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Commit f94fe388 authored by Antoine Cyril David Hoffmann's avatar Antoine Cyril David Hoffmann
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src/moments_eq_rhs.F90
+ 95
− 93
View file @ f94fe388
......@@ -6,153 +6,154 @@ SUBROUTINE moments_eq_rhs
USE fields
USE fourier_grid
USE model
use prec_const
USE prec_const
IMPLICIT NONE
INTEGER :: ip,ij, ikr,ikz ! loops indices
REAL(dp) :: ip_dp, ij_dp
REAL(dp) :: kr, kz, kperp2
REAL(dp) :: taue_qe_etaB, taui_qi_etaB
REAL(dp) :: kernelj, kerneljp1, kerneljm1, b_e2, b_i2 ! Kernel functions and variable
REAL(dp) :: factj, xb_e2, xb_i2 ! Auxiliary variables
REAL(dp) :: xNapj, xNapp2j, xNapm2j, xNapjp1, xNapjm1 ! factors depending on the pj loop
REAL(dp) :: xphij, xphijp1, xphijm1, xColl
REAL(dp) :: kr, kz, kperp2
REAL(dp) :: taue_qe_etaB, taui_qi_etaB
REAL(dp) :: kernelj, kerneljp1, kerneljm1, b_e2, b_i2 ! Kernel functions and variable
REAL(dp) :: factj, sigmae2_taue_o2, sigmai2_taui_o2 ! Auxiliary variables
REAL(dp) :: xNapj, xNapp2j, xNapm2j, xNapjp1, xNapjm1 ! factors depending on the pj loop
REAL(dp) :: xphij, xphijp1, xphijm1, xColl
COMPLEX(dp) :: TNapj, TNapp2j, TNapm2j, TNapjp1, TNapjm1, Tphi
COMPLEX(dp) :: TColl, TColl20, TColl01, TColl10 ! terms of the rhs
!Precompute species dependant factors
taue_qe_etaB = tau_e/q_e * eta_B
xb_e2 = sigma_e**2 * tau_e!/2.0 ! species dependant factor of the Kernel, squared
taui_qi_etaB = tau_i/q_i * eta_B
xb_i2 = sigma_i**2 * tau_i!/2.0 ! species dependant factor of the Kernel, squared
taue_qe_etaB = tau_e/q_e * eta_B ! factor of the magnetic moment coupling
taui_qi_etaB = tau_i/q_i * eta_B
sigmae2_taue_o2 = sigma_e**2 * tau_e/2.0 ! factor of the Kernel argument
sigmai2_taui_o2 = sigma_i**2 * tau_i/2.0
!!!!!!!!! Electrons moments RHS !!!!!!!!!
Tphi = 0 ! electrostatic potential term
ploope : DO ip = ips_e, ipe_e ! This loop is from 1 to pmaxe+1
ip_dp = REAL(ip-1.,dp) ! REAL index is one minus the loop index (0 to pmax)
ip_dp = REAL(ip-1,dp) ! REAL index is one minus the loop index (0 to pmax)
! N_e^{p+2,j} multiplicator
IF (ip+2 .LE. ipe_e) THEN
IF (ip+2 .LE. pmaxe+1) THEN
xNapp2j = -taue_qe_etaB * SQRT((ip_dp + 1.) * (ip_dp + 2.))
ELSE
xNapp2j = 0.
ENDIF
! N_e^{p-2,j} multiplicator
IF (ip-2 .GE. ips_e) THEN
IF (ip-2 .GE. 1) THEN
xNapm2j = -taue_qe_etaB * SQRT(ip_dp*(ip_dp - 1.))
ELSE
xNapm2j = 0.
