!_____________________________________________________________________________!
!_____________________________________________________________________________!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!! Electrons moments RHS !!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!_____________________________________________________________________________!
SUBROUTINE moments_eq_rhs_e
USE basic
USE time_integration
USE array
USE fields
USE grid
USE model
USE prec_const
USE collision
use geometry
IMPLICIT NONE
INTEGER :: p_int, j_int ! loops indices and polynom. degrees
REAL(dp) :: kx, ky, kperp2, dzlnB_o_J
COMPLEX(dp) :: Tnepj, Tnepp2j, Tnepm2j, Tnepjp1, Tnepjm1, Tpare, Tphi ! Terms from b x gradB and drives
COMPLEX(dp) :: Tmir, Tnepp1j, Tnepm1j, Tnepp1jm1, Tnepm1jm1 ! Terms from mirror force with non adiab moments
COMPLEX(dp) :: UNepm1j, UNepm1jp1, UNepm1jm1 ! Terms from mirror force with adiab moments
COMPLEX(dp) :: TColl ! terms of the rhs
COMPLEX(dp) :: i_ky
REAL(dp) :: delta_p0, delta_p1, delta_p2
INTEGER :: izm2, izm1, izp1, izp2 ! indices for centered FDF ddz
! Measuring execution time
CALL cpu_time(t0_rhs)
ploope : DO ip = ips_e, ipe_e ! loop over Hermite degree indices
p_int = parray_e(ip) ! Hermite polynom. degree
delta_p0 = 0._dp; delta_p1 = 0._dp; delta_p2 = 0._dp
IF(p_int .EQ. 0) delta_p0 = 1._dp
IF(p_int .EQ. 1) delta_p1 = 1._dp
IF(p_int .EQ. 2) delta_p2 = 1._dp
jloope : DO ij = ijs_e, ije_e ! loop over Laguerre degree indices
j_int = jarray_e(ij)
! Loop on kspace
zloope : DO iz = izs,ize
! Obtain the index with an array that accounts for boundary conditions
! e.g. : 4 stencil with periodic BC, izarray(Nz+2) = 2, izarray(-1) = Nz-1
izp1 = izarray(iz+1); izp2 = izarray(iz+2);
izm1 = izarray(iz-1); izm2 = izarray(iz-2);
!
kxloope : DO ikx = ikxs,ikxe
kx = kxarray(ikx) ! radial wavevector
kyloope : DO iky = ikys,ikye
ky = kyarray(iky) ! toroidal wavevector
i_ky = imagu * ky ! toroidal derivative
IF (Nky .EQ. 1) i_ky = imagu * kxarray(ikx) ! If 1D simulation we put kx as ky
! kperp2= gxx(iz)*kx**2 + 2._dp*gxy(iz)*kx*ky + gyy(iz)*ky**2
kperp2= kparray(ikx,iky,iz)**2
!! Compute moments mixing terms
! Perpendicular dynamic
! term propto n_e^{p,j}
Tnepj = xnepj(ip,ij)* nadiab_moments_e(ip,ij,ikx,iky,iz)
! term propto n_e^{p+2,j}
Tnepp2j = xnepp2j(ip) * nadiab_moments_e(ip+pp2,ij,ikx,iky,iz)
! term propto n_e^{p-2,j}
Tnepm2j = xnepm2j(ip) * nadiab_moments_e(ip-pp2,ij,ikx,iky,iz)
! term propto n_e^{p,j+1}
Tnepjp1 = xnepjp1(ij) * nadiab_moments_e(ip,ij+1,ikx,iky,iz)
! term propto n_e^{p,j-1}
Tnepjm1 = xnepjm1(ij) * nadiab_moments_e(ip,ij-1,ikx,iky,iz)
! Parallel dynamic
! ddz derivative for Landau damping term
