!_____________________________________________________________________________!
!_____________________________________________________________________________!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!! 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
USE calculus, ONLY : interp_z, grad_z
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) :: i_ky
INTEGER :: izm2, izm1, izp1, izp2 ! indices for centered FDF ddz
! To store derivatives and odd-even z grid interpolations
COMPLEX(dp), DIMENSION(izs:ize) :: ddznepp1j, ddznepm1j, &
nepp1j, nepp1jm1, nepm1j, nepm1jm1, nepm1jp1
! Measuring execution time
CALL cpu_time(t0_rhs)
! Kinetic loops
ploope : DO ip = ips_e, ipe_e ! loop over Hermite degree indices
p_int = parray_e(ip) ! Hermite polynom. degree
eo = MODULO(p_int,2) ! Indicates if we are on even or odd z grid
jloope : DO ij = ijs_e, ije_e ! loop over Laguerre degree indices
j_int = jarray_e(ij)
! Spatial loops
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
! Compute z derivatives and odd-even z interpolations
CALL grad_z(eo,nadiab_moments_e(ip+1,ij ,ikx,iky,:),ddznepp1j(:))
CALL grad_z(eo,nadiab_moments_e(ip-1,ij ,ikx,iky,:),ddznepm1j(:))
CALL interp_z(eo,nadiab_moments_e(ip+1,ij ,ikx,iky,:), nepp1j (:))
CALL interp_z(eo,nadiab_moments_e(ip+1,ij-1,ikx,iky,:), nepp1jm1(:))
CALL interp_z(eo,nadiab_moments_e(ip-1,ij ,ikx,iky,:), nepm1j (:))
CALL interp_z(eo,nadiab_moments_e(ip-1,ij+1,ikx,iky,:), nepm1jp1(:))
CALL interp_z(eo,nadiab_moments_e(ip-1,ij-1,ikx,iky,:), nepm1jm1(:))
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);
!
kperp2= kparray(ikx,iky,iz,eo)**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
Tpare = 0._dp; Tmir = 0._dp
IF(Nz .GT. 1) THEN
! ddz derivative for Landau damping term
Tpare = xnepp1j(ip) * ddznepp1j(iz) + xnepm1j(ip) * ddznepm1j(iz)
! Mirror terms
Tnepp1j = ynepp1j (ip,ij) * nepp1j (iz)
Tnepp1jm1 = ynepp1jm1(ip,ij) * nepp1jm1(iz)
Tnepm1j = ynepm1j (ip,ij) * nepm1j (iz)
Tnepm1jm1 = ynepm1jm1(ip,ij) * nepm1jm1(iz)
! Trapping terms
UNepm1j = znepm1j (ip,ij) * nepm1j (iz)
UNepm1jp1 = znepm1jp1(ip,ij) * nepm1jp1(iz)
UNepm1jm1 = znepm1jm1(ip,ij) * nepm1jm1(iz)
Tmir = Tnepp1j + Tnepp1jm1 + Tnepm1j + Tnepm1jm1 + UNepm1j + UNepm1jp1 + UNepm1jm1
ENDIF
!! 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,eo) &
+ xphijp1(ip,ij)*kernel_e(ij+1,ikx,iky,iz,eo) &
+ xphijm1(ip,ij)*kernel_e(ij-1,ikx,iky,iz,eo) )
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,eo)*hatR(iz,eo)* (Tnepj + Tnepp2j + Tnepm2j + Tnepjp1 + Tnepjm1)&
! Parallel coupling (Landau Damping)
- Tpare*inv_deltaz*gradz_coeff(iz,eo) &
! Mirror term (parallel magnetic gradient)
- gradzB(iz,eo)* Tmir *gradz_coeff(iz,eo) &
! 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_x*kx**4 + mu_y*ky**4)*moments_e(ip,ij,ikx,iky,iz,updatetlevel) &
! Collision term
+ TColl_e(ip,ij,ikx,iky,iz)
!! Adding non linearity
moments_rhs_e(ip,ij,ikx,iky,iz,updatetlevel) = &
