korc_energy_pdfs Module

@brief KORC derived type that contains information about a given Gamma distribution function @f$f_\Gamma(x,\kappa,\theta)@f$. @details We write a given Gamma distribution function in terms of its shape factor @f$\kappa@f$ and scale factor @f$\theta@f$, so that:

Components

@brief Function that converts @f$x@f$ from degrees to radians.

Arguments

Return Value real(kind=rp)

@brief Function that calculates the value of the Gamma distribution @f$f_\Gamma(x,\kappa,\theta) = \frac{1}{\Gamma(\kappa) \theta^\kappa}x^{\kappa-1}\exp{\left(-x/\theta\right)}@f$.

Arguments

Return Value real(kind=rp)

Evaluation of the energy distribution function @f$f_{RE}(\mathcal{E})@f$ of runaway electrons as function of the normalized momentum @f$p' = p/m_ec@f$. Here, @f$p'@f$ is the normalized momentum and @f$m_e@f$ and @f$c@f$ are the electron mass and the speed of light.

Arguments

Return Value real(kind=rp)

@brief Gaussian random number generator. @details This function returns a deviate of a Gaussian distribution @f$f_G(x;\mu,\sigma) = \frac{1}{\sigma\sqrt{2\pi}} \exp{\left( -(x-\mu)^2/2\sigma^2 \right)}@f$, with mean @f$\mu@f$, and standard deviation @f$\sigma@f$.

Arguments

Return Value real(kind=rp)

@brief Subroutine that contains calls to subroutine to generate a gamma distribution for the energy distribution of a given species in the simulation.

Arguments

@brief Subroutine that reads from the input file the parameters of the Gamma distribution @f$f_\Gamma(x,\kappa,\theta) = \frac{1}{\Gamma(\kappa) \theta^\kappa}x^{\kappa-1}\exp{\left(-x/\theta\right)}@f$.

Arguments

@brief Subroutine that samples a Gamma distribution representing the runaways' (marginal) energy distribution function. @details This subroutine uses the Metropolis-Hastings method for sampling the Gamma distribution representing the runaways' (marginal) energy distribution function. Unlike the typical Metropolis-Hasting method, after setting the boundaries of the region we want to sample, we perform a sampling in a larger region that contains the original sampling area plus a buffer region. After finishing the first sampling, we only keep the particles in the original sampling region, the particles in the p_buffer are sampled again until all of them lie within the original sampling region. This method ensures that the boundaries are well sampled.

Arguments

@brief Surboutine that saves the Gamma distribution parameters to the HDF5 file gamma_distribution_parameters.h5.

Arguments