ENDIF
factj = 1.0 ! Start of the recursive factorial
jloope : DO ij = ijs_e, ije_e ! This loop is from 1 to jmaxe+1
ij_dp = REAL(ij-1.,dp) ! REAL index is one minus the loop index (0 to jmax)
ij_dp = REAL(ij-1,dp) ! REAL index is one minus the loop index (0 to jmax)
IF (ij_dp .GT. 0) THEN
factj = factj * ij_dp; ! Recursive factorial
ENDIF
! N_e^{p,j+1} multiplicator
IF (ij+1 .LE. ije_e) THEN
IF (ij+1 .LE. jmaxe+1) THEN
xNapjp1 = taue_qe_etaB * (ij_dp + 1.)
ELSE
xNapjp1 = 0.
ENDIF
! N_e^{p,j-1} multiplicator
IF (ij-1 .GE. ijs_e) THEN
IF (ij-1 .GE. 1) THEN
xNapjm1 = taue_qe_etaB * ij_dp
ELSE
xNapjm1 = 0.
ENDIF
! N_e^{pj} multiplicator
xNapj = -taue_qe_etaB * 2.*(ip_dp + ij_dp + 1.)
xNapj = -taue_qe_etaB * 2.*(ip_dp + ij_dp + 1.)
! Collision operator (DK Lenard-Bernstein basis)
xColl = ip_dp + 2.*ij_dp
! ... adding Dougherty terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) ) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) ) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_e(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! phi multiplicator for different kernel numbers
IF (ip .EQ. 1) THEN !(kronecker delta_p^0)
xphij = (eta_n + 2.*ij_dp*eta_T - 2.*eta_B*(ij_dp+1.) )
xphijp1 = -(eta_T - eta_B)*(ij_dp+1.)
xphijm1 = -(eta_T - eta_B)* ij_dp
factj = REAL(Factorial(ij-1),dp)
ELSE IF (ip .EQ. 3) THEN !(kronecker delta_p^2)
xphij = (eta_T/SQRT2 - SQRT2*eta_B)
factj = REAL(Factorial(ij-1),dp)
xphijp1 = 0.; xphijm1 = 0.
ELSE
xphij = 0.; xphijp1 = 0.; xphijm1 = 0.
factj = 1
ENDIF
!write(*,*) '(ip,ij) = (', ip,',', ij,')'
! Loop on kspace
krloope : DO ikr = ikrs,ikre
kzloope : DO ikz = ikzs,ikze
kr = krarray(ikr) ! Poloidal wavevector
kz = kzarray(ikz) ! Toroidal wavevector
kperp2 = kr**2 + kz**2 ! perpendicular wavevector
b_e2 = kperp2 * xb_e2 ! Bessel argument
b_e2 = kperp2 * sigmae2_taue_o2 ! Bessel argument
!! Compute moments and mixing terms
! term propto N_e^{p,j}
TNapj = moments_e(ip,ij,ikr,ikz,updatetlevel) * xNapj
! term propto N_e^{p+2,j}
IF (ip+2 .LE. ipe_e) THEN
IF (ip+2 .LE. pmaxe+1) THEN
TNapp2j = moments_e(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j
ELSE
TNapp2j = 0.
ENDIF
! term propto N_e^{p-2,j}
IF (ip-2 .GE. ips_e) THEN
IF (ip-2 .GE. 1) THEN
TNapm2j = moments_e(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j
ELSE
TNapm2j = 0.
ENDIF
! xterm propto N_e^{p,j+1}
IF (ij+1 .LE. ije_e) THEN
IF (ij+1 .LE. jmaxe+1) THEN
TNapjp1 = moments_e(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1
ELSE
TNapjp1 = 0.
ENDIF
! term propto N_e^{p,j-1}
IF (ij-1 .GE. ijs_e) THEN
IF (ij-1 .GE. 1) THEN
TNapjm1 = moments_e(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1
ELSE
TNapjm1 = 0.
