In order to simulate the background environment in orbit with SwiMM, we develop the primary generator that is randomized uniform and isotropy within a region, firstly.
We can generate the randomized photons to repeat from STEP1 up to STEP3, as follow
STEP 1.Before a photon is projected, we decide any point (P1) on a sphere (radius = R), randomly. Also we can be free to set the radius, "R".
STEP 2.Next, we think a length, "L", of tangent plane at P1. Also we can be free to set the plane length, "L".
STEP 3.And any point (P2) is determined randomly on the plane, the photon is generated to a normal direction of the plane.
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In order to see if the new primary generator is really randomized, we run an test simulation.
The geometry of the simulation shows Fig4. There are four balls with radius 10 cm on the origin (G0) and each axis which separates 1 meter from the origin. The generated particle is a "geantino", which is a virtual particle used for simulation and which does not interact with materials. The number of geantino is 10^9 events and the beam region is 3 meter square.
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When the geantino hits a ball, we record a total counts, the initial theta and phi in each event. If the primary generator is perfectly random, the number of count should be almost same in each ball and the coming direction should be isotropic.
We show the total detected counts in Fig.5. The number of position on X-axis "0, 1, 2, 3" means the ball name, "G0, G1, G2, G3", respectively.
In order to check whether detected counts are same for all positions or not, we assay to use t-test. We show two confidence intervals in Figure.5 , 68 % (cyan) and 99 % (green). Since there are 4 positions within 99 % significance level, we can say the detected counts are same each other.
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Here is a phi distribution of arrival photons. The color legends are as follows,
G0: Black G1: Red G2: Green G3: Blue
Because of the flat plots, the phi distribution is uniform and isotropic at all positions.
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Here is a theta distribution of arrival photons. The color legends are same above. Due to be sine-theta effect, each angular bin is divided by the sin theta. As a result, the plots become flat, the theta distribution is uniform and isotropic, too.
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