moments_rhs_e(ip,ij,ikx,iky,iz,updatetlevel) - Sepj(ip,ij,ikx,iky,iz)
END DO zloope
END DO kyloope
END DO kxloope
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
USE calculus, ONLY : interp_z, grad_z
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) :: i_ky
INTEGER :: izm2, izm1, izp1, izp2 ! indices for centered FDF ddz
! To store derivatives and odd-even z grid interpolations
COMPLEX(dp), DIMENSION(izs:ize) :: ddznipp1j, ddznipm1j, &
nipp1j, nipp1jm1, nipm1j, nipm1jm1, nipm1jp1
! Measuring execution time
CALL cpu_time(t0_rhs)
! Kinetic loops
ploopi : DO ip = ips_i, ipe_i ! Hermite loop
p_int = parray_i(ip) ! Hermite degree
eo = MODULO(p_int,2) ! Indicates if we are on odd or even z grid
jloopi : DO ij = ijs_i, ije_i ! This loop is from 1 to jmaxi+1
j_int = jarray_i(ij)
! Spatial loops
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
! Compute z derivatives and odd-even z interpolations
CALL grad_z(eo,nadiab_moments_i(ip+1,ij ,ikx,iky,:),ddznipp1j(:))
CALL grad_z(eo,nadiab_moments_i(ip-1,ij ,ikx,iky,:),ddznipm1j(:))
CALL interp_z(eo,nadiab_moments_i(ip+1,ij ,ikx,iky,:), nipp1j (:))
CALL interp_z(eo,nadiab_moments_i(ip+1,ij-1,ikx,iky,:), nipp1jm1(:))
CALL interp_z(eo,nadiab_moments_i(ip-1,ij ,ikx,iky,:), nipm1j (:))
CALL interp_z(eo,nadiab_moments_i(ip-1,ij+1,ikx,iky,:), nipm1jp1(:))
CALL interp_z(eo,nadiab_moments_i(ip-1,ij-1,ikx,iky,:), nipm1jm1(:))
zloopi : DO iz = izs,ize
! kperp2= gxx(iz)*kx**2 + 2._dp*gxy(iz)*kx*ky + gyy(iz)*ky**2
kperp2= kparray(ikx,iky,iz,eo)**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
Tpari = 0._dp; Tmir = 0._dp
IF(Nz .GT. 1) THEN
! term propto N_i^{p,j+1}, centered FDF
Tpari = xnipp1j(ip) * ddznipp1j(iz) + xnipm1j(ip) * ddznipm1j(iz)
! Mirror terms
Tnipp1j = ynipp1j (ip,ij) * nipp1j (iz)
Tnipp1jm1 = ynipp1jm1(ip,ij) * nipp1jm1(iz)
Tnipm1j = ynipm1j (ip,ij) * nipm1j (iz)
Tnipm1jm1 = ynipm1jm1(ip,ij) * nipm1jm1(iz)
! Trapping terms
UNipm1j = znipm1j (ip,ij) * nipm1j (iz)
UNipm1jp1 = znipm1jp1(ip,ij) * nipm1jp1(iz)
UNipm1jm1 = znipm1jm1(ip,ij) * nipm1jm1(iz)
Tmir = Tnipp1j + Tnipp1jm1 + Tnipm1j + Tnipm1jm1 + UNipm1j + UNipm1jp1 + UNipm1jm1
ENDIF
!! 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,eo) &
+ xphijp1(ip,ij)*kernel_i(ij+1,ikx,iky,iz,eo) &
+ xphijm1(ip,ij)*kernel_i(ij-1,ikx,iky,iz,eo) )
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,eo)*hatR(iz,eo)*(Tnipj + Tnipp2j + Tnipm2j + Tnipjp1 + Tnipjm1)&
! Parallel coupling (Landau Damping)
- Tpari*inv_deltaz*gradz_coeff(iz,eo) &
! Mirror term (parallel magnetic gradient)
- gradzB(iz,eo)*Tmir*gradz_coeff(iz,eo) &
! 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_x*kx**4 + mu_y*ky**4)*moments_i(ip,ij,ikx,iky,iz,updatetlevel) &
! Collision term
+ TColl_i(ip,ij,ikx,iky,iz)
!! Adding non linearity
moments_rhs_i(ip,ij,ikx,iky,iz,updatetlevel) = &
moments_rhs_i(ip,ij,ikx,iky,iz,updatetlevel) - Sipj(ip,ij,ikx,iky,iz)
END DO zloopi
END DO kyloopi
END DO kxloopi
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