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nonlinsK.f90
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nonlinsK.f90
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MODULE NONLIN
! routines for 3-wave interactions and S-wave evolution
CONTAINS
!
!SUBROUTINE soundwaves(w_s, w_l_new, omega, density)
!
! USE CONSTANTS
!
! USE PARAMETERS
!
! IMPLICIT NONE
!
! REAL(KIND=8), DIMENSION(-n_kv:n_kv,n_xp+3), INTENT(INOUT) :: W_s, w_l_new
! REAL(KIND=8), DIMENSION(:), INTENT(IN) :: omega, density
! REAL(KIND=8), DIMENSION(:,:), ALLOCATABLE :: gamma_s_kd
! REAL(KIND=8), DIMENSION(-n_kv:n_kv) :: omega_s_om, s_terms, damping,s_terms2, a_l2, l_terms
! REAL(KIND=8), DIMENSION(-n_kv:n_kv) :: n_l, n_s, a_l, a_s, a_s2, omega_l_om, a_lnew, a_l2new
! REAL(KIND=8), DIMENSION(:), ALLOCATABLE :: alpha_is_d
! REAL(KIND=8):: t_is, dt_is, t_is_new, frac1, frac2, NL1, NL2, ns1, ns2
! INTEGER(KIND=4)::i, j
!
!
!
! ALLOCATE(gamma_s_kd(-n_kv:n_kv,n_xp+3))
! ALLOCATE(alpha_is_d(n_xp+3))
!
!
!! defining the various constants involved...................................................
!
!
!
! DO j= 1, n_xp+3
! gamma_s_kd(:,j) = gamma_s*omega(j)*abs(k_x)
!
! ENDDO
!
! alpha_is_d = alpha_is*density/omega/omega
!
!
!
!! define frequency for L, S waves ..........................................
! omega_l_om = (1.+3.*k_x**2/2.)
! omega_s_om = v_s*abs(k_x)*k_s_stretch/v_t
!
!
!! subcyling all IS wave processes.......................................................
!
! DO j= 3, n_xp+2
! t_is=0.
! dt_is = dt_ql/4.
!
! DO WHILE (abs(t_is - dt_ql) .GE. tiny(1.e0))
!
!! wave occupation numbers.................................................................
!
! n_l(:) = w_l_new(:,j)/omega_l_om(:)
! n_s(:) = w_s(:,j)/omega_s_om(:)
!
! n_s(0)=0.
! n_l(0)=0.
!!wave wave square bracket terms............................................................
! a_s(:)=0.
! a_s2(:)=0.
! a_l(:)=0.
! a_l2(:)=0.
!
!
!
! DO i=-lpc, -1
!
!
! nl2 = sum(N_L(ind_2pl(i)+up_2pl(i):ind_2pl(i)))
! ns2 = sum(N_s(ind_pls(i):ind_pls(i)+up_pls(i)))
!
!
!! evolution of all wave spectral energy densities in SINGLE L <--> L /pm s encounter
!! forces conservation of energy in the scattering process
!! handles both 1-1, 1-many and many-1 situations
!
! a_l(i) = a_l(i) + ns2*nl2 !+ Ns1*NL1
! a_l2(i) = a_l2(i) - nl2 - ns2 !+ nl1 - nl2
!
! a_l(ind_2pl(i)+up_2pl(i):ind_2pl(i)) = a_l(ind_2pl(i)+up_2pl(i):ind_2pl(i)) + ns2*n_l(i)*frac_2pl(i)
! a_l2(ind_2pl(i)+up_2pl(i):ind_2pl(i)) = a_l2(ind_2pl(i)+up_2pl(i):ind_2pl(i)) - (ns2 -n_l(i))*frac_2pl(i)
!
! a_s(ind_pls(i):ind_pls(i)+up_pls(i)) = a_s(ind_pls(i):ind_pls(i)+up_pls(i)) + n_l(i)*nl2*frac_pls(i)
! a_s2(ind_pls(i):ind_pls(i)+up_pls(i)) = a_s2(ind_pls(i):ind_pls(i)+up_pls(i)) + (n_l(i) - nl2)*frac_pls(i)
!
!