ENDIF
! Collision term completed (DK Dougherty)
! Dougherty Collision terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) .AND. (pmaxe .GE. 2) ) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) .AND. (jmaxe .GE. 1)) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_e(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_e(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_e(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! Total collisional term
TColl = -nu * (xColl * moments_e(ip,ij,ikr,ikz,updatetlevel) &
+ TColl01 + TColl10 + TColl20)
+ TColl01 + TColl10 + TColl20)
!! Electrical potential term
Tphi = 0
IF ( (ip .eq. 1) .or. (ip .eq. 3) ) THEN ! 0 otherwise (krokecker delta_p^0)
IF ( (ip .EQ. 1) .OR. (ip .EQ. 3) ) THEN ! kronecker delta_p^0, delta_p^2
kernelj = b_e2**(ij-1) * exp(-b_e2)/factj
kerneljp1 = kernelj * b_e2 /(ij_dp + 1.)
kerneljm1 = kernelj * ij_dp / b_e2
Tphi = (xphij*Kernelj + xphijp1*Kerneljp1 + xphijm1*Kerneljm1) * phi(ikr,ikz)
Tphi = (xphij*kernelj + xphijp1*kerneljp1 + xphijm1*kerneljm1) * phi(ikr,ikz)
ELSE
Tphi = 0
ENDIF
! Sum of all precomputed terms
moments_rhs_e(ip,ij,ikr,ikz,updatetlevel) = &
imagu * kz * (TNapj + TNapp2j + TNapm2j + TNapjp1 + TNapjm1 + Tphi) + TColl
END DO kzloope
END DO krloope
......@@ -160,37 +161,41 @@ SUBROUTINE moments_eq_rhs
END DO ploope
!!!!!!!!! Ions moments RHS !!!!!!!!!
Tphi = 0 ! electrostatic potential term
ploopi : DO ip = ips_i, ipe_i
ip_dp = REAL(ip-1.,dp)
ip_dp = REAL(ip-1,dp)
! x N_i^{p+2,j}
IF (ip+2 .LE. ipe_i) THEN
IF (ip+2 .LE. pmaxi+1) THEN
xNapp2j = -taui_qi_etaB * SQRT((ip_dp + 1.) * (ip_dp + 2.))
ELSE
xNapp2j = 0.
ENDIF
! x N_i^{p-2,j}
IF (ip-2 .GE. ips_i) THEN
IF (ip-2 .GE. 1) THEN
xNapm2j = -taui_qi_etaB * SQRT(ip_dp * (ip_dp - 1.))
ELSE
xNapm2j = 0.
ENDIF
factj = 1.0 ! Start of the recursive factorial
jloopi : DO ij = ijs_i, ije_i
ij_dp = REAL(ij-1.,dp)
ij_dp = REAL(ij-1,dp)
IF (ij_dp .GT. 0) THEN
factj = factj * ij_dp; ! Recursive factorial
ENDIF
! x N_i^{p,j+1}
IF (ij+1 .LE. ije_i) THEN
IF (ij+1 .LE. jmaxi+1) THEN
xNapjp1 = taui_qi_etaB * (ij_dp + 1.)
ELSE
xNapjp1 = 0.
ENDIF
! x N_i^{p,j-1}
IF (ij-1 .GE. ijs_i) THEN
IF (ij-1 .GE. 1) THEN
xNapjm1 = taui_qi_etaB * ij_dp
ELSE
xNapjm1 = 0.
......@@ -199,38 +204,19 @@ SUBROUTINE moments_eq_rhs
! x N_i^{pj}
xNapj = -taui_qi_etaB * 2.*(ip_dp + ij_dp + 1.)
