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gyacomo/src/poisson.F90
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poisson.F90
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SUBROUTINE poisson
! Solve poisson equation to get phi
USE time_integration, ONLY: updatetlevel
USE array
USE fields
USE grid
use model, ONLY : tau_e, tau_i, sigma_e, sigma_i, q_e, q_i, lambdaD, DK
USE prec_const
IMPLICIT NONE
INTEGER :: ini,ine, i0j
REAL(dp) :: ini_dp, ine_dp
REAL(dp) :: kr, kz, kperp2
REAL(dp) :: Kne, Kni ! sub kernel factor for recursive build
REAL(dp) :: be_2, bi_2, alphaD
REAL(dp) :: sigmae2_taue_o2, sigmai2_taui_o2, qe2_taue, qi2_taui ! To avoid redondant computation
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._dp ! factor of the Kernel argument
sigmai2_taui_o2 = sigma_i**2 * tau_i/2._dp ! (b_a/2)^2 = (kperp sqrt(2 tau_a) sigma_a/2)^2
! = kperp^2 tau_a sigma_a^2/2
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)
kperp2 = kr**2 + kz**2
! non dim kernel argument (kperp2 sigma_a sqrt(2 tau_a))
be_2 = kperp2 * sigmae2_taue_o2
bi_2 = kperp2 * sigmai2_taui_o2
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!! Electrons sum(Kernel * Ne0n) (skm) and sum(Kernel**2) (sk2)
!! Sum(kernel * Moments_0n)
! Initialization for n = 0 (ine = 1)
Kne = exp(-be_2)
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=2,jmaxe+1 ! ine = n+1
ine_dp = REAL(ine-1,dp)
! We update iteratively the kernel functions (to spare factorial computations)
Kne = Kne * be_2/ine_dp
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
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!! Ions sum(Kernel * Ni0n) (skm) and sum(Kernel**2) (sk2)
!! Sum(kernel * Moments_0n)
! Initialization for n = 0 (ini = 1)
Kni = exp(-bi_2)
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=2,jmaxi+1
ini_dp = REAL(ini-1,dp) ! Real index (0 to jmax)
! We update iteratively to spare factorial computations
Kni = Kni * bi_2/ini_dp
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
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!! Assembling the poisson equation !!!!!!!!!!!!!!!!!!!!!!!!!!
alphaD = kperp2 * lambdaD**2
gammaD = alphaD + qe2_taue * (1._dp - sum_kernel2_e) & ! Called Poisson_ in MOLI
+ qi2_taui * (1._dp - sum_kernel2_i)
gammaD_phi = q_e * sum_kernel_mom_e + q_i * sum_kernel_mom_i
IF ( (gammaD .EQ. 0) .AND. (abs(kr)+abs(kz) .NE. 0._dp) ) THEN
WRITE(*,*) 'Warning gammaD = 0', sum_kernel2_i
ENDIF
phi(ikr, ikz) = gammaD_phi/gammaD
END DO
END DO
! Cancel origin singularity
phi(ikr_0,ikz_0) = 0
END SUBROUTINE poisson
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