BinaryCollisionUtils.H

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/* Copyright 2021 Neil Zaim
 *
 * This file is part of WarpX.
 *
 * License: BSD-3-Clause-LBNL
 */
 
#ifndef WARPX_BINARY_COLLISION_UTILS_H_
#define WARPX_BINARY_COLLISION_UTILS_H_
 
#include <string>
 
#include "Particles/MultiParticleContainer.H"
 
#include <AMReX_Math.H>
 
enum struct CollisionType { DeuteriumTritiumToNeutronHeliumFusion,
                            DeuteriumDeuteriumToProtonTritiumFusion,
                            DeuteriumDeuteriumToNeutronHeliumFusion,
                            DeuteriumHeliumToProtonHeliumFusion,
                            ProtonBoronToAlphasFusion,
                            Bremsstrahlung,
                            DSMC,
                            PairwiseCoulomb,
                            LinearBreitWheeler,
                            LinearCompton,
                            Undefined };
 
enum struct NuclearFusionType {
                                DeuteriumTritiumToNeutronHelium,
                                DeuteriumDeuteriumToProtonTritium,
                                DeuteriumDeuteriumToNeutronHelium,
                                DeuteriumHeliumToProtonHelium,
                                ProtonBoronToAlphas,
                                Undefined };
 
namespace BinaryCollisionUtils{
 
    NuclearFusionType get_nuclear_fusion_type (const std::string& collision_name,
                                               MultiParticleContainer const * mypc);
 
    CollisionType get_collision_type (const std::string& collision_name,
                                      MultiParticleContainer const * mypc);
 
    CollisionType nuclear_fusion_type_to_collision_type (NuclearFusionType fusion_type);

    AMREX_GPU_HOST_DEVICE AMREX_INLINE
    void get_collision_parameters (
        const amrex::ParticleReal& p1x, const amrex::ParticleReal& p1y,
        const amrex::ParticleReal& p1z, const amrex::ParticleReal& p2x,
        const amrex::ParticleReal& p2y, const amrex::ParticleReal& p2z,
        const amrex::ParticleReal& m1, const amrex::ParticleReal& m2,
        amrex::ParticleReal& E_kin_COM, amrex::ParticleReal& v_rel_COM,
        amrex::ParticleReal& lab_to_COM_lorentz_factor )
    {
        // General notations in this function:
        //     x_sq denotes the square of x
        //     x_star denotes the value of x in the center of mass frame
 
        using namespace amrex::literals;
        using namespace amrex::Math;
 
        constexpr double c = PhysConst::c;
        constexpr double c_sq = PhysConst::c * PhysConst::c;
        constexpr double inv_c = 1./PhysConst::c;
 
        // Cast input parameters to double before computing collision properties
        // This is needed to avoid errors when using single-precision particles
        const auto m1_dbl = static_cast<double>(m1);
        const auto m2_dbl = static_cast<double>(m2);
        const auto p1x_dbl = static_cast<double>(p1x);
        const auto p1y_dbl = static_cast<double>(p1y);
        const auto p1z_dbl = static_cast<double>(p1z);
        const auto p2x_dbl = static_cast<double>(p2x);
        const auto p2y_dbl = static_cast<double>(p2y);
        const auto p2z_dbl = static_cast<double>(p2z);
 
        const double m1_sq = m1_dbl*m1_dbl;
        const double m2_sq = m2_dbl*m2_dbl;
 
        // Square norm of the total (sum between the two particles) momenta in the lab frame
        const double p_total_sq = powi<2>(p1x_dbl + p2x_dbl) + powi<2>(p1y_dbl + p2y_dbl) + powi<2>(p1z_dbl + p2z_dbl);
 
        // Total energy in the lab frame
        // Note the use of `double` for energy since this calculation is prone to error with single precision.
        const double E1_lab = std::sqrt( m1_sq * c_sq + p1x_dbl*p1x_dbl + p1y_dbl*p1y_dbl + p1z_dbl*p1z_dbl ) * c;
        const double E2_lab = std::sqrt( m2_sq * c_sq + p2x_dbl*p2x_dbl + p2y_dbl*p2y_dbl + p2z_dbl*p2z_dbl ) * c;
        const double E_lab = E1_lab + E2_lab;
        // Total energy squared in the center of mass frame, calculated using the Lorentz invariance
        // of the four-momentum norm
        const double E_star_sq = E_lab*E_lab - c_sq*p_total_sq;
 
