to their large mass (see equation 4.18). It is therefore assumed that monopoles travel through the detector in a straight line and with a constant velocity.
4.5
Simulation of monopole signals
The Monte Carlo program GEASIM (see section 1.8.3) has been adapted to simulate the response of the detector to monopole signals. The program performs tracking of monopoles through a cylindrical volume surrounding the detector, simulating the emission, propagation and detection of the direct and δ-ray induced Cherenkov light. Only photons with wavelengths between 300 and 600 nm are considered, as these correspond to the sensitive range of the PMTs. The monopoles are simulated as straight, through-going tracks and are generated in the velocity range β ≥ 0.55 and γ ≤ 10. The directions of the generated monopoles are distributed uniformly over the hemisphere above and below the detector.
The cylindrical volume around the instrumented detector volume in which the simula- tion is performed, is referred to as the can. It extends typically a few absorption lengths beyond the instrumented volume to include light that is produced outside the detector. In the case of monopoles, the can volume needs to be enlarged because of the very intense Cherenkov radiation.
The direct Cherenkov light emission is simulated for monopoles with β > 1/n ' 0.74. Equations 4.2 and 4.3 are used to calculate the velocity-dependent emission angle and light yield on the monopole track. The propagation of the direct light is simulated in accordance with the known decrease of the light intensity I with the photon path length r, which is given by
I (r)∝ 1 re
−r/λabs . (4.19)
Here, λabs is the absorption length of light in the sea water. The absorption length and
consequently the light intensity depend on the wavelength of the light. This dependence is taken into account in the simulation.
The δ-ray induced Cherenkov light emission is simulated for monopoles with β ≥ 0.55. The emission angle and light yield are determined from the angular distribution of the Cherenkov photons as shown in figure 4.8. The distribution has been determined for 10 monopole velocities in the range β ≥ 0.55 and γ ≤ 10. Logarithmic interpolation is used to determine the δ-ray light emission by monopoles with velocities for which no distribution is available. Since the path lengths of the δ-rays are generally much smaller than the typical distance between the monopole track and the point where the light is detected§, this distance is calculated assuming that the photons are emitted from the
monopole track. The propagation of the δ-ray light is simulated taking into account the decrease of the δ-ray light intensity Ie with the photon path length. The decrease can be
expressed as
Ie(r)∝
1 r2e
−r/λabs (4.20)
§The path length of a δ-ray increases with its kinetic energy. For a monopole with γ≤ 10, the largest
because of its approximately isotropic nature (see figure 4.8).
The simulated response of the detector to monopole signals is summarised in figures 4.9 to 4.11 for different monopole velocities. For each velocity, the same sample of 2000 upward going monopole tracks was used. The distance between the can surface and the instrumented volume was 200 m. In the figures, only monopoles that produced hits on at least 5 different PMTs have been considered. In the following, a hit is defined as a pulse of light that is detected by a PMT which is separated in arrival time from other light pulses by at least 1 ns. Thus, the effect of the read-out electronics is not taken into account.
Figure 4.9 shows the number of hits produced by monopoles with β = 0.65, 0.75, 0.85, 0.95. The number of hits increases with the monopole velocity, as does the fraction of monopoles that produce hits. This is due to the increasing light yield as monopoles move faster, as is shown in figure 4.5.
0 5000 10000 15000 10-1 1 10 102 103 number of hits
Figure 4.9: The number of hits that are pro- duced in the detector by monopoles with β = 0.65 (solid line), 0.75 (dashed line), 0.85 (dotted line) and 0.95 (dash-dotted line).
As can be expected from figure 4.5, the number of detected photons from a monopole with a velocity above the Cherenkov limit is dominated by the direct Cherenkov light emitted by the monopole. This is reflected by the ratio of the number of detected δ-ray photons to the number of detected direct photons, which is shown in figure 4.10a for velocities 0.85 c and 0.95 c. The ratio is significantly smaller than 1 for both velocities. Only photons that are detected within a radius of one absorption length around the monopole track have been considered. The number of hits produced within this radius, however, is primarily due to the light emitted by the δ-rays. This follows from figure 4.10b, which depicts the ratio of the number of hits due to δ-ray light to the number of hits due to direct light. This ratio is considerably larger than 1 for both velocities. These features are caused by the difference in angular distribution and light yield of the two types of light emission. The very intense direct Cherenkov light is concentrated in a narrow cone, which results in relatively few hits with very large amplitudes. The less
4.5 Simulation of monopole signals 0 0.05 0.1 0.15 0.2 0.25 0.3 0 50 100 150 200 250 300 350
ratio δ-ray to direct photons a 0 5 10 15 20 25 30 0 50 100 150 200 250
ratio δ-ray to direct hits b
Figure 4.10: The ratio of detected δ-ray photons to detected direct photons (a), and the ratio of δ-ray hits to direct hits (b), for monopoles with velocities 0.85 c (solid line) and 0.95 c (dashed line).
intense δ-ray light has a much wider angular distribution, which produces many separate hits with relatively small amplitudes.
The effect of the different angular distributions is also evident in the arrival times of the photons on the PMTs. Figure 4.11a shows the time difference between the first and last hit on a PMT due to direct and δ-ray light separately for monopoles with γ = 10. PMTs with only one hit are included, which causes a peak at zero. Almost all direct hits occur within 20 ns after the first hit, whereas the time difference between δ-ray hits can run up to several hundreds of nanoseconds. The time difference for both light contributions combined is shown in figure 4.11b for monopoles with β = 0.55, 0.65, 0.85 and γ = 10. The spread in arrival times decreases with the monopole velocity. This is due to the smaller angular spread of the δ-ray light at lower velocities, as shown in figure 4.8.
The intense light produced by monopoles can result in the simultaneous arrival of many thousands of photons on a PMT. This causes a large current in the PMT, which may result in the collapse of the PMT’s high voltage and consequently in some dead-time of the PMT. This possible saturation of the PMTs is not included in the simulation. Furthermore, the measurement of the charge contained in a PMT signal is limited by the dynamic range of the ARS chip. In this simulation, this dynamic range is set to 12 p.e.
The monopole simulation described in this section is based on the direct and δ-ray induced Cherenkov light emission by monopoles with one Dirac charge gD. This is the
basic unit of magnetic charge, larger magnetic charges g are an integer multiple k of this, g = k gD. Since the direct and δ-ray light yield are proportional to the square
0 100 200 300 400 10-1 1 10 102 103 104 105 time difference (ns) a 0 100 200 300 400 10-1 1 10 102 103 104 105 time difference (ns) b
Figure 4.11: a: The time difference between the first and last hit on a PMT due to direct light (solid line) and δ-ray light (dashed line) for monopoles with γ = 10. b: The time difference between the first and last hit on a PMT due to both types of light combined, for monopole velocities 0.55 c (solid line), 0.65 c (dashed line), 0.85 c (dotted line) and γ = 10 (dash-dotted line).
monopoles with larger charges by multiplying the light yield with k2. It is assumed here
that the quantum-mechanical lower impact parameter also prevails for these monopoles. Moreover, the simulation can be used for any heavy particle with electric charge ze. The direct Cherenkov light emission by such a particle is related to that of a monopole by a factor (ze/gn)2, and the δ-ray Cherenkov light production by a factor (ze/gβ)2.