Line data    Source code

       1            0 : // Distributed under the MIT License.
       2              : // See LICENSE.txt for details.
       3              : 
       4              : #pragma once
       5              : 
       6              : #include "DataStructures/Tensor/TypeAliases.hpp"
       7              : #include "Utilities/Gsl.hpp"
       8              : 
       9              : namespace hydro {
      10              : 
      11              : /// @{
      12              : /*!
      13              :  * \brief The comoving magnetic field vector $b^\mu$ and one-form $b_\mu$
      14              :  *
      15              :  * The components of the comoving magnetic field vector are:
      16              :  *
      17              :  * \begin{align}
      18              :  * b^0 &= W B^j v^k \gamma_{j k} / \alpha \\
      19              :  * b^i &= B^i / W + B^j v^k \gamma_{j k} u^i
      20              :  * \end{align}
      21              :  *
      22              :  * where $u^i = W(v^i - \beta^i/\alpha)$.
      23              :  *
      24              :  * Using the spacetime metric, the corresponding one-form components are:
      25              :  *
      26              :  * \begin{align}
      27              :  * b_0 &= - \alpha W v^i B_i + \beta^i b_i \\
      28              :  * b_i &= B_i / W + B^j v^k \gamma_{j k} W v_i
      29              :  * \end{align}
      30              :  *
      31              :  * The square of the vector is:
      32              :  *
      33              :  * \begin{equation}
      34              :  * b^2 = B^i B^j \gamma_{i j} / W^2 + (B^i v^j \gamma_{i j})^2
      35              :  * \end{equation}
      36              :  *
      37              :  * See also Eq. (5.173) in \cite BaumgarteShapiro, with the difference that we
      38              :  * work in Heaviside-Lorentz units where the magnetic field is rescaled by
      39              :  * $1/\sqrt{4\pi}$, following \cite Moesta2013dna .
      40              :  */
      41              : template <typename DataType>
      42            1 : void comoving_magnetic_field(
      43              :     gsl::not_null<tnsr::A<DataType, 3>*> result,
      44              :     const tnsr::I<DataType, 3>& spatial_velocity,
      45              :     const tnsr::I<DataType, 3>& magnetic_field,
      46              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      47              :     const Scalar<DataType>& lorentz_factor, const tnsr::I<DataType, 3>& shift,
      48              :     const Scalar<DataType>& lapse);
      49              : 
      50              : template <typename DataType>
      51            1 : tnsr::A<DataType, 3> comoving_magnetic_field(
      52              :     const tnsr::I<DataType, 3>& spatial_velocity,
      53              :     const tnsr::I<DataType, 3>& magnetic_field,
      54              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      55              :     const Scalar<DataType>& lorentz_factor, const tnsr::I<DataType, 3>& shift,
      56              :     const Scalar<DataType>& lapse);
      57              : 
      58              : template <typename DataType>
      59            1 : void comoving_magnetic_field_one_form(
      60              :     gsl::not_null<tnsr::a<DataType, 3>*> result,
      61              :     const tnsr::i<DataType, 3>& spatial_velocity_one_form,
      62              :     const tnsr::i<DataType, 3>& magnetic_field_one_form,
      63              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      64              :     const Scalar<DataType>& lorentz_factor, const tnsr::I<DataType, 3>& shift,
      65              :     const Scalar<DataType>& lapse);
      66              : 
      67              : template <typename DataType>
      68            1 : tnsr::a<DataType, 3> comoving_magnetic_field_one_form(
      69              :     const tnsr::i<DataType, 3>& spatial_velocity_one_form,
      70              :     const tnsr::i<DataType, 3>& magnetic_field_one_form,
      71              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      72              :     const Scalar<DataType>& lorentz_factor, const tnsr::I<DataType, 3>& shift,
      73              :     const Scalar<DataType>& lapse);
      74              : 
      75              : template <typename DataType>
      76            1 : void comoving_magnetic_field_squared(
      77              :     gsl::not_null<Scalar<DataType>*> result,
      78              :     const Scalar<DataType>& magnetic_field_squared,
      79              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      80              :     const Scalar<DataType>& lorentz_factor);
      81              : 
      82              : template <typename DataType>
      83            1 : Scalar<DataType> comoving_magnetic_field_squared(
      84              :     const Scalar<DataType>& magnetic_field_squared,
      85              :     const Scalar<DataType>& magnetic_field_dot_spatial_velocity,
      86              :     const Scalar<DataType>& lorentz_factor);
      87              : /// @}
      88              : 
      89              : }  // namespace hydro