Procedures

Calls radiation_force_p in korc_ppusher.

Calls radiation_force_p in korc_ppusher.

Calls radiation_force_p in korc_ppusher.

@brief Subroutine that allocates the mesh information and 2-D arrays for keeping the data of pre-computed plasma profiles.

@brief Subroutine that allocates the variables keeping the 3-D fields data.

@brief Subroutine that allocates the cylindrical components of an axisymmetric field.

@brief Subroutine that allocates the cartesian components of an axisymmetric field.

@brief Subroutine that allocates the cylindrical components of a 3-D field.

@brief Subroutine taken from "Numerical Recipes" that calculates the modified Bessel function of

@brief Subroutine that calculates the axisymmetric magnetic field to the particles' position using the poloidal magnetic flux. @details When the poloidal magnetic flux $\Psi(R,Z)$ is used in a KORC simulation, the magnetic field components are calculated as it follows:

With units

With units

With units

With units

For multiple-species collisions J. R. Martin-Solis et al. PoP 22, 092512 (2015) if (params%collisions .AND. (TRIM(params%collisions_model) .EQ. 'MULTIPLE_SPECIES')) then call collision_force(spp(ii),U_os,Fcoll) U_RC = U_RC + a*Fcoll/spp(ii)%q end if

@brief Subroutine that deallocates all the variables of the electric and magnetic fields.

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

@brief Subroutine that generates an exponentially decaying radial distribution in an elliptic torus as the initial spatial condition of a given particle species in the simulation. @details As a first step, we generate an exponentially decaying radial distribution in a circular cross-section torus as in \ref korc_spatial_distribution.exponential_torus. Then we transform this spatial distribution to a one in an torus with an elliptic cross section, this following the same approach as in \ref korc_spatial_distribution.elliptic_torus.

@brief Subroutine that generates a exponentially decaying radial distribution of particles in a circular cross-section torus of major and minor radi $R_0$ and $r_0$, respectively. @details We generate this exponentially decaying radial distribution $f(r)$ following the same approach as in \ref korc_spatial_distribution.disk, but this time, the radial distribution is given by:

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

@brief Subroutine that frees memory allocated for PSPLINE interpolants.

@brief Subroutine for finalizing MPI communications. @details This subroutine finalizes all the MPI communications and looks for errors durignt this procces.

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.

With units

Dimensionless ne and Te

@brief Subroutine that generates a Gaussian radial distribution in an elliptic torus as the initial spatial condition of a given particle species in the simulation. @details As a first step, we generate an Gaussian radial distribution in a circular cross-section torus as in \ref korc_spatial_distribution.gaussian_torus. Then we transform this spatial distribution to a one in an torus with an elliptic cross section, this following the same approach as in \ref korc_spatial_distribution.elliptic_torus.

@brief Subroutine that generates a Gaussian radial distribution of particles in a circular cross-section torus of major and minor radi $R_0$ and $r_0$, respectively. @details We generate this exponentially decaying radial distribution $f(r)$ following the same approach as in \ref korc_spatial_distribution.disk, but this time, the radial distribution is given by:

@brief Subroutine for generating a 2-D Hammersley sequence. @details This subroutine uses the algorithm for generating a 1-D Hammersley sequence. Each MPI process in KORC generates a (different) subset of pairs (X,Y) of a 2-D Hammersley sequence. The total number of pairs (X,Y) is NMPIS*N, where NMPIS is the number of MPI processes in the simulation and N is the number of particles followed by each MPI process. Each subset of pairs (X,Y) has N elements.

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

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html".

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

This subroutine performs a Stochastic collision process consistent with the Fokker-Planck model for relativitic electron colliding with a thermal (Maxwellian) plasma. The collision operator is in spherical coordinates of the form found in Papp et al., NF (2011). CA corresponds to the parallel (speed diffusion) process, CF corresponds to a slowing down (momentum loss) process, and CB corresponds to a perpendicular diffusion process. Ordering of the processes are $$\sqrt{CB}\gg CB \gg CF \sim \sqrt{CA} \gg CA,$$ and only the dominant terms are kept.

This subroutine performs a Stochastic collision process consistent with the Fokker-Planck model for relativitic electron colliding with a thermal (Maxwellian) plasma. The collision operator is in spherical coordinates of the form found in Papp et al., NF (2011). CA corresponds to the parallel (speed diffusion) process, CF corresponds to a slowing down (momentum loss) process, and CB corresponds to a perpendicular diffusion process. Ordering of the processes are $$\sqrt{CB}\gg CB \gg CF \sim \sqrt{CA} \gg CA,$$ and only the dominant terms are kept.

Compares argument psi to chosen psi_max, returning step function.

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

Computes the auxiliary fields $\nabla|{\bf B}|$ and $\nabla\times\hat{b}$ that are used in the RHS of the evolution equations for the GC orbit model.

Computes the auxiliary fields $\nabla|{\bf B}|$ and $\nabla\times\hat{b}$ that are used in the RHS of the evolution equations for the GC orbit model.

@brief Extended trapezoidal rule for integrating the modified Bessel function of second kind. See Sec. 4.2 of Numerical Recipies in Fortran 77.

@brief Subroutine for interpolating the pre-computed, axisymmetric electric field to the particles' position.

@brief Subroutine for interpolating the pre-computed, 3-D magnetic field to the particles' position.

@brief Subroutine for interpolating the pre-computed 3-D electric field to the particles' position.

@brief Extended trapezoidal rule for integrating the Gamma PDF. See Sec. 4.2 of Numerical Recipies in Fortran 77.

For each primary RE, calculating probability to generate a secondary RE

@brief Subroutine that loads the size of the arrays having the electric and magnetic field data. @details All the information of externally calculated fields must be given in a rectangular, equally spaced mesh in the $(R,\phi,Z)$ space of cylindrical coordinates. If the fields are axisymmetric, then the fields must be in a rectangular mesh on the $RZ$-plane.

@brief Subroutine that loads the fields data from the HDF5 input file.

Calculate constant quantities used in various functions within this module

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

Calculates value of argument of 2D Gaussian spatial distribution with with counter-clockwise rotation.

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

@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$\sigma@f$.

@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.

MCMC and MH algorithm perfomred on single MPI process to sample distribution function fRE_H

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

@brief For more info please visit "https://people.sc.fsu.edu/~jburkardt/f_src/hammersley/hammersley.html". ************80

Updates the avalanche parameters aval_params% at each step in the MCMC after the profiles are interpolated at the sampled R,Z location.

Dimensionless temperature

@brief Subroutine that queries the HDF5 file what data are present in the HDF5 input file (sanity check).