README.rst

Atmospheric Cherenkov response

Cosmic particles, such as gamma-rays, can be detected with the help of the atmospheric Cherenkov-method. The cosmic particles enter earth's atmosphere and induce showers of new particles which run down to ground. Among these new particles is Cherenkov-light which can be detected on ground. This library helps to estimate how good a given instrument can detect a certain type of cosmic particle at a certain energy (response-function).

Algorithm

1. Pick a threshold photon number T1 where trigger curve starts rising (for a given type of primary)
2. Generate shower such that particle direction hits ground at 0,0; shower direction spread over large solid angle Omega (energy-dep.) (for charged particles) {could also pick (0,0) at some height, but I believe for z =0 the photon scatter is smallest}
3. Divide ground in grid of spacing = mirror diameter; could e.g. without too much trouble use up to M x M = 1000 x 1000 grid cells = 70 x 70 km^2; grid area is A, grid centered on (0,0)
4. Reset photon counter for each cell
5. For each shower, shift grid randomly in x, y by 1/2 mirror diameter
6. Loop over shower photons
   1. reject photon if angle outside FOV
   2. for each photon, calculate grid cell index ix, iy (easy since square grid)
   3. calculate distance of photon from cell center; keep photon if distance < R_Mirror
   4. increment photon counter for cell
   5. optionally save photon in a buffer
7. Loop over grid cells
   1. count cells with photons > T1 : N_1
   2. using trigger curve for given particle type; calculate trigger prob. for (real) trigger and randomly reject events: keep N_2 (or simply use a 2nd threshold where trigger prob=0.5)
   3. Increment event counters by N_1 , N_2 Increment error counters by N_1 ^2, N_2 ^2
8. For detailed simulation, optionally output photons for few randomly selected T1 -triggered cells (up to 10 should be fine, given that probably only one of 10 triggers the detailed simulation)
9. Toy effective area (x solid angle): (N_1 event counter/M ^2 / Nevent)* A * Omega error = sqrt(error counter) ... Somewhat better effective area: N_2 event counter ... Final eff. area: N1_eff area x fraction of events kept in detailed sim.

Coordinate system

                                  | z
                                  |                               starting pos.
                                  |                                  ___---O
                                  |                            ___---    / |
                                  |                      ___---     n  /   |
                                  |                ___---         io /     |
                                  |          ___---             ct /       |
                                  |    ___---                 re /         |
              starting altitude __|_---                     di /           |
                                  |                       y- /             |
                                  | _-------__          ar /               |
                                  |-    th    |_      im /                 |
                                  |   ni        |_  pr /                   |
                                  | ze            |  /                     |
                                  |               |/                       |
                      ____________|______________/________________________ |
                     /            |            /            /            / |
                    /            /|          //            /            /  |
                  3/            / |        / /            /            /   |
                  /            /  |      /  /            /            /    |
                 /____________/___|____/___/____________/____________/     |
                /            /    |  /    /            /            /      |
obs. level     /            /     |/     /    grid    /            /       |
altitude -  -2/-  -  -  -  /  -  -X-----/  <-shift y /            /        |
             /            /      /|    /            /            /         |
            /____________/______/_____/____________/____________/          |
           /            /     -|  |  /            /            /           |
          /            /      /   | /            /            /            |
        1/            /  grid     |/            /            /             |
        /            /  shift x   /            /            /              |
       /____________/____________/____________/____________/               |
      /            /            / |          /            /                |
     /            /            /  |         /            /                 |
   0/            /            /   |        /            /                  |
   /            /            /    |       /            /                   |
  /____________/____________/____________/____________/                    |
        0            1           2|             3                          |
                                  |                                  ___---O
                                  |                            ___---
                                  |                      ___--- |
                                  |                ___---        |
                                  |          ___---               |
                                  |    ___---       azimuth       |
                sea leavel z=0    |_---__________________________/______ x
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                        / y