! ENDDO
!
!
! DO i=-1, lpc
!
!! wave ocupation numbers involved
!
! nl2 = sum(N_L(ind_2pl(i):ind_2pl(i)+up_2pl(i)))
! ns2 = sum(N_s(ind_pls(i):ind_pls(i)+up_pls(i)))
!
!
!! evolution of all wave spectral energy densities in SINGLE L <--> L /pm s encounter
!! forces conservation of energy in the scattering process
!! handles both 1-1, 1-many and many-1 situations
!
! a_l(i) = a_l(i) + ns2*nl2 !+ Ns1*NL1
! a_l2(i) = a_l2(i) - nl2 - ns2 !+ nl1 - nl2
!
! a_l(ind_2pl(i):ind_2pl(i)+up_2pl(i)) = a_l(ind_2pl(i):ind_2pl(i)+up_2pl(i)) + ns2*n_l(i)*frac_2pl(i)
! a_l2(ind_2pl(i):ind_2pl(i)+up_2pl(i)) = a_l2(ind_2pl(i):ind_2pl(i)+up_2pl(i)) - (ns2 -n_l(i))*frac_2pl(i)
!
! a_s(ind_pls(i):ind_pls(i)+up_pls(i)) = a_s(ind_pls(i):ind_pls(i)+up_pls(i)) + n_l(i)*nl2*frac_pls(i)
! a_s2(ind_pls(i):ind_pls(i)+up_pls(i)) = a_s2(ind_pls(i):ind_pls(i)+up_pls(i)) + (n_l(i) - nl2)*frac_pls(i)
!
!
!
!
! ENDDO
!
!
! a_L(0)=0.
! A_L2(0)=0.
! a_s(0)=0.
! a_s2(0)=0.
!
! s_terms= (alpha_is_d(j)*a_s2/2. -gamma_s_kd(:,j))
! s_terms2 = a_s *alpha_is_d(j)*omega_s_om/2.
! l_terms = a_L2*alpha_is_d(j)
!
!! subcycle timestep determination at given space pt
! dt_is =min(0.1/(maxval(s_terms)+tiny(1.d0)), 1./(maxval(l_terms(-lpc:lpc))+tiny(1.d0)), dt_ql/4.)
!! if(j== 50) print*, j, dt_is
!! dt_is=dt_ql/5.
! t_is_new=min(t_is + dt_is, dt_ql)
! dt_is = t_is_new-t_is
! t_is = t_is_new
!
!! w_l_new(:,j) = W_L_new(:,j) + alpha_is_d(j)*omega_l_om*dt_is*(a_L + a_l2*N_L)
! w_l_new(:,j) = (W_L_new(:,j) + a_L*alpha_is_d(j)*omega_l_om*dt_is)/(1. - dt_is*l_terms)
!
! W_s(:,j) = (W_s(:,j) + s_terms2*dt_is)/(1.- dt_is*s_terms)
!! w_s(:,j) = w_s(:,j) + dt_is *(s_terms
!
!! semi-implicit evolution of wave spectral enery densities
!
! where(w_s(:,j) .LE. 0) w_s(:,j) = 0.
! w_s(0 , j) = 0.
!
!
! ENDDO
!! time loop
!! print*, 'done subloop.....................................', j
! ENDDO
!! spatial coordinate loop
!
! DEALLOCATE( gamma_s_kd, alpha_is_d)
!
