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/* Copyright 2021 Luca Fedeli
*
* This file is part of WarpX.
*
* License: BSD-3-Clause-LBNL
*/
#ifndef PARTICLES_KINETIC_ENERGY_H_
#define PARTICLES_KINETIC_ENERGY_H_
#include "Utils/WarpXConst.H"
#include "AMReX_Extension.H"
#include "AMReX_GpuQualifiers.H"
#include "AMReX_REAL.H"
#include <cmath>
namespace Algorithms{
// This marks the gamma threshold to switch between the full relativistic expression
// for particle kinetic energy and a Taylor expansion.
static constexpr auto gamma_relativistic_threshold =
static_cast<amrex::Real>(1.005);
/**
* \brief Computes the kinetic energy of a particle. Below a threshold for the
* Lorentz factor (gamma_relativistic_threshold) it uses a Taylor expansion instead of
* the full relativistic expression. This method should not be used with photons.
*
* @param[in] ux x component of the particle momentum (code units)
* @param[in] uy y component of the particle momentum (code units)
* @param[in] uz z component of the particle momentum (code units)
* @param[in] mass mass of the particle (in S.I. units)
*
* @return the kinetic energy of the particle (in S.I. units)
*/
AMREX_GPU_HOST_DEVICE AMREX_INLINE
amrex::Real KineticEnergy(
const amrex::Real ux, const amrex::Real uy, const amrex::Real uz,
const amrex::Real mass)
{
using namespace amrex;
constexpr auto c2 = PhysConst::c * PhysConst::c;
constexpr auto inv_c2 = 1.0_rt/c2;
const auto u2 = (ux*ux + uy*uy + uz*uz)*inv_c2;
const auto gamma = std::sqrt(1.0_rt + u2);
const auto kk = (gamma > gamma_relativistic_threshold)?
(gamma-1.0_rt):
(u2*0.5_rt - u2*u2*(1.0_rt/8.0_rt) + u2*u2*u2*(1.0_rt/16.0_rt)-
u2*u2*u2*u2*(5.0_rt/128.0_rt) + (7.0_rt/256_rt)*u2*u2*u2*u2*u2); //Taylor expansion
return kk*mass*c2;
}
/**
* \brief Computes the kinetic energy of a photon.
*
* @param[in] ux x component of the particle momentum (code units)
* @param[in] uy y component of the particle momentum (code units)
* @param[in] uz z component of the particle momentum (code units)
*
* @return the kinetic energy of the photon (in S.I. units)
*/
AMREX_GPU_HOST_DEVICE AMREX_INLINE
amrex::Real KineticEnergyPhotons(
const amrex::Real ux, const amrex::Real uy, const amrex::Real uz)
{
// Photons have zero mass, but ux, uy and uz are calculated assuming a mass equal to the
// electron mass. Hence, photons need a special treatment to calculate the total energy.
constexpr auto me_c = PhysConst::m_e * PhysConst::c;
return me_c * std::sqrt(ux*ux + uy*uy + uz*uz);
}
}
#endif // PARTICLES_ALGORITHMS_H_
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