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For large fields, deviations are observed which can be modeled better with a Polya distribution.
[Default: none, you have to specify the mean multiplication.]
[Default: none, you have to specify the multiplication factor.]
The multiplications obtained with this option are constant for a given drift path. They may vary when the Monte Carlo drift line integration routines are used since these introduce variations in the drift path.
Please note that the 2nd argument is a relative, not an absolute, standard deviation. If you use for instance
avalanche gaussian 20000 0.5
then you'll end up with normally distributed multiplication with mean 20000 and a sigma of 10000.
[Default: none, you have to specify both the mean and the relative standard deviation.]
The Polya distribution is a gamma distribution that matches reasonably well the fluctuations in a cylindrically symmetric amplication region. The meaning of the parameter theta is described in the paper by G. D. Alkhazov, NIM 89 (1970) 155-165.
When theta is set to 0, an exponential distribution is obtained.
[The default value for the mean multiplication is 1, the default setting of the theta parameter is 0.5.]
The Polya distribution is a gamma distribution that matches reasonably well the fluctuations in a cylindrically symmetric amplication region. The meaning of the parameter theta is described in the paper by G. D. Alkhazov, NIM 89 (1970) 155-165.
When theta is set to 0, an exponential distribution is obtained. If theta < 0, the distribution is "concave", while for theta > 0 the distribution assumes the more usual shape with a maximum.
The shapes can be examined with the following statements:
Say "Please enter theta" Parse terminal theta Call book_histogram(ref,100,0.0,5.0) For i From 1 To 50000 Do Call fill_histogram(ref,rnd_polya(theta)) Enddo !opt log-y Call plot_histogram(ref,`Multiplication`,`Polya distribution`) Call plot_end
Additional fluctuations are obtained when the Monte Carlo drift line integration routines are used since these introduce variations in the drift path.
[The default value for theta is 0.5.]
This is similar to the EXPONENTIAL option, but here the mean of the distribution may be different for each cluster.
Additional fluctuations are obtained when the Monte Carlo drift line integration routines are used since these introduce variations in the drift path.
Formatted on 0099-12-08 at 15:52.