! Collision term completed (DK Dougherty)
TColl = -nu * (xColl * moments_i(ip,ij,ikr,ikz,updatetlevel) &
+ TColl01 + TColl10 + TColl20)
! ... adding Dougherty terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) ) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) ) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_i(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! Collision operator (DK Lenard-Bernstein basis)
xColl = ip_dp + 2.*ij_dp
! x phi
IF (ip .EQ. 1) THEN !(krokecker delta_p^0)
xphij = (eta_n + 2.*ij_dp*eta_T - 2.*eta_B*(ij_dp+1.) )
xphijp1 = -(eta_T - eta_B)*(ij_dp+1.)
xphijm1 = -(eta_T - eta_B)* ij_dp
factj = REAL(Factorial(ij-1),dp)
ELSE IF (ip .EQ. 3) THEN !(krokecker delta_p^2)
xphij = (eta_T/SQRT2 - SQRT2*eta_B)
factj = REAL(Factorial(ij-1),dp)
xphijp1 = 0.; xphijm1 = 0.
ELSE
xphij = 0.; xphijp1 = 0.; xphijm1 = 0.
factj = 1.
ENDIF
! Loop on kspace
......@@ -239,52 +225,68 @@ SUBROUTINE moments_eq_rhs
kr = krarray(ikr) ! Poloidal wavevector
kz = kzarray(ikz) ! Toroidal wavevector
kperp2 = kr**2 + kz**2 ! perpendicular wavevector
b_i2 = kperp2 * xb_i2 ! Bessel argument
b_i2 = kperp2 * sigmai2_taui_o2 ! Bessel argument
!! Compute moments and mixing terms
! term propto N_i^{p,j}
TNapj = moments_i(ip,ij,ikr,ikz,updatetlevel) * xNapj
! term propto N_i^{p+2,j}
IF (ip+2 .LE. ipe_i) THEN
IF (ip+2 .LE. pmaxi+1) THEN
TNapp2j = moments_i(ip+2,ij,ikr,ikz,updatetlevel) * xNapp2j
ELSE
TNapp2j = 0.
ENDIF
! term propto N_i^{p-2,j}
IF (ip-2 .GE. ips_i) THEN
IF (ip-2 .GE. 1) THEN
TNapm2j = moments_i(ip-2,ij,ikr,ikz,updatetlevel) * xNapm2j
ELSE
TNapm2j = 0.
ENDIF
! xterm propto N_i^{p,j+1}
IF (ij+1 .LE. ije_i) THEN
IF (ij+1 .LE. jmaxi+1) THEN
TNapjp1 = moments_i(ip,ij+1,ikr,ikz,updatetlevel) * xNapjp1
ELSE
TNapjp1 = 0.
ENDIF
! term propto N_i^{p,j-1}
IF (ij-1 .GE. ijs_i) THEN
IF (ij-1 .GE. 1) THEN
TNapjm1 = moments_i(ip,ij-1,ikr,ikz,updatetlevel) * xNapjm1
ELSE
TNapjm1 = 0.
ENDIF
! Collision term completed (Dougherty)
TColl = -nu* (xColl * moments_i(ip,ij,ikr,ikz,updatetlevel))
! Dougherty Collision terms
IF ( (ip .EQ. 1) .AND. (ij .EQ. 2) .AND. (pmaxi .GE. 2)) THEN ! kronecker p0 * j1
TColl01 = 2.0/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl20 = 0.0; TColl10 = 0.0;
ELSEIF ( (ip .EQ. 3) .AND. (ij .EQ. 1) .AND. (jmaxi .GE. 1)) THEN ! kronecker p2 * j0
TColl20 = -SQRT2/3.0*(SQRT2*moments_i(3,1,ikr,ikz,updatetlevel)&
- 2.0*moments_i(1,2,ikr,ikz,updatetlevel))
TColl10 = 0.0; TColl01 = 0.0;
ELSEIF ( (ip .EQ. 2) .AND. (ij .EQ. 1) ) THEN ! kronecker p1 * j0
TColl10 = moments_i(2,1,ikr,ikz,updatetlevel)
TColl20 = 0.0; TColl01 = 0.0;
ELSE
TColl10 = 0.0; TColl20 = 0.0; TColl01 = 0.0;
ENDIF
! Total collisional term
TColl = -nu * (xColl * moments_e(ip,ij,ikr,ikz,updatetlevel) &
+ TColl01 + TColl10 + TColl20)
!! Electrical potential term
Tphi = 0
IF ( (ip .eq. 1) .or. (ip .eq. 3) ) THEN ! 0 otherwise (krokecker delta_p^0, delta_p^2)
IF ( (ip .eq. 1) .or. (ip .eq. 3) ) THEN ! kronecker delta_p^0, delta_p^2
kernelj = b_i2**(ij-1) * exp(-b_i2)/factj
kerneljp1 = kernelj * b_i2 /(ij_dp + 1.)
