&SIGNAL: AVALANCHE
The multiplication factors are approximately exponentially
distributed provided the mean multiplication is "average".
For large fields, deviations are observed which can be
modeled better with a Polya distribution.
[Default: none, you have to specify the mean multiplication.]
Results in a fixed multiplication by the factor that you specify.
[Default: none, you have to specify the multiplication factor.]
The Townsend coefficient is integrated over the drift line, and
the integral is exponentiated yielding a 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.
Not a physical choice for a single avalanche but sometimes used
when many exponentially distributed avalanches overlap, resulting
in a gamma distribution - which is similar in shape to a Gaussian.
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 mean multiplication does not depend on the drift line (you
specify the number as first argument) but the fluctuations are
according to a Polya distribution with parameter theta.
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 mean multiplication is obtained by integrating the Townsend
coefficient over the curent drift line and the fluctuations are
according to a Polya distribution with parameter theta.
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.
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.]
The Townsend coefficient is integrated over the drift line, and
the integral is exponentiated. The result is used as mean of an
exponential distribution of multiplications.
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.
Keyword index.
Formatted on 10/11/98.