!END SUBROUTINE soundwaves
SUBROUTINE soundwaves_with_em(w_s, w_l_new, w_em, omega, density)
USE CONSTANTS
USE PARAMETERS
IMPLICIT NONE
REAL(KIND=8), DIMENSION(-n_kv:n_kv,n_xp+3), INTENT(INOUT) :: W_s, w_l_new, w_em
REAL(KIND=8), DIMENSION(:), INTENT(IN) :: omega, density
REAL(KIND=8), DIMENSION(:,:), ALLOCATABLE :: gamma_s_kd, gamma_d_f
REAL(KIND=8), DIMENSION(-n_kv:n_kv) :: omega_s_om, s_terms, damping,s_terms2, a_l2, l_terms, em_terms
REAL(KIND=8), DIMENSION(-n_kv:n_kv):: omega_emf_om, w_f0_om, w_f0
REAL(KIND=8), DIMENSION(-n_kv:n_kv) :: n_l, n_s, a_l, a_s, a_s2, omega_l_om, a_eme,a_eml, a_ems, n_em, a_eme2
REAL(KIND=8), DIMENSION(:), ALLOCATABLE :: alpha_is_d, alpha_em
INTEGER(KIND=4)::i, j
REAL(KIND=8):: t_is, dt_is, t_is_new, frac1, frac2, NL1, NL2, ns1, ns2, nee, nel, nes
ALLOCATE(gamma_s_kd(-n_kv:n_kv,n_xp+3))
ALLOCATE(gamma_d_f(-n_kv:n_kv,n_xp+3))
ALLOCATE(alpha_is_d(n_xp+3))
ALLOCATE(alpha_em(n_xp+3))
! defining the various constants involved...................................................
DO j= 3, n_xp+2
gamma_s_kd(:,j) = gamma_s*omega(j)*abs(k_x)
gamma_d_f(:,j) = gamma_d_emf*omega(j)*omega(j)
ENDDO
alpha_is_d = alpha_is*density/omega/omega
alpha_em = alpha_em_f*omega*omega/density
W_f0_om = kbTe_1d *k_f*k_f/(v_t*v_t)
! define frequency for L, S, T waves ..........................................
omega_l_om = (1.+3.*k_x**2/2.)
omega_s_om = v_s*abs(k_x)*k_s_stretch/v_t
omega_emf_om = sqrt(1.+v_c**2/v_t**2 *k_f**2)
! subcyling all IS wave processes.......................................................
DO j= 3, n_xp+2
w_f0=w_f0_om*omega(j)*omega(j)
t_is=0.
dt_is = dt_ql/5.
DO WHILE (abs(t_is - dt_ql) .GE. tiny(1.e0))
! wave occupation numbers.................................................................
n_l = w_l_new(:,j)/omega_l_om
n_s = w_s(:,j)/omega_s_om
n_em = w_em(:,j)/omega_emf_om
n_s(0)=0.
n_l(0)=0.
n_em(0)=0.
!wave wave square bracket terms............................................................
a_s=0.
a_s2=0.
a_l=0.
a_l2=0.
a_eme=0.
a_eme2=0.
a_eml=0.
a_ems=0.
DO i=-lpc, -2
! cycle
nl2 = sum(N_L(ind_2pl(i)-up_2pl(i)+1:ind_2pl(i)-1))+ frac_2pl(i,2)*n_l(ind_2pl(i)-up_2pl(i))+ frac_2pl(i,1)*n_l(ind_2pl(i))
ns2 = sum(N_s(ind_pls(i)+1:ind_pls(i)+up_pls(i)-1))+frac_pls(i,1)*n_s(ind_2pl(i))+ frac_pls(i,2)*n_s(ind_pls(i)+up_pls(i))
! evolution of all wave spectral energy densities in SINGLE L <--> L /pm s encounter
! forces conservation of energy in the scattering process
! handles both 1-1, 1-many and many-1 situations
a_l(i) = a_l(i) + ns2*nl2 !+ Ns1*NL1
a_l2(i) = a_l2(i) - nl2 - ns2 !+ nl1 - nl2
