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 //------------------------------- -*- C++ -*- -------------------------------//
 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details
 // SPDX-License-Identifier: (Apache-2.0 OR MIT)
 //---------------------------------------------------------------------------//
 //! \file celeritas/optical/CherenkovDndxCalculator.hh
 //---------------------------------------------------------------------------//
 #pragma once
 
 #include <cmath>
 
 #include "corecel/Assert.hh"
 #include "corecel/Macros.hh"
 #include "corecel/Types.hh"
 #include "corecel/grid/VectorUtils.hh"
 #include "celeritas/Quantities.hh"
 #include "celeritas/grid/NonuniformGridCalculator.hh"
 
 #include "CherenkovData.hh"
 #include "MaterialView.hh"
 
 namespace celeritas
 {
 namespace optical
 {
 //---------------------------------------------------------------------------//
 /*!
  * Calculate the mean number of Cherenkov photons produced per unit length.
  *
  * The average number of photons produced is given by
  * \f[
    \dif N = \frac{\alpha z^2}{\hbar c}\sin^2\theta \dif\epsilon \dif x =
    \frac{\alpha z^2}{\hbar c}\left(1 - \frac{1}{n^2\beta^2}\right) \dif\epsilon
    \dif x,
  * \f]
  * where \f$ n \f$ is the refractive index of the material, \f$ \epsilon \f$
  * is the photon energy, and \f$ \theta \f$ is the angle of the emitted photons
  * with respect to the incident particle direction, given by \f$ \cos\theta = 1
  * / (\beta n) \f$. Note that in a dispersive medium, the index of refraction
  * is an inreasing function of photon energy. The mean number of photons per
  * unit length is given by
  * \f[
    \difd{N}{x} = \frac{\alpha z^2}{\hbar c}
    \int_{\epsilon_\text{min}}^{\epsilon_\text{max}} \left(1 -
    \frac{1}{n^2\beta^2} \right) \dif\epsilon
    = \frac{\alpha z^2}{\hbar c}
    \left[\epsilon_\text{max} - \epsilon_\text{min} - \frac{1}{\beta^2}
    \int_{\epsilon_\text{min}}^{\epsilon_\text{max}}
    \frac{1}{n^2(\epsilon)}\dif\epsilon \right].
  * \f]
  */
 class CherenkovDndxCalculator
 {
   public:
     // Construct from optical materials and Cherenkov angle integrals
     inline CELER_FUNCTION
     CherenkovDndxCalculator(MaterialView const& material,
                            NativeCRef<CherenkovData> const& shared,
                            units::ElementaryCharge charge);
 
     // Calculate the mean number of Cherenkov photons produced per unit length
     inline CELER_FUNCTION real_type operator()(units::LightSpeed beta);
 
   private:
     // Calculate refractive index [MeV -> unitless]
     NonuniformGridCalculator calc_refractive_index_;
 
     // Calculate the Cherenkov angle integral [MeV -> unitless]
     NonuniformGridCalculator calc_integral_;
 
     // Square of particle charge
     real_type zsq_;
 };
 
 //---------------------------------------------------------------------------//
 // INLINE DEFINITIONS
 //---------------------------------------------------------------------------//
 /*!
  * Construct from optical materials and Cherenkov angle integrals.
  */
 CELER_FUNCTION
 CherenkovDndxCalculator::CherenkovDndxCalculator(
     MaterialView const& material,
     NativeCRef<CherenkovData> const& shared,
     units::ElementaryCharge charge)
     : calc_refractive_index_(material.make_refractive_index_calculator())
     , calc_integral_{shared.angle_integral[material.material_id()],
                      shared.reals}
     , zsq_(ipow<2>(charge.value()))
 {
     CELER_EXPECT(charge != zero_quantity());
 }
 
 //---------------------------------------------------------------------------//
 /*!
  * Calculate the mean number of Cherenkov photons produced per unit length.
  *
  * \todo define a "generic grid extents" class for finding the lower/upper x/y
  * coordinates on grid data. In the future we could cache these if the memory
  * lookups result in too much indirection.
  */
 CELER_FUNCTION real_type
 CherenkovDndxCalculator::operator()(units::LightSpeed beta)
 {
     CELER_EXPECT(beta.value() > 0 && beta.value() <= 1);
 
     real_type inv_beta = 1 / beta.value();
     real_type energy_max = calc_refractive_index_.grid().back();
     if (inv_beta > calc_refractive_index_(energy_max))
     {
         // Incident particle energy is below the threshold for Cherenkov
         // emission (i.e., beta < 1 / n_max)
         return 0;
     }
 
     // Calculate \f$ \int_{\epsilon_\text{min}}^{\epsilon_\text{max}}
     // \dif\epsilon \left(1 - \frac{1}{n^2\beta^2}\right) \f$
     real_type energy;
     if (inv_beta < calc_refractive_index_[0])
     {
         energy = energy_max - calc_refractive_index_.grid().front()
                  - calc_integral_(energy_max) * ipow<2>(inv_beta);
     }
     else
     {
         // Find the energy where the refractive index is equal to 1 / beta.
         // Both energy and refractive index are monotonically increasing, so
         // the grid and values can be swapped and the energy can be calculated
         // from a given index of refraction
         real_type energy_min = calc_refractive_index_.make_inverse()(inv_beta);
         energy = energy_max - energy_min
                  - (calc_integral_(energy_max) - calc_integral_(energy_min))
                        * ipow<2>(inv_beta);
     }
 
     // Calculate number of photons. This may be negative if the incident
     // particle energy is very close to (just above) the Cherenkov production
     // threshold
     return clamp_to_nonneg(zsq_
                            * (constants::alpha_fine_structure
                               / (constants::hbar_planck * constants::c_light))
                            * native_value_from(units::MevEnergy(energy)));
 }
 
 //---------------------------------------------------------------------------//
 }  // namespace optical
 }  // namespace celeritas

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