Tpare = xnepp1j(ip) * &
( onetwelfth*nadiab_moments_e(ip+1,ij,ikx,iky,izm2)&
- twothird*nadiab_moments_e(ip+1,ij,ikx,iky,izm1)&
+ twothird*nadiab_moments_e(ip+1,ij,ikx,iky,izp1)&
-onetwelfth*nadiab_moments_e(ip+1,ij,ikx,iky,izp2))&
+xnepm1j(ip) * &
( onetwelfth*nadiab_moments_e(ip-1,ij,ikx,iky,izm2)&
- twothird*nadiab_moments_e(ip-1,ij,ikx,iky,izm1)&
+ twothird*nadiab_moments_e(ip-1,ij,ikx,iky,izp1)&
-onetwelfth*nadiab_moments_e(ip-1,ij,ikx,iky,izp2))
! Mirror terms
Tnepp1j = ynepp1j(ip,ij) * nadiab_moments_e(ip+1,ij ,ikx,iky,iz)
Tnepp1jm1 = ynepp1jm1(ip,ij) * nadiab_moments_e(ip+1,ij-1,ikx,iky,iz)
Tnepm1j = ynepm1j(ip,ij) * nadiab_moments_e(ip-1,ij ,ikx,iky,iz)
Tnepm1jm1 = ynepm1jm1(ip,ij) * nadiab_moments_e(ip-1,ij-1,ikx,iky,iz)
! Trapping terms
UNepm1j = zNepm1j(ip,ij) * nadiab_moments_e(ip-1,ij ,ikx,iky,iz)
UNepm1jp1 = zNepm1jp1(ip,ij) * nadiab_moments_e(ip-1,ij+1,ikx,iky,iz)
UNepm1jm1 = zNepm1jm1(ip,ij) * nadiab_moments_e(ip-1,ij-1,ikx,iky,iz)
Tmir = Tnepp1j + Tnepp1jm1 + Tnepm1j + Tnepm1jm1 + UNepm1j + UNepm1jp1 + UNepm1jm1
!! Electrical potential term
IF ( p_int .LE. 2 ) THEN ! kronecker p0 p1 p2
Tphi = phi(ikx,iky,iz) * (xphij(ip,ij)*kernel_e(ij,ikx,iky,iz) &
+ xphijp1(ip,ij)*kernel_e(ij+1,ikx,iky,iz) &
+ xphijm1(ip,ij)*kernel_e(ij-1,ikx,iky,iz) )
ELSE
Tphi = 0._dp
ENDIF
!! Collision
IF (CO .EQ. 0) THEN ! Lenard Bernstein
CALL LenardBernstein_e(ip,ij,ikx,iky,iz,TColl)
ELSEIF (CO .EQ. 1) THEN ! GK Dougherty
CALL DoughertyGK_e(ip,ij,ikx,iky,iz,TColl)
ELSE ! COSOLver matrix
TColl = TColl_e(ip,ij,ikx,iky,iz)
ENDIF
!! Sum of all linear terms (the sign is inverted to match RHS)
moments_rhs_e(ip,ij,ikx,iky,iz,updatetlevel) = &
! Perpendicular magnetic gradient/curvature effects
- imagu*Ckxky(ikx,iky,iz)*hatR(iz)* (Tnepj + Tnepp2j + Tnepm2j + Tnepjp1 + Tnepjm1)&
! Parallel coupling (Landau Damping)
- Tpare*inv_deltaz*gradz_coeff(iz) &
! Mirror term (parallel magnetic gradient)
- gradzB(iz)* Tmir *gradz_coeff(iz) &
! Drives (density + temperature gradients)
- i_ky * Tphi &
! Electrostatic background gradients
- i_ky * K_E * moments_e(ip,ij,ikx,iky,iz,updatetlevel) &
! Numerical hyperdiffusion (totally artificial, for stability purpose)
- mu*kperp2**2 * moments_e(ip,ij,ikx,iky,iz,updatetlevel) &
! Collision term
+ TColl
!! Adding non linearity
IF ( NON_LIN ) THEN
moments_rhs_e(ip,ij,ikx,iky,iz,updatetlevel) = &
moments_rhs_e(ip,ij,ikx,iky,iz,updatetlevel) - Sepj(ip,ij,ikx,iky,iz)
ENDIF
END DO kyloope
END DO kxloope
END DO zloope
END DO jloope
END DO ploope
! Execution time end
CALL cpu_time(t1_rhs)
tc_rhs = tc_rhs + (t1_rhs-t0_rhs)
END SUBROUTINE moments_eq_rhs_e
!_____________________________________________________________________________!
