I also want to thank Professor Rochus Vogt for the many insights he provided both regarding this work and the role of physicists in the world. Frank Hagen contributed greatly in both efforts and ideas to the development of the experiment. Stoker kindly provided suggestions and materials to help build the hodoscope system.
INSTRUMENTATION
Here the function s(E/M) is the specific ionization (or average rate of energy loss per unit matter traversed) of a proton in the materia I of interest, and is expressed in MeV/(g/cm">. solid curves in the figure is calculated for ~ =0.3 units and the dashed curves are calculated for a;; =0.25 units (where the separation between the centers of the two Gaussian distributions is defined as one unit). As an estimate of the required mass resolution we calculated the mass resolution for which an inflection point is obtained between two Gaussian distributions whose means are separated by one unit, as a function of the ratio of the number of counts in the two distributions (Stone, 19l3; Hagen, 19lb>.
RATIO OF STANDARD DEVIATION TO PEAK SEPA RATION
However, there are cases where the mass peaks we are trying to resolve are separated by two atomic mass units. The fundamental limitation regarding the mass resolution that can be achieved with the bE-E' technique is due to the statistical nature of the ionization energy loss process. This results in Landau fluctuations - a distribution of possible ~E values for a monoenergetic beam of identical particles striking the detector.
It can be seen that the increasing separation of the mass traces sufficiently compensates for the increasing Landau fluctuations as we increase the thickness of the ~E detector. The sawtooth pattern is primarily due to the variation in the L/R ratio as discussed above. In addition to precise measurements of dE and E1, it is necessary to measure the trajectories of the cosmic ray particles precisely.
HODOSCOPE SECTOR BOUNDARIES
PLASTIC
BOUNDARY OF
HODOSCOPE ACTIVE AREA
Intervals of charge and energy at the top of Earth's atmosphere accessible to the HEIST normally incident particle instrument. Curves indicating the upper and lower mimics of the energy intervals that can be detected are shown for atmospheric depths of 0, 3, b and 10 g/cm.
1500MV cutoff
800MV • cutoff
PARTICLE CHARGE, Z
The curves in each set are labeled according to the amount of overlying material (air plus material above the scintillator stack in the nacelle). The so I i d box corresponds to a flight at a 1500 MV cutoff with 6 g/cm~ remaining atmosphere~. The relatively high magnetic cutoff in this case limits observations to elements with z~5 and severely limits the energy interval obtained for elements with Z$13. The error bars are the result of the limited number of trajectories used in the Monte Carlo calculation.
EVENTS
First, the effects of the residual atmosphere are: the loss of ionization energy in the air causes a given energy interval on the instrument to map to a higher energy interval at the top of the atmosphere, causing particles that had higher stiffness above the atmosphere, and second, nuclear interactions between cosmic ray particles and air depletes the population of surviving cosmic rays. The fraction of particles that have undergone nuclear interactions at various depths in the atmosphere can be seen by comparing the velocities I have given for the 800 MV limit in Table Y for those depths. In larger regions, about 1/3 of the incident iron particles undergo nuclear interaction and become useless for mass determination.
CATHODE
ANODE
SIGNAL CATHODE
SUPPRESSOR
Error bars represent uncertainty in the determination of the mean of the pooled distributions of p u I se heights. The timing circuit requires that the received signals at both ends of the delay I ine be of approximately the same shape and amplitude. Our estimates for the energy deposited in the action thickness of 1-3~ mg/cm~ of the chamber are shown in the figure.
At any given value of the anode voltage, the measured charges do not increase in proportion to the deposited energy. The figure shows that there is a significant deviation from linearity near each of the taps. The shape of this curve is the result of random noise in the input stages of the delay line amplifiers.
This is mainly the result of the finite size of the coli imator used. The areas of the hodoscope from which events are selected are discussed in the text. This contribution depends on the accuracy with which we can determine the position at which the particle passed through each of the scintillators.
M i I i pore sheets in contact with each of the crystal faces enhance I ght transport in I gh t pipes. However, the onset of saturation occurs near the upper end of the range of pulse heights which. The LED was placed at the center point of a lens located between the LED and the face of the photomultiplier.
LOOY
- CALCULATIONS
About 3000 r-ray pulse heights are recorded per hour from each of the eight pm tubes. The temperature fluctuation was smooth and the maximum temperature gradient achieved was Q.Sl°C/hour. Additional information on scintillation efficiency variation and photomultiplier gain can be obtained from the cosmic ray data themselves.