        // Kinetic energy in the center of mass frame
        const double E_star = std::sqrt(E_star_sq);
 
        // Cast back to chosen precision for output
        E_kin_COM = static_cast<amrex::ParticleReal>(E_star - (m1_dbl + m2_dbl)*c_sq);
 
        // Find the norm of the momentum of each particles in the center of mass frame
        // This is done by solving the following system (in the COM frame)
        // E_1^2 = p^2 c^2 + m_1^2 c^4  (for the first particle)
        // E_2^2 = p^2 c^2 + m_2^2 c^4  (for the second particle ; same p since we are in the COM frame)
        // to find the expression of the p as a function of E = E_1 + E_2.
        // Here is an abbreviation derivation:
        // - By summing the above equations
        // E^2 = E_1^2 + E_2^2 + 2 E_1 E_2 = 2 p^2 c^2 + (m_1^2 + m_2^2) c^4 + 2 E_1 E_2
        // - Rearranging and squaring
        // ( E^2 - 2 p^2 c^2 - (m_1^2 + m_2^2) c^4 )^2 = 4 E_1^2 E_2^2 = 4 (p^2 c^2 + m_1^2 c^4) (p^2 c^2 + m_2^2 c^4)
        // - By rearranging, we get:
        // p^2 = E^2/4c^2 - (m_1^2 + m_2^2)c^2/2 + (m_1^2-m_2^2)^2 c^6/4E^2
        double p_star_sq;
        if (m1_dbl + m2_dbl == 0) {
            p_star_sq = powi<2>( 0.5 * E_star * inv_c );
        } else {
            // The expression below is specifically written in a form that avoids returning
            // small negative numbers due to machine precision errors, for low-energy particles
            const double E_ratio = E_star/((m1_dbl + m2_dbl)*c_sq);
            p_star_sq = m1_dbl*m2_dbl*c_sq * ( powi<2>(E_ratio) - 1.0 )
                + powi<2>(m1_dbl - m2_dbl)*c_sq/4.0 * powi<2>( E_ratio - 1.0/E_ratio);
        }
 
        // Energy of each particle in the center of mass frame
        const double E1_star = std::sqrt(m1_sq*c_sq + p_star_sq) * c;
        const double E2_star = std::sqrt(m2_sq*c_sq + p_star_sq) * c;
 
        // relative velocity in the center of mass frame, cast back to chosen precision
        v_rel_COM = PhysConst::c * static_cast<amrex::ParticleReal>(std::sqrt(p_star_sq) * c * (1.0/E1_star + 1.0/E2_star));
 
        // Cross sections and relative velocity are computed in the center of mass frame.
        // On the other hand, the particle densities (weight over volume) in the lab frame are used.
        // To take this discrepancy into account, it is needed to multiply the
        // collision probability by the ratio between the Lorentz factors in the
        // COM frame and the Lorentz factors in the lab frame (see Perez et al.,
        // Phys.Plasmas.19.083104 (2012)). The correction factor is calculated here.
        lab_to_COM_lorentz_factor = static_cast<amrex::ParticleReal>(E1_star*E2_star/(E1_lab*E2_lab));
    }

    AMREX_GPU_HOST_DEVICE AMREX_INLINE
    void remove_weight_from_colliding_particle (
        amrex::ParticleReal& weight, uint64_t& idcpu,
        const amrex::ParticleReal reaction_weight )
    {
        // Remove weight from given particle
        amrex::Gpu::Atomic::AddNoRet(&weight, -reaction_weight);
 
        // If the colliding particle weight decreases to zero, remove particle by
        // setting its id to invalid
        if (weight <= std::numeric_limits<amrex::ParticleReal>::min())
        {
#if defined(AMREX_USE_OMP)
#pragma omp atomic write
            idcpu = amrex::ParticleIdCpus::Invalid;
#else
            amrex::Gpu::Atomic::Exch(
                (unsigned long long *)&idcpu,
                (unsigned long long)amrex::ParticleIdCpus::Invalid
            );
#endif
        }
    }
}
 
#endif // WARPX_BINARY_COLLISION_UTILS_H_