!_____________________________________________________________________________!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!! Ions moments RHS !!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!_____________________________________________________________________________!
SUBROUTINE moments_eq_rhs_i
USE basic
USE time_integration, ONLY: updatetlevel
USE array
USE fields
USE grid
USE model
USE prec_const
USE collision
IMPLICIT NONE
INTEGER :: p_int, j_int ! loops indices and polynom. degrees
REAL(dp) :: kx, ky, kperp2
COMPLEX(dp) :: Tnipj, Tnipp2j, Tnipm2j, Tnipjp1, Tnipjm1, Tpari, Tphi
COMPLEX(dp) :: Tmir, Tnipp1j, Tnipm1j, Tnipp1jm1, Tnipm1jm1 ! Terms from mirror force with non adiab moments
COMPLEX(dp) :: UNipm1j, UNipm1jp1, UNipm1jm1 ! Terms from mirror force with adiab moments
COMPLEX(dp) :: TColl ! terms of the rhs
COMPLEX(dp) :: i_ky
REAL(dp) :: delta_p0, delta_p1, delta_p2
INTEGER :: izm2, izm1, izp1, izp2 ! indices for centered FDF ddz
! Measuring execution time
CALL cpu_time(t0_rhs)
ploopi : DO ip = ips_i, ipe_i ! Hermite loop
p_int= parray_i(ip) ! Hermite degree
delta_p0 = 0._dp; delta_p1 = 0._dp; delta_p2 = 0._dp
IF(p_int .EQ. 0) delta_p0 = 1._dp
IF(p_int .EQ. 1) delta_p1 = 1._dp
IF(p_int .EQ. 2) delta_p2 = 1._dp
jloopi : DO ij = ijs_i, ije_i ! This loop is from 1 to jmaxi+1
j_int = jarray_i(ij)
! Loop on kspace
zloopi : DO iz = izs,ize
! Obtain the index with an array that accounts for boundary conditions
! e.g. : 4 stencil with periodic BC, izarray(Nz+2) = 2, izarray(-1) = Nz-1
izp1 = izarray(iz+1); izp2 = izarray(iz+2);
izm1 = izarray(iz-1); izm2 = izarray(iz-2);
!
kxloopi : DO ikx = ikxs,ikxe
kx = kxarray(ikx) ! radial wavevector
kyloopi : DO iky = ikys,ikye
ky = kyarray(iky) ! toroidal wavevector
i_ky = imagu * ky ! toroidal derivative
IF (Nky .EQ. 1) i_ky = imagu * kxarray(ikx) ! If 1D simulation we put kx as ky
! kperp2= gxx(iz)*kx**2 + 2._dp*gxy(iz)*kx*ky + gyy(iz)*ky**2
kperp2= kparray(ikx,iky,iz)**2
!! Compute moments mixing terms
! Perpendicular dynamic
! term propto n_i^{p,j}
Tnipj = xnipj(ip,ij) * nadiab_moments_i(ip,ij,ikx,iky,iz)
! term propto n_i^{p+2,j}
Tnipp2j = xnipp2j(ip) * nadiab_moments_i(ip+pp2,ij,ikx,iky,iz)
! term propto n_i^{p-2,j}
Tnipm2j = xnipm2j(ip) * nadiab_moments_i(ip-pp2,ij,ikx,iky,iz)
! term propto n_e^{p,j+1}
Tnipjp1 = xnipjp1(ij) * nadiab_moments_i(ip,ij+1,ikx,iky,iz)
! term propto n_e^{p,j-1}
Tnipjm1 = xnipjm1(ij) * nadiab_moments_i(ip,ij-1,ikx,iky,iz)
! Parallel dynamic
! term propto N_i^{p,j+1}, centered FDF
Tpari = xnipp1j(ip) * &
( onetwelfth*nadiab_moments_i(ip+1,ij,ikx,iky,izm2)&