a_l(ind_2pl(i)-up_2pl(i)+1:ind_2pl(i)-1) = a_l(ind_2pl(i)-up_2pl(i)+1:ind_2pl(i)-1) + ns2*n_l(i)/frac_2pl(i,3)
a_l(ind_2pl(i)-up_2pl(i))= a_l(ind_2pl(i)-up_2pl(i)) + ns2*n_l(i)*frac_2pl(i,2)/frac_2pl(i,3)
a_l(ind_2pl(i))= a_l(ind_2pl(i)) + ns2*n_l(i)*frac_2pl(i,1)/frac_2pl(i,3)
a_l2(ind_2pl(i)-up_2pl(i)+1:ind_2pl(i)-1) = a_l2(ind_2pl(i)-up_2pl(i)+1:ind_2pl(i)-1) - (ns2 -n_l(i))/frac_2pl(i,3)
a_l2(ind_2pl(i)-up_2pl(i))= a_l2(ind_2pl(i)-up_2pl(i)) -(ns2 -n_l(i))*frac_2pl(i,2)/frac_2pl(i,3)
a_l2(ind_2pl(i))= a_l2(ind_2pl(i)) -(ns2 -n_l(i))*frac_2pl(i,1)/frac_2pl(i,3)
a_s(ind_pls(i)+1:ind_pls(i)+up_pls(i)-1) = a_s(ind_pls(i)+1:ind_pls(i)+up_pls(i)-1) + n_l(i)*nl2/frac_pls(i,3)
a_s(ind_pls(i)) = a_s(ind_pls(i)) + n_l(i)*nl2*frac_pls(i,1)/frac_pls(i,3)
a_s(ind_pls(i)+up_pls(i)) = a_s(ind_pls(i)+up_pls(i)) + n_l(i)*nl2*frac_pls(i,2)/frac_pls(i,3)
a_s2(ind_pls(i)+1:ind_pls(i)+up_pls(i)-1) = a_s2(ind_pls(i)+1:ind_pls(i)+up_pls(i)-1) + (n_l(i) - nl2)/frac_pls(i,3)
a_s2(ind_pls(i)) = a_s2(ind_pls(i)) + (n_l(i) - nl2)*frac_pls(i,1)/frac_pls(i,3)
a_s2(ind_pls(i)+up_pls(i)) = a_s2(ind_pls(i)+up_pls(i)) + (n_l(i) - nl2)*frac_pls(i,2)/frac_pls(i,3)
ENDDO
DO i=2, lpc
! wave ocupation numbers involved
nl2 = sum(N_L(ind_2pl(i)+1:ind_2pl(i)+up_2pl(i)-1))+frac_2pl(i,1)*n_l(ind_2pl(i))+frac_2pl(i,2)*n_l(ind_2pl(i)+up_2pl(i))
ns2 = sum(N_s(ind_pls(i)-up_pls(i)+1:ind_pls(i)-1))+frac_pls(i,2)*n_s(ind_pls(i)-up_pls(i))+frac_pls(i,1)*n_s(ind_pls(i))
! evolution of all wave spectral energy densities in SINGLE L <--> L /pm s encounter
! forces conservation of energy in the scattering process
! handles both 1-1, 1-many and many-1 situations
a_l(i) = a_l(i) + ns2*nl2
a_l2(i) = a_l2(i) - nl2 - ns2
a_l(ind_2pl(i)+1:ind_2pl(i)+up_2pl(i)-1 )= a_l(ind_2pl(i)+1:ind_2pl(i)+up_2pl(i)-1) + ns2*n_l(i)/frac_2pl(i,3)
a_l(ind_2pl(i))= a_l(ind_2pl(i)) + ns2*n_l(i)*frac_2pl(i,1)/frac_2pl(i,3)
a_l(ind_2pl(i)+up_2pl(i))= a_l(ind_2pl(i)+up_2pl(i)) + ns2*n_l(i)*frac_2pl(i,2)/frac_2pl(i,3)
a_l2(ind_2pl(i)+1:ind_2pl(i)+up_2pl(i)-1)= a_l2(ind_2pl(i)+1:ind_2pl(i)+up_2pl(i)-1) - (ns2 -n_l(i))/frac_2pl(i,3)
a_l2(ind_2pl(i))= a_l2(ind_2pl(i)) -(ns2 -n_l(i))*frac_2pl(i,1)/frac_2pl(i,3)
a_l2(ind_2pl(i)+up_2pl(i))= a_l2(ind_2pl(i)+up_2pl(i)) -(ns2 -n_l(i))*frac_2pl(i,2)/frac_2pl(i,3)
! a_l2(ind_2pl(i):ind_2pl(i)+up_2pl(i)) = a_l2(ind_2pl(i):ind_2pl(i)+up_2pl(i)) - (ns2 -n_l(i))*frac_2pl(i)
a_s(ind_pls(i)-up_pls(i)+1:ind_pls(i)-1) = a_s(ind_pls(i)-up_pls(i)+1:ind_pls(i)-1) + n_l(i)*nl2/frac_pls(i,3)
a_s(ind_pls(i)-up_pls(i)) = a_s(ind_pls(i)-up_pls(i)) + n_l(i)*nl2*frac_pls(i,2)/frac_pls(i,3)
