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0001 //------------------------------- -*- C++ -*- -------------------------------// 0002 // Copyright Celeritas contributors: see top-level COPYRIGHT file for details 0003 // SPDX-License-Identifier: (Apache-2.0 OR MIT) 0004 //---------------------------------------------------------------------------// 0005 //! \file celeritas/optical/model/RayleighMfpCalculator.hh 0006 //---------------------------------------------------------------------------// 0007 #pragma once 0008 0009 #include "corecel/Macros.hh" 0010 #include "corecel/Types.hh" 0011 #include "celeritas/Constants.hh" 0012 #include "celeritas/Quantities.hh" 0013 #include "celeritas/grid/NonuniformGridCalculator.hh" 0014 #include "celeritas/io/ImportOpticalMaterial.hh" 0015 #include "celeritas/mat/MaterialView.hh" 0016 #include "celeritas/optical/MaterialView.hh" 0017 #include "celeritas/optical/detail/OpticalUtils.hh" 0018 0019 namespace celeritas 0020 { 0021 namespace optical 0022 { 0023 //---------------------------------------------------------------------------// 0024 /*! 0025 * Calculate the Rayleigh MFP for a given set of material properties. 0026 * 0027 * Uses the Einstein-Smoluchowski formula to calculate the mean free path 0028 * at a given energy. In Landau and Lifshitz Electrodynamics of Continuous 0029 * Media, the mean free path is given by equation (120.2): 0030 * \f[ 0031 l^{-1} = \frac{1}{6\pi} k^4 \rho k_B T \left(\frac{\partial \rho}{\partial 0032 P}\right)_T \left(\frac{\partial \varepsilon}{\partial \rho}\right)_T^2 0033 * \f] 0034 * where we only consider density fluctations at constant temperature. The 0035 * first partial derivative may be rewritten in terms of the isothermal 0036 * compressibility \f$ \beta_T \f$: 0037 * \f[ 0038 \left(\frac{\partial \rho}{\partial P}\right)_T = \rho \beta_T. 0039 * \f] 0040 * The latter partial derivative may be calculated via the Clausius-Mossetti 0041 * equation 0042 * \f[ 0043 \frac{\varepsilon - 1}{\varepsilon + 2} = A \rho 0044 * \f] 0045 * for constant \f$ A \f$, giving 0046 * \f[ 0047 \left(\frac{\partial \varepsilon}{\partial \rho}\right)_T = 0048 \frac{(\varepsilon - 1)(\varepsilon + 2)}{3\rho}. 0049 * \f] 0050 * The final equation for the MFP in terms of energy: 0051 * \f[ 0052 l^{-1} = \frac{k_B T \beta_T}{6\pi} \left(\frac{E}{\hbar c}\right)^4 \left[ 0053 \frac{(\varepsilon - 1)(\varepsilon + 2)}{3} \right]^2. 0054 * \f] 0055 * 0056 * The scale factor is a unitless user customizable factor that's multiplied 0057 * to the inverse MFP. 0058 */ 0059 class RayleighMfpCalculator 0060 { 0061 public: 0062 //!@{ 0063 //! \name Type aliases 0064 using Energy = units::MevEnergy; 0065 using Grid = typename NonuniformGridCalculator::Grid; 0066 //!@} 0067 0068 public: 0069 // Construct from material and Rayleigh properties 0070 inline CELER_FUNCTION 0071 RayleighMfpCalculator(MaterialView const& material, 0072 ImportOpticalRayleigh const& rayleigh, 0073 ::celeritas::MaterialView const& core_material); 0074 0075 // Calculate the MFP for the given energy 0076 inline CELER_FUNCTION real_type operator()(Energy) const; 0077 0078 //! Retrieve the underlying energy grid used to calculate the MFP 0079 inline CELER_FUNCTION Grid const& grid() const 0080 { 0081 return calc_rindex_.grid(); 0082 } 0083 0084 private: 0085 // Calculate refractive index [MeV -> unitless] 0086 NonuniformGridCalculator calc_rindex_; 0087 0088 // Constant prefactor at all energies 0089 real_type density_fluctuation_; 0090 }; 0091 0092 //---------------------------------------------------------------------------// 0093 // INLINE DEFINITIONS 0094 //---------------------------------------------------------------------------// 0095 /*! 0096 * Construct with defaults. 0097 */ 0098 RayleighMfpCalculator::RayleighMfpCalculator( 0099 MaterialView const& material, 0100 ImportOpticalRayleigh const& rayleigh, 0101 ::celeritas::MaterialView const& core_material) 0102 : calc_rindex_(material.make_refractive_index_calculator()) 0103 , density_fluctuation_(rayleigh.scale_factor * rayleigh.compressibility 0104 * core_material.temperature() 0105 * celeritas::constants::k_boltzmann 0106 / (6 * celeritas::constants::pi)) 0107 { 0108 CELER_EXPECT(rayleigh); 0109 CELER_EXPECT(material.material_id() == core_material.optical_material_id()); 0110 CELER_EXPECT(density_fluctuation_ > 0); 0111 } 0112 0113 //---------------------------------------------------------------------------// 0114 /*! 0115 * Calculate the optical Rayleigh mean free path at the given energy. 0116 */ 0117 CELER_FUNCTION real_type RayleighMfpCalculator::operator()(Energy energy) const 0118 { 0119 CELER_EXPECT(energy > zero_quantity()); 0120 0121 real_type rindex = calc_rindex_(value_as<Energy>(energy)); 0122 CELER_ASSERT(rindex > 1); 0123 0124 real_type wave_number = 2 * celeritas::constants::pi 0125 / detail::energy_to_wavelength(energy); 0126 real_type permitivity_fluctuation = (ipow<2>(rindex) - 1) 0127 * (ipow<2>(rindex) + 2) / 3; 0128 0129 return 1 0130 / (density_fluctuation_ * ipow<4>(wave_number) 0131 * ipow<2>(permitivity_fluctuation)); 0132 } 0133 0134 //---------------------------------------------------------------------------// 0135 } // namespace optical 0136 } // namespace celeritas
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