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3 4 Set transverse through the foil. These low energy electrons (typically < 10 eV) are immediately affected by the accelerating voltages within PEPSSI (the high energy ions are not significantly affected by the accelerating voltages) and are steered towards the MCP. An important issue is the dispersion in the arrival times of the secondary electrons as a function of foil position and the angle of emittance of the secondary electrons from the foil. Such dispersion adds to the error in the measurement of time-of-flight. Figure 13 (top) shows the time dispersion associated with varying angles for electrons emitted from the center of the foil. In Fig. 13 (bottom) the dispersion shown for any one column is associated with varying the emission position over the ~6 mm vertical extent of the foil. The combination of position and angle yields a time dispersion of roughly 1.5-2 ns. Combining the dispersions associated with the start and stop detections in a root-mean-square sense yields a total time dispersion error of roughly 2.1-2.8 ns. Combining that value in a root-mean-square sense with the ~1.5 ns electronic dispersion yields a total time dispersion that resides between 2.5 and 3.2 ns.

4.2.2.2 Ion Energy Losses As ions transverse the TOF section of PEPSSI through the front foil (~10 |g/cm2), back foil (~ 19 |g/cm2), dead layer of the solid state detector (~550 A), and eventually stop and deposit their total energy in the SSD, they lose energy and scatter depending upon the ion's initial energy, mass, and the medium through which they pass. We have incorporated data from the SRIM particle-interaction-with-matter code (Biersack and Haggmark 1980) in our simulation to simulate realistically the energy loss and scattering as ions transverse through different materials in the PEPSSI sensor.

4.2.2.3 TOF Measurements When ions penetrate through the front foil, a distribution of ion velocities is created, as calculated using SRIM. This distribution of ions is then used to calculate the distributions of ion TOFs. The uncertainty due to secondary electron dispersion and electron noise together with SRIM data are all incorporated in our simulation. Figure 14 shows the simulated response of PEPSSI TOF spectra as a function of particle initial energy for four species (H, 4He, 16O, and 56Fe). At low energy (~10 s of keV), ions lose significant amounts of energy and scatter significantly when going through the front foil. These effects explain the spread in TOF measurement at low energy. However, at higher energy (~100 s of keV), the TOF spreads are mostly consequences of the uncertainties in the TOF measurement from both the electronics jitter (~1.5 ns), and secondary-electron dispersion in the TOF optics as discussed in previous section (except for very heavy ions, e.g., Fe).

4.2.2.4 Total Energy Measurement If an ion has sufficient energy left once it transits the front and back foil, it ends up in the SSD. Depending on the ion's final energy and mass when it reaches the SSD, it can penetrate through the dead layer of the SSD and produce an electronic signal to be measured. Figure 15 shows the simulated measured energy by PEPSSI as a function of the ion's initial energy before entry into PEPSSI. The measured energy shows the cumulative effect of the energy spread due to energy lost throughout the PEPSSI detector (start foil, stop foil, dead layer, and electron hole pair production). The energy loss is greatest for ions with the greatest nuclear charge, here Fe.

4.2.2.5 TOF Versus Energy Finally, the energy measurement is combined with the TOF measurement on a particle-by-particle basis. Even with a ~3 ns time dispersion, the major elemental species of interest (H, He, CNO, Fe) are discriminated except at the lowest energies for CNO and Fe, where the error in the energy measurements dominates.

4.2.2.6 Efficiencies The efficiency for detection of an ion within the SSDs is roughly ~100% (except at the very lowest energies where energy straggling can position the energy below the low energy threshold). The efficiency for obtaining a TOF measurement is estimated using the efficiency of generating secondary electrons in both the front and the rear foil. To emit a secondary electron, such electrons must be generated close enough (distance "p") to the surface of the foil so that the electron can escape before it is re-assimilated. Thus, very roughly, it is expected that the efficiency for the generation of a secondary electron is proportional to the amount of energy per unit distance (dE/dx [keV/micron]) that

Fig. 14 Simulated TOF spectra as a function of accelerator beam energy for protons and oxygen, helium and iron nuclei

an ion deposits as it goes through this outer thin layer of the foil. The canonical number of secondary electrons generated out of each surface as a proton with 10's of keV energy encounters the foil is between 0.5 and 1 on average (Frischkorn et al. 1983); R.W. McEn-tire, private communication, 2004; estimated here as 0.75). Since we require a simultaneous start and stop electron, the efficiency of proton detection at 10's of keV is (1 — e-0 75)2, where (1 — e—0 75) is the Poisson probability of having at least 1 or more electrons emitted when the mean emission number is 0.75. Thus, the efficiency is roughly 28%. Other energies and species may be roughly scaled with this number using tabulated dE/dx values. For example, at 50 keV total energy the dE/dx values for protons and oxygen ions are 120 and 250 keV/micron, respectively (we ignore for now the energy losses suffered by the ion in getting to the position in either foil where the secondary electron is generated). Thus, since the average number of secondary electrons for oxygen will by ~0.75 x (250/120), or 1.56. Poisson statistics tells us that the probability of detecting an oxygen ion with 50 keV energy is (1 — e—L56)2 or 62%.

4.2.3 Electron Measurements

The PEPSSI electron measurement strategy depends on the use of the aluminum flashing on the electron SSD. We therefore need to understand the effect of that flashing on both the ion and electron measurements within the electron SSDs. Based on simulations with GEANT-4 (Agostinelli et al. 2003), Fig. 16 shows the effect of Al flashing on proton measurements, and Fig. 17 shows the effect on electron measurements, for a varying thickness of Al flashing. The baseline spectrum assumed for both protons and electrons is a power-law spectrum with

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