a_s(ind_pls(i)) = a_s(ind_pls(i)) + n_l(i)*nl2*frac_pls(i,1)/frac_pls(i,3)
a_s2(ind_pls(i)-up_pls(i)+1:ind_pls(i)-1) = a_s2(ind_pls(i)-up_pls(i)+1:ind_pls(i)-1) + (n_l(i) - nl2)/frac_pls(i,3)
a_s2(ind_pls(i)-up_pls(i)) = a_s2(ind_pls(i)-up_pls(i)) + (n_l(i) - nl2)*frac_pls(i,2)/frac_pls(i,3)
a_s2(ind_pls(i)) = a_s2(ind_pls(i)) + (n_l(i) - nl2)*frac_pls(i,1)/frac_pls(i,3)
ENDDO
DO i=-n_kv, -lpe
nel = n_l(i)
nes = n_s(ind_fs(i))
nee = sum(n_em(ind_fe(i):ind_fe(i)+up_fe(i)))
! evolution of all wave spectral energy densities in SINGLE L <--> T + s encounter
! forces conservation of energy in the scattering process
! WILL BE FIXED TO handle both 1-1, 1-many and many-1 situations
a_eml(i) = a_eml(i) + nes*nel - nes*nee + nel*nee
a_ems(ind_fs(i)) = a_ems(ind_fs(i)) + nes*nel - nes*nee + nel*nee
a_eme(ind_fe(i):ind_fe(i)+up_fe(i)) = a_eme(ind_fe(i):ind_fe(i)+up_fe(i)) + (-nes*nel)*frac_fe(i)
a_eme2(ind_fe(i):ind_fe(i)+up_fe(i)) = a_eme2(ind_fe(i):ind_fe(i)+up_fe(i)) + (nes - nel)*frac_fe(i)
ENDDO
DO i=lpe, n_kv
nel = n_l(i)
nes = n_s(ind_fs(i))
nee = sum(n_em(ind_fe(i):ind_fe(i)+up_fe(i)))
! evolution of all wave spectral energy densities in SINGLE L <--> T + s encounter
! forces conservation of energy in the scattering process
! WILL BE FIXED TO handle both 1-1, 1-many and many-1 situations
a_eml(i) = a_eml(i) + nes*nel - nes*nee + nel*nee
a_ems(ind_fs(i)) = a_ems(ind_fs(i)) + nes*nel - nes*nee + nel*nee
! a_eme(ind_fe(i)) = a_eme(ind_fe(i)) - nes*nel + nes*nee - nel*nee
a_eme(ind_fe(i):ind_fe(i)+up_fe(i)) = a_eme(ind_fe(i):ind_fe(i)+up_fe(i)) + (-nes*nel)*frac_fe(i)
a_eme2(ind_fe(i):ind_fe(i)+up_fe(i)) = a_eme2(ind_fe(i):ind_fe(i)+up_fe(i)) + ( nes - nel)*frac_fe(i)
ENDDO
DO i=-n_kv, -lpe
nel = n_l(i)
nes = n_s(ind_fs(i))
nee = sum(n_em(ind_fe2(i):ind_fe2(i)+up_fe2(i)))
! evolution of all wave spectral energy densities in SINGLE L <--> T - s encounter
! forces conservation of energy in the scattering process
! WILL BE FIXED TO handle both 1-1, 1-many and many-1 situations
a_eml(i) = a_eml(i) - nes*nel + nes*nee + nel*nee
a_ems(ind_fs(i)) = a_ems(ind_fs(i)) - nes*nel + nes*nee + nel*nee
a_eme(ind_fe2(i):ind_fe2(i)+up_fe2(i)) = a_eme(ind_fe2(i):ind_fe2(i)+up_fe2(i)) + (nes*nel)*frac_fe2(i)
a_eme2(ind_fe2(i):ind_fe2(i)+up_fe2(i)) = a_eme2(ind_fe2(i):ind_fe2(i)+up_fe2(i)) + (- nes - nel)*frac_fe2(i)
ENDDO
DO i=lpe, n_kv
nel = n_l(i)
nes = n_s(ind_fs(i))
nee = sum(n_em(ind_fe2(i):ind_fe2(i)+up_fe2(i)))
! evolution of all wave spectral energy densities in SINGLE L <--> T - s encounter
