! =============================================================================
!> This submodule defines an equilibrium in Cartesian geometry with a constant
!! resistivity value. Parameters are taken in such a way as to allow for
!! resistive tearing modes. The geometry can be overridden using the parfile.
!!
!! This equilibrium is taken from section 14.3, p. 551 in
!! _Goedbloed, H., Keppens, R., & Poedts, S. (2019). Magnetohydrodynamics of Laboratory
!! and Astrophysical Plasmas. Cambridge University Press._ [DOI](http://doi.org/10.1017/9781316403679).
!! @note Default values are given by
!!
!! - k2 = 0.49
!! - k3 = 0
!! - cte_rho0 = 1 : used to set the density value.
!! - alpha = 4.73884 : parameter in the magnetic field prescription.
!! - beta = 0.25 : used to constrain the temperature value.
!! - fixed resistivity value of 0.0001
!!
!! and can all be changed in the parfile. @endnote
submodule (mod_equilibrium) smod_equil_resistive_tearing
use mod_equilibrium_params, only: alpha, beta, cte_rho0
implicit none
contains
!> Sets the equilibrium
module procedure resistive_tearing_modes_eq
if (settings%equilibrium%use_defaults) then ! LCOV_EXCL_START
call settings%grid%set_geometry("Cartesian")
call settings%grid%set_grid_boundaries(-0.5_dp, 0.5_dp)
call settings%physics%enable_resistivity(fixed_resistivity_value=0.0001_dp)
k2 = 0.49_dp
k3 = 0.0_dp
alpha = 4.73884_dp
beta = 0.15_dp
cte_rho0 = 1.0_dp
end if ! LCOV_EXCL_STOP
call background%set_density_funcs(rho0_func=rho0)
call background%set_temperature_funcs(T0_func=T0)
call background%set_magnetic_2_funcs(B02_func=B02, dB02_func=dB02, ddB02_func=ddB02)
call background%set_magnetic_3_funcs(B03_func=B03, dB03_func=dB03, ddB03_func=ddB03)
end procedure resistive_tearing_modes_eq
real(dp) function rho0()
rho0 = cte_rho0
end function rho0
real(dp) function T0(x)
real(dp), intent(in) :: x
T0 = beta * (B0(x))**2 / (2.0_dp * cte_rho0)
end function T0
real(dp) function B02(x)
real(dp), intent(in) :: x
B02 = sin(alpha * x)
end function B02
real(dp) function dB02(x)
real(dp), intent(in) :: x
dB02 = alpha * cos(alpha * x)
end function dB02
real(dp) function ddB02(x)
real(dp), intent(in) :: x
ddB02 = -alpha**2 * sin(alpha * x)
end function ddB02
real(dp) function B03(x)
real(dp), intent(in) :: x
B03 = cos(alpha * x)
end function B03
real(dp) function dB03(x)
real(dp), intent(in) :: x
dB03 = -alpha * sin(alpha * x)
end function dB03
real(dp) function ddB03(x)
real(dp), intent(in) :: x
ddB03 = -alpha**2 * cos(alpha * x)
end function ddB03
real(dp) function B0(x)
real(dp), intent(in) :: x
B0 = sqrt(B02(x)**2 + B03(x)**2)
end function B0
end submodule smod_equil_resistive_tearing