200 lines
6.7 KiB
Fortran
200 lines
6.7 KiB
Fortran
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!
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!=======================================================================
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!
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MODULE COULOMB_LOG
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!
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! This module provides Coulomb logarithms
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!
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USE ACCURACY_REAL
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!
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CONTAINS
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!
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!
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!=======================================================================
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!
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FUNCTION COU_LOG(I_CL,DMN,T,RS)
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!
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! This function computes the Coulomb logarithm Log(Gamma)
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!
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! References: (1) F. L. Hinton, chapter 1.5, in "Handbook of Plasma Physics",
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! Eds. M. N. Rosenbluth and R. Z. Sagdeev,
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! Vol.1 (1983)
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! (2) https://ocw.mit.edu/courses/nuclear-engineering/
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! 22-611j-introduction-to-plasma-physics-i-fall-2006/
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! readings/chap3.pdf
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! (3) http://homepages.cae.wisc.edu/~callen/chap2.pdf
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! (4) https://www.nrl.navy.mil/ppd/sites/www.nrl.navy.mil.ppd/
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! files/pdfs/NRL_FORMULARY_18.pdf
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!
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! Input parameters:
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!
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! * I_CL : Switch to compute the Coulomb logarithm
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! I_CL = 1 --> using reference (1)
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! I_CL = 2 --> using reference (2)
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! I_CL = 3 --> using reference (3)
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! I_CL = 4 --> using reference (4)
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! I_CL = 5 --> using reference (5)
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! * DMN : dimension of the system
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! DMN = '3D'
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! DMN = '2D'
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! DMN = '1D'
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! * T : system temperature in SI
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! * RS : Wigner-Seitz radius (in units of a_0)
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!
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!
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! Output parameters:
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!
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! * COU_LOG : Coulomb logarithm Log(Gamma)
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 11 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : ONE,TWO,THIRD
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USE CONSTANTS_P1, ONLY : H_BAR,M_E,E,EPS_0,COULOMB,K_B
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USE PI_ETC, ONLY : PI_INV
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USE SCREENING_VEC, ONLY : DEBYE_VECTOR
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USE ENE_CHANGE, ONLY : EV
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!
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IMPLICIT NONE
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!
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CHARACTER*2 DMN
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!
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INTEGER I_CL
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!
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REAL*8 T,RS
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REAL*8 COU_LOG,G,LG
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REAL*8 KD_SI,V_TH,T_TH,LD,B0,B1,B2,BM,N0
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!
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! Computing the Debye vector
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!
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CALL DEBYE_VECTOR(DMN,T,RS,KD_SI) !
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!
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V_TH=DSQRT(TWO*K_B*T/M_E) ! thermal velocity in 3D
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T_TH=K_B*T/EV ! temperature in eV
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!
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IF(I_CL.EQ.1) THEN !
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!
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LD=ONE/KD_SI ! Spitzer value
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B0=E*E*THIRD/(K_B*T) !
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COU_LOG=DLOG(LD/B0) ! ref. (2) eq. (5)
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!
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ELSE IF(I_CL.EQ.2) THEN !
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!
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G=DSQRT(EPS_0*T/(N0*E*E))*M_E*V_TH*V_TH/COULOMB ! ref. (2) eq. (3.63)
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COU_LOG=DLOG(G) !
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!
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ELSE IF(I_CL.EQ.3) THEN !
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!
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B1=KD_SI*KD_SI*PI_INV/(12.0E0_WP*N0) !
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B2=H_BAR/(TWO*M_E*V_TH) !
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BM=MAX(B1,B2) ! ref. (3) eq. (2.11)
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G=KD_SI/BM !
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COU_LOG=DLOG(G) !
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!
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ELSE IF(I_CL.EQ.4) THEN !
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!
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LG=23.5E0_WP - DLOG(DSQRT(N0)*(T_TH**(-1.25E0_WP))) - & !
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DSQRT(1.0E-5_WP + (DLOG(T_TH)-TWO)**2 / 16.0E0_WP) !
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COU_LOG=LG !
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!
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ELSE IF(I_CL.EQ.5) THEN !
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!
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CONTINUE
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!
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END IF !
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!
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END FUNCTION COU_LOG
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!
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!
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!=======================================================================
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!
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FUNCTION DALI_CL_3D(X)
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!
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! This function computes Daligault' expression of the Coulomb logarithm
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!
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!
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! Reference: (1) J. Daligault, Phys. Rev. Lett. 119, 045002 (2017)
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!
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!
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! Input parameters:
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!
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! * X : dimensionless factor --> X = q / (2 * k_F)
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!
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!
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! Note: It is defined as
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!
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! / A 3
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! | q
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! CL = | ---------------- dq with q the screening vector
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! | 2 2 2 s
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! / 0 ( q + q )
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! s
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! _____________
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! /
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! and A ~ k \ / 4 Theta / 3 with Theta the degeneracy parameter
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! F \/
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!
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!
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! We use here the fact that CL writes
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! _ _
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! | 2 | A
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! | q |
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! 1 | s ( 2 2 ) |
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! --- | ----------- + Log( q + q ) |
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! 2 | 2 2 ( s ) |
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! | q + q |
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! |_ s _| 0
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!
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!
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! Author : D. Sébilleau
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!
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!
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! Last modified : 12 Oct 2020
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!
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!
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USE MATERIAL_PROP, ONLY : RS
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USE EXT_FIELDS, ONLY : T
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!
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USE REAL_NUMBERS, ONLY : ONE,FOUR,HALF,THIRD
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USE FERMI_SI, ONLY : KF_SI
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!
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USE PLASMON_SCALE_P, ONLY : NONID
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USE SCREENING_TYPE
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USE SCREENING_VEC
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: X
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REAL (WP) :: DALI_CL_3D
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REAL (WP) :: TH
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REAL (WP) :: KS,DQT2,NUM,DEN
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REAL (WP) :: INT_0,INT_A
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!
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REAL (WP) :: LOG
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!
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TH = ONE / NONID ! Theta
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DQT2 = KF_SI * KF_SI * FOUR * THIRD * TH ! (upper integration bound)^2
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!
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! Computing the screening vector
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!
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IF(SC_TYPE == 'NO') THEN !
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CALL SCREENING_VECTOR('TF','3D',X,RS,T,KS) !
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ELSE !
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CALL SCREENING_VECTOR(SC_TYPE,'3D',X,RS,T,KS) ! in SI
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END IF !
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!
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NUM = KS * KS !
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DEN = NUM + DQT2 !
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!
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INT_0 = HALF * ( ONE + LOG(NUM) ) !
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INT_A = HALF * ( NUM / DEN + LOG(DEN) ) !
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!
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DALI_CL_3D = INT_A - INT_0 !
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!
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END FUNCTION DALI_CL_3D
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!
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END MODULE COULOMB_LOG
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