! forces conservation of energy in the scattering process
! WILL BE FIXED TO handle both 1-1, 1-many and many-1 situations
a_eml(i) = a_eml(i) - nes*nel + nes*nee + nel*nee
a_ems(ind_fs(i)) = a_ems(ind_fs(i)) - nes*nel + nes*nee + nel*nee
! a_eme(ind_fe(i)) = a_eme(ind_fe(i)) - nes*nel + nes*nee - nel*nee
a_eme(ind_fe2(i):ind_fe2(i)+up_fe2(i)) = a_eme(ind_fe2(i):ind_fe2(i)+up_fe2(i)) + (nes*nel)*frac_fe2(i)
a_eme2(ind_fe2(i):ind_fe2(i)+up_fe2(i)) = a_eme2(ind_fe2(i):ind_fe2(i)+up_fe2(i)) + (- nes - nel)*frac_fe2(i)
ENDDO
a_L(0)=0.
A_L2(0)=0.
a_s(0)=0.
a_s2(0)=0.
a_eml(0)=0.
a_eme(0)=0.
a_ems(0)=0.
s_terms= (alpha_is_d(j)*a_s2/2. -gamma_s_kd(:,j))
s_terms2 = a_s *alpha_is_d(j)*omega_s_om/2.
l_terms = a_L2*alpha_is_d(j)
em_terms = a_eme2*alpha_em(j)*k2
! subcycle timestep determination at given space pt
dt_is=dt_ql/6.
dt_is =min(0.1/(maxval(s_terms)+tiny(1.d0)),0.1/(maxval(em_terms)+tiny(1.d0)), &
0.1/(maxval(l_terms(-lpc:lpc))+tiny(1.d0)), dt_ql/8.)
! if(j== n_xp/2) print*,rank, dt_is, 1./(maxval(l_terms(-lpc:lpc))+tiny(1.d0))
! dt_is=dt_ql/8.
t_is_new=min(t_is + dt_is, dt_ql)
dt_is = t_is_new-t_is
t_is = t_is_new
!w_l_new(:,j) = W_L_new(:,j) +alpha_is_d(j)*omega_l_om*dt_is*(a_L + a_l2*N_L)
w_l_new(:,j) = (W_L_new(:,j) + a_L*alpha_is_d(j)*omega_l_om*dt_is)/(1. - dt_is*l_terms)
W_s(:,j) = (W_s(:,j) + s_terms2*dt_is)/(1.- dt_is*s_terms)
! w_s(:,j) = w_s(:,j) + dt_is *(s_terms
! semi-implicit evolution of wave spectral enery densities
! W_em(:,j) = w_em(:,j) + (a_eme + a_eme2*n_em)*alpha_em(j)*k2*dt_is &
! - (w_em(:,j) - w_f0)*gamma_d_f(:,j)/omega_emf_om**2 *dt_is
! w_l_new(:,j) = w_l_new(:,j) + a_eml*alpha_em(j)*dt_is*k2
! w_s(:,j) = w_s(:,j)+ a_ems*alpha_em(j)*dt_is*k2
where(w_s(:,j) .LE. 0) w_s(:,j) = 0.
w_s(0 , j) = 0.
where (w_em(:,j) .le. w_f0) w_em(:,j) = w_f0
ENDDO
! time loop
! print* 'done subloop.....................................', j
ENDDO
! spatial coordinate loop
! print*, rank, 'done space loop'
DEALLOCATE( gamma_s_kd, alpha_is_d, alpha_em, gamma_d_f)
END SUBROUTINE soundwaves_with_em
SUBROUTINE harmonic(w_l, w_em_new, omega, density)
USE CONSTANTS
USE PARAMETERS
IMPLICIT NONE
REAL(KIND=8), DIMENSION(-n_kv:, :), INTENT(INOUT) :: W_L, w_em_new
REAl(KIND=8), DIMENSION(:),INTENT(IN) :: omega, density
REAL(KIND=8), DIMENSION(-n_kv:n_kv):: a_em, n_l, w_h0, omega_emh_om, n_em, w_em_tmp,omega_emh2,W_h0_om
INTEGER(KIND=4)::i, j
REAL(KIND=8):: alpha_em, gamma_d, omega_sq, cosine, k_1, k_2, a_em_tmp
! define space unvarying parts of various quantities.....................................................