Measurements of the isotopic composition of cosmic rays are expected to place important constraints on theories of cosmic ray synthesis, acceleration, and propagation. Additional motivation for measuring the isotopic composition of cosmic rays has been provided by the suggestion of several authors that cosmic rays undergo elemental separation effects before they are accelerated. Such charge-dependent selection mechanisms will not affect the relative abundance of different isotopes of a given element.
Much of the current knowledge concerning the propagation of the cosmic rays through the interstitial medium is derived from the abundances of those elements which are thought to be absent from the cosmic ray sources. Many of the even-Z elements have one or more isotopes that should be of purely secondary origin. If these isotopes are not produced a+ the cosmic ray sources one gets a measure of the residence time of cosmic rays in the galaxy. as determined by the rate of loss due to nuclear annihilation and the escape from the galaxy).
Uncertainties in the abundances of parent nuclei, in nuclear fragmentation cross sections, and in estimates of the path length in the interstellar medium can easily obscure differences of this magnitude.
YlHeln.,) MHe
We can write analogous expressions for the source abundance, qk, of a third species and the source ratio. Below we discuss the degree of precision to which these quantities must be known to obtain useful estimates of the qj/qq source abundance ratio. In evaluating equation 12 we use fragmentation cross sections obtained from the semiempirical formulas of Silberberg and Tsao <19l3a> with modifications given by Silberberg et al.
Note that in evaluating equation 12 we require ratios of the fluxes of parent species (used to calculate s: , s j and s. For this reason, we assume that the three isotopes of interest make up the entire local abundance of the element under consideration This assumption is not a mimetic when isotopic abundance observations of the elements we consider become available, as it will then be possible to appropriately renormalize the elemental abundances.
Note that the secondary tracer technique for obtaining source abundance ratios can only be applied in the case of elements with an isotope that is thought to be absent from the cosmic ray sources. Before starting a detailed treatment of the ef feet of uncertainties in the measured quantities in equation 12. Therefore, a small relative error in one of these two terms translates into a relative error.
If we now use assumptions <3> and (~) and also assume that the uncertainties in the observed fluxes are completely statistical and given by First, note that along the line I ine flJ;Ifllt.,=O wij This is due to our assumption that species are absent from the cosmic ray sources. Third, for each value of ~/pk there is a minimum value of Pf!Jlf,._ that can be achieved (corresponding to If the measured ratio ~·I~ falls far enough below this value of the curve corresponding to the The measured ratio fli:/flfk is inconsistent with error. In measuring these ratios and calculating the location of the curves we would conclude that the species is unsuitable. In some cases, for example with the isotopes of Ar, it would be possible to use consistency checks between source abundances obtained using more than one possible tracer to rule out this possibility. When calculating statistical uncertainties, we assumed that we have 1000 events distributed among the three isotopes of interest. The number of events of each of these isotopes is assumed to be statistically independent. The dashed tones in Figures 32a to 32e are the constant partial uncertainties in the calculated values of qJ/q~ due to statistical errors in local abundance measurements. Uncertainties can be increased by a factor of {1000/N' if the total number of events is N. To estimate the uncertainty in the source ratios caused by the uncertainty in the location of the various constant qj/qk curves in Figures 32a to 32e we repeated the procedure used to obtain of these curves while randomly varying the ion fragmentation cross sections and the isotopic abundances of the parent nuclei. As shown in Section 3-3-2, the uncertainty in the calculated source abundance is almost entirely due to uncorrelated errors in the fragmentation cross sections if the local abundances are known precisely. Calculating the effective deviation of a number of qllqk values generated at constant f?J, 1¢"' and fl>JI¢" yields the required. The calculation uncertainties shown in Figure 32 can be increased in proportion to this percentage uncertainty. This is because in this region the secondary component of the local flux of .l.0Ne is becoming a significant part of the total flux, so that the denominator in equation 12 is relatively small. Since we are trying to produce a family of curves that can be scaled to yield uncertainties in the source ratios due to cross-section errors of ~35%, we have recalculated the curves in the region where the local value of ~'N e I ::tCI Ne is greater than 0.35 using cross-sectional errors of 1l.5%. These results (after being scaled up by a factor of 2) are plotted in Figure 32b in place of the corresponding results obtained for cross-sectional errors of 35%. In this way we obtain a family of curves that can be scaled to smaller cross-sectional errors.
