determine the time-per-channel for the MCA spectra, known time delays are inserted into the time-of-flight electronics between the CEMAl CFD and the stop on the TAC (see section 2.7.1). For each time delay the channel number at which the positron peak occurs is recorded. A linear plot of the time delay versus channel number may then be made, from which the time per channel, tch, is calculated from the gradient. Figure 3.5 shows the time-per-channel measurements made for two remoderator potentials, F^. The greater uncertainty inherent with the F^^IOV measurements is due to the larger time spread associated with lower beam energies on a time-of-flight spectrum.
Chapter 3 - Ps Beam Techniques 74
Km(V) tch(ns)
10 0.959+0.002
100 0.962+0.001
Table 3.1 Time per channel values obtained at two values o f the remoderator potential. 1000 80 0 - 6 0 0 - V^= lOOV / .=0,963±0.00lns 200 - /,= 0.959±0.002ns
0 1e-7 2 e-7 3 e-7 4 e -7 5 e -7
T im e D e la y (s )
Figure 3.5 Time per channel calibration plot.
Table 3.1 shows the tch values obtained in this study. As can be seen from table 3.1, there is an excellent agreement between the tch values determined for the two moderator potentials.
3.2.3 Determination of the Absolute Positron Energy
In order to determine the absolute energy of the positron and Ps beams, the sum of the magnitude of the remoderator workfunction and contact potential, \ W\ + C,
are required. The expected position of the positron peak, P+, on the time-of-flight spectrum, is given by
Chapter 3 - Ps Beam Techniques___________________________________________75
P , = l O - ^ , (3.3)
Ch
where tO is the t=0 peak channel number (see section 2.7.1), L is the time between the tagger and CEMA2 pulses respectively and can be written as
C = Const - C- + Cets , (3-4)
where with reference to figure 3.6, and are respectively the acceleration times for secondary electrons and remoderated positrons at the tagger, trets is the time taken for acceleration through the grids in front of CEMA2 and tconst corresponds to the time for a positron of constant velocity ( v+= . j l E j m ) to traverse the distance between the tagger earth grid and R1.
T agger C E M A 2
C hannel P la te s R em oderator Earth Grid R1 R2 R3 C h an n el plates
Figure 3.6 Schematic definition o f the times relevant to the determination of\W\+C.
The positron kinetic energy, E+, is determined by the remoderator potential, and the remoderator workfunction and contact potential, \fV\+C, i.e.
E^=eV„+\W\ + C. (3.5)
Therefore, a value for \W\+C may be determined by comparing the calculated P+
values with corresponding measurements for differing Vm and iterating over \ W\+C to fit to the measured data. The full fitting equation is given in Appendix B. Figure 3.7 shows the comparison of the measured peak positions to the calculated values, from which a value for \ W]+C of 1.0+0. leV has been determined.
Chapter 3 - Ps Beam Techniques 76 600 500 - c o 400 -
I
300 -M easu red e ^ p eak p o sitio n s
200
0 20 40 60 80 100 120
Figure 3.7 Calculated positron peaks fitted to experimentally determined positions.
Figure 3.8 shows the positron energy distributions determined from the time-of-flight spectra, using values for tch and |PF|+C determined above. The time-of-flight peak energy and FWHM of these plots are given in table 3.2. As can be seen from the table, the distribution peaks are in fairly good agreement with values determined using Equation 3.5. Any slight deviation can be attributed to small drifts on the remoderator potential.
Vm(y) Peak Energy (eV) FWHMiéW)
21 22.2+0.1 3.0+0.1
27 27.8+0.1 2.8+0.1
34 34.9+0.1 3.0+0.1
42 42.9±0.1 3.0±0.1
Table 3.2 Summary o f the remoderated positron time-of-flight peak energies and FHWM.
The FWHM of the positron energy distributions obtained from the time-of-flight spectra are widened with respect to that obtained by a retarding field analyser by the
Chapter 3 - Ps Beam Techniques 11
system resolutions. For a discussion on the time-of-flight timing resolutions see section 5.6. a ) | / „ = 2 1 V ^ i 50 1 40 ■ b ) V ,n = 2 7 W i i 30 - i
Ï
i i i K 10 - I ■ ^ M - . , y * ... ' ? ' ‘ 0 - • • . , 16 17 18 19 20 21 22 23 24 2 5 26 27 26 29 30 Fn/»rov c ) / „ , = 3 4 V 21 2 2 23 24 25 26 2 7 28 29 30 31 32 33 34 35 Energy (cV ) 27 28 29 30 31 32 33 34 35 36 37 38 3 9 4 0 41 42 4 3 44 45 Energy (cV ) d) JV42V 30 20 10 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Energy (cV )Figure 3.8 Remoderated positron energy distributions determined with the time-of-flight system.
3.2.4 Ps Energy Distributions
The Ps energy spread is calculated from the time-of-flight spectrum using
V ^/'.v y
(3.6)
where m is the mass of the positron, Lps is the Ps flight-length and tps corresponds to the flight-time for a Ps atom to travel from the middle of the production cell to CEMA2 and is given by
Chapter 3 - Ps Beam Techniques 78
where with reference to figure 3.9, and are the acceleration times for secondary electrons and remoderated positrons at the tagger, tceii corresponds to the time taken for a remoderated positron, with energy £+, to reach the middle of the production cell,
ttof, is the measured time between the tagger and CEMA2 pulses respectively and is given by
(3.8)
where tO is the t=0 channel number (see section 2.7.1), chnps is the corresponding Ps peal channel number and tch is the time-per-channel. A schematic definition of the times needed to determine the Ps absolute energy are shown in figure 3.9.
T a g g e r
C h a n n e l P lates R em o d era to r Earth G rid P ro d u c tio n c e ll
t t
C E M A 2