- twothird*nadiab_moments_i(ip+1,ij,ikx,iky,izm1)&
+ twothird*nadiab_moments_i(ip+1,ij,ikx,iky,izp1)&
-onetwelfth*nadiab_moments_i(ip+1,ij,ikx,iky,izp2))&
+xnipm1j(ip) * &
( onetwelfth*nadiab_moments_i(ip-1,ij,ikx,iky,izm2)&
- twothird*nadiab_moments_i(ip-1,ij,ikx,iky,izm1)&
+ twothird*nadiab_moments_i(ip-1,ij,ikx,iky,izp1)&
-onetwelfth*nadiab_moments_i(ip-1,ij,ikx,iky,izp2))
! Mirror terms
Tnipp1j = ynipp1j(ip,ij) * nadiab_moments_i(ip+1,ij ,ikx,iky,iz)
Tnipp1jm1 = ynipp1jm1(ip,ij) * nadiab_moments_i(ip+1,ij-1,ikx,iky,iz)
Tnipm1j = ynipm1j(ip,ij) * nadiab_moments_i(ip-1,ij ,ikx,iky,iz)
Tnipm1jm1 = ynipm1jm1(ip,ij) * nadiab_moments_i(ip-1,ij-1,ikx,iky,iz)
! Trapping terms
Unipm1j = znipm1j(ip,ij) * nadiab_moments_i(ip-1,ij ,ikx,iky,iz)
Unipm1jp1 = znipm1jp1(ip,ij) * nadiab_moments_i(ip-1,ij+1,ikx,iky,iz)
Unipm1jm1 = znipm1jm1(ip,ij) * nadiab_moments_i(ip-1,ij-1,ikx,iky,iz)
Tmir = Tnipp1j + Tnipp1jm1 + Tnipm1j + Tnipm1jm1 + UNipm1j + UNipm1jp1 + UNipm1jm1
!! Electrical potential term
IF ( p_int .LE. 2 ) THEN ! kronecker p0 p1 p2
Tphi = phi(ikx,iky,iz) * (xphij(ip,ij)*kernel_i(ij,ikx,iky,iz) &
+ xphijp1(ip,ij)*kernel_i(ij+1,ikx,iky,iz) &
+ xphijm1(ip,ij)*kernel_i(ij-1,ikx,iky,iz) )
ELSE
Tphi = 0._dp
ENDIF
!! Collision
IF (CO .EQ. 0) THEN ! Lenard Bernstein
CALL LenardBernstein_i(ip,ij,ikx,iky,iz,TColl)
ELSEIF (CO .EQ. 1) THEN ! GK Dougherty
CALL DoughertyGK_i(ip,ij,ikx,iky,iz,TColl)
ELSE! COSOLver matrix (Sugama, Coulomb)
TColl = TColl_i(ip,ij,ikx,iky,iz)
ENDIF
!! Sum of all linear terms (the sign is inverted to match RHS)
moments_rhs_i(ip,ij,ikx,iky,iz,updatetlevel) = &
! Perpendicular magnetic gradient/curvature effects
- imagu*Ckxky(ikx,iky,iz)*hatR(iz)*(Tnipj + Tnipp2j + Tnipm2j + Tnipjp1 + Tnipjm1)&
! Parallel coupling (Landau Damping)
- Tpari*inv_deltaz*gradz_coeff(iz) &
! Mirror term (parallel magnetic gradient)
- gradzB(iz)*Tmir*gradz_coeff(iz) &
! Drives (density + temperature gradients)
- i_ky * Tphi &
! Electrostatic background gradients
- i_ky * K_E * moments_i(ip,ij,ikx,iky,iz,updatetlevel) &
! Numerical hyperdiffusion (totally artificial, for stability purpose)
- mu*kperp2**2 * moments_i(ip,ij,ikx,iky,iz,updatetlevel) &
! Collision term
+ TColl
!! Adding non linearity
IF ( NON_LIN ) THEN
moments_rhs_i(ip,ij,ikx,iky,iz,updatetlevel) = &
moments_rhs_i(ip,ij,ikx,iky,iz,updatetlevel) - Sipj(ip,ij,ikx,iky,iz)
ENDIF
END DO kyloopi
END DO kxloopi
END DO zloopi
END DO jloopi
END DO ploopi
! Execution time end
CALL cpu_time(t1_rhs)
tc_rhs = tc_rhs + (t1_rhs-t0_rhs)
END SUBROUTINE moments_eq_rhs_i