kerneljm1 = kernelj * ij_dp / b_i2
Tphi = (xphij*Kernelj + xphijp1*Kerneljp1 + xphijm1*Kerneljm1) * phi(ikr,ikz)
Tphi = (xphij*kernelj + xphijp1*kerneljp1 + xphijm1*kerneljm1) * phi(ikr,ikz)
ELSE
Tphi = 0
ENDIF
! Sum of all precomputed terms
moments_rhs_i(ip,ij,ikr,ikz,updatetlevel) = &
imagu * kz * (TNapj + TNapp2j + TNapm2j + TNapjp1 + TNapjm1 + Tphi) + TColl
END DO kzloopi
END DO krloopi
......
src/poisson.F90
+ 28
− 36
View file @ f94fe388
......@@ -13,82 +13,74 @@ SUBROUTINE poisson
INTEGER :: ikr,ikz, ini,ine, i0j
REAL(dp) :: ini_dp, ine_dp
REAL(dp) :: kr, kz, kperp2
REAL(dp) :: Kn, Kn2 ! sub kernel factor for recursive build
REAL(dp) :: Kne, Kni ! sub kernel factor for recursive build
REAL(dp) :: b_e2, b_i2, alphaD
REAL(dp) :: sigmae2_taue_o2, sigmai2_taui_o2, qe2_taue, qi2_taui ! To avoid redondant computation
COMPLEX(dp) :: gammaD, gammaphi
COMPLEX(dp) :: sum_kernel2_e, sum_kernel2_i ! Store to compute sum Kn^2
COMPLEX(dp) :: sum_kernel_mom_e, sum_kernel_mom_i ! Store to compute sum Kn*Napn
REAL(dp) :: sum_kernel2_e, sum_kernel2_i ! Store sum Kn^2
COMPLEX(dp) :: sum_kernel_mom_e, sum_kernel_mom_i ! Store sum Kn*Napn
REAL(dp) :: gammaD
COMPLEX(dp) :: gammaD_phi
!Precompute species dependant factors
sigmae2_taue_o2 = sigma_e**2 * tau_e/2.
sigmae2_taue_o2 = sigma_e**2 * tau_e/2. ! factor of the Kernel argument
sigmai2_taui_o2 = sigma_i**2 * tau_i/2.
qe2_taue = (q_e**2)/tau_e
qe2_taue = (q_e**2)/tau_e ! factor of the gammaD sum
qi2_taui = (q_i**2)/tau_i
DO ikr=ikrs,ikre
DO ikz=ikzs,ikze
kr = krarray(ikr)
kz = kzarray(ikz)
kr = krarray(ikr)
kz = kzarray(ikz)
kperp2 = kr**2 + kz**2
!! Electrons sum(Kernel * Ne0n) (skm) and sum(Kernel**2) (sk2)
b_e2 = kperp2 * sigmae2_taue_o2 ! non dim kernel argument (kperp2 sigma_a sqrt(2 tau_a))
! Initialization for n = 0 (ine = 1)
Kn = 1.
Kn2 = 1.
sum_kernel_mom_e = moments_e(1,1,ikr,ikz,updatetlevel)
sum_kernel2_e = Kn2
Kne = exp(-b_e2)
sum_kernel_mom_e = Kne*moments_e(1, 1, ikr, ikz, updatetlevel)
sum_kernel2_e = Kne**2
! loop over n only if the max polynomial degree is 1 or more
if (jmaxe .GT. 0) then
DO ine=1,jmaxe+1 ! ine = n+1
DO ine=2,jmaxe+1 ! ine = n+1
ine_dp = REAL(ine-1,dp)
Kn = Kn * b_e2/(ine_dp+1) ! We update iteratively the kernel functions (to spare factorial computations)
Kn2 = Kn2 *(b_e2/(ine_dp+1))**2 ! the exp term is still missing but does not depend on ine ...
Kne = Kne * b_e2/ine_dp ! We update iteratively the kernel functions (to spare factorial computations)
sum_kernel_mom_e = sum_kernel_mom_e + Kn * moments_e(1,ine,ikr,ikz,updatetlevel)
sum_kernel2_e = sum_kernel2_e + Kn2 ! ... sum recursively ...
sum_kernel_mom_e = sum_kernel_mom_e + Kne * moments_e(1, ine, ikr, ikz, updatetlevel)
sum_kernel2_e = sum_kernel2_e + Kne**2 ! ... sum recursively ...
END DO
endif
sum_kernel_mom_e = sum_kernel_mom_e * exp(-b_e2) ! ... multiply the final sum with the missing exponential term
sum_kernel2_e = sum_kernel2_e * exp(-2.*b_e2) ! and its squared using exp(x)^2 = exp(2x).
!! Ions sum(Kernel * Ni0n) (skm) and sum(Kernel**2) (sk2)
b_i2 = kperp2 * sigmai2_taui_o2
! Initialization for n = 0 (ini = 1)
Kn = 1.
Kn2 = 1.
sum_kernel_mom_i = moments_i(1, 1, ikr, ikz, updatetlevel)
sum_kernel2_i = Kn2
Kni = exp(-b_i2)
sum_kernel_mom_i = Kni*moments_i(1, 1, ikr, ikz, updatetlevel)
sum_kernel2_i = Kni**2
! loop over n only if the max polynomial degree is 1 or more
if (jmaxi .GT. 0) then
DO ini=1,jmaxi+1
DO ini=2,jmaxi+1
ini_dp = REAL(ini-1,dp) ! Real index (0 to jmax)
Kn = Kn * b_i2/(ini_dp+1) ! We update iteratively the kernel functions this time for ions ...
Kn2 = Kn2 *(b_i2/(ini_dp+1.))**2
Kni = Kni * b_i2/ini_dp ! We update iteratively the kernel functions this time for ions ...
sum_kernel_mom_i = sum_kernel_mom_i + Kn * moments_i(1,ini,ikr,ikz,updatetlevel)
sum_kernel2_i = sum_kernel2_i + Kn2 ! ... sum recursively ...
sum_kernel_mom_i = sum_kernel_mom_i + Kni * moments_i(1, ini, ikr, ikz, updatetlevel)
sum_kernel2_i = sum_kernel2_i + Kni**2 ! ... sum recursively ...
END DO
endif
sum_kernel_mom_i = sum_kernel_mom_i * exp(-b_i2) ! ... multiply the final sum with the missing exponential term.
sum_kernel2_i = sum_kernel2_i * exp(-2.*b_i2)
!!! Assembling the poisson equation
alphaD = kperp2 * lambdaD**2.
alphaD = kperp2 * lambdaD**2
gammaD = alphaD + qe2_taue * (1. - sum_kernel2_e) &
+ qi2_taui * (1. - sum_kernel2_i)
gammaphi = q_e * sum_kernel_mom_e + q_i * sum_kernel_mom_i ! gamma_D * phi term
gammaD_phi = q_e * sum_kernel_mom_e + q_i * sum_kernel_mom_i ! gamma_D * phi term
phi(ikr, ikz) = gammaphi/gammaD
phi(ikr, ikz) = gammaD_phi/gammaD
END DO
END DO
......
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