omega_emH_om = sqrt(1.+v_c**2/v_t**2 *k_h**2)
W_h0_om = kbTe_1d *k_h*k_h/(v_t*v_t)
cosine = sqrt(2.)/2.
DO j = 3, n_xp+2
! timesaveing variable
omega_sq=omega(j)*omega(j)
omega_emH2=omega_emH_om*omega(j)
alpha_em = omega(j)/density(j)*alpha_em_h
gamma_d=omega_sq*gamma_d_em
! coefficients
w_h0=w_h0_om*omega_sq
! thermal level
n_em = tiny(0d0) !w_em_new(:,j)/omega_emH2
! Defining n_em but it appears to be too low to make a difference to the result
n_l = w_l(:,j)/(omega(j) + 3.*omega(j)*k_x**2/2.)
! number density of Langmuir waves
a_em = 0.
k_1=k_x(ind_h1(-n_kv))
k_2=k_x(ind_h2(-n_kv))
a_em(-n_kv) = (omega(j)/v_t)**2*(k_1**2 - k_2**2)**2/k_2**2/abs(3.*v_t*(2.*k_1-abs(k_h(-n_kv))*cosine))* &
(k_h(-n_kv)**2/k_2**2*16.*(n_l(ind_h1(-n_kv))*n_l(-ind_h2(-n_kv))) -n_em(-n_kv)*(n_l(ind_h1(-n_kv))+ n_l(-ind_h2(-n_kv)) ))
k_1=k_x(ind_h1(-n_kv+1))
k_2=k_x(ind_h2(-n_kv+1))
a_em_tmp = (omega(j)/v_t)**2*(k_1**2 - k_2**2)**2/k_2**2/abs(3.*v_t*(2.*k_1-abs(k_h(-n_kv+1))*cosine))* &
(k_h(-n_kv+1)**2/k_2**2*16.*(n_l(ind_h1(-n_kv+1))*n_l(-ind_h2(-n_kv+1))) &
-n_em(-n_kv+1)*(n_l(ind_h1(-n_kv+1))+ n_l(-ind_h2(-n_kv+1)) ))
a_em(-n_kv) = a_em(-n_kv) + a_em_tmp
DO i=-n_kv+1, n_kv-1
k_1=k_x(ind_h1(i+1))
k_2=k_x(ind_h2(i+1))
a_em(i) = a_em_tmp
a_em_tmp = (omega(j)/v_t)**2*(k_1**2- &
k_2**2)**2/k_2**2/abs(3.*v_t*(2.*k_1-abs(k_h(i))*cosine))* &
(k_h(i)**2/k_2**2*16.*(n_l(ind_h1(i+1))*n_l(-ind_h2(i+1))) -n_em(i+1)*(n_l(ind_h1(i+1))+ n_l(-ind_h2(i+1)) ))
a_em(i)=(a_em(i) + a_em_tmp)*0.5
ENDDO
k_1=k_x(ind_h1(n_kv))
k_2=k_x(ind_h2(n_kv))
a_em(n_kv) = (omega(j)/v_t)**2*(k_1**2 - k_2**2)**2/k_2**2/abs(3.*v_t*(2.*k_1-abs(k_h(n_kv))*cosine))* &
(k_h(n_kv)**2/k_2**2*16.*(n_l(ind_h1(n_kv))*n_l(-ind_h2(n_kv))) -n_em(n_kv)*(n_l(ind_h1(n_kv))+ n_l(-ind_h2(n_kv)) ))
a_em(0) = 0.
w_em_new(:,j) = w_em_new(:,j) + alpha_em*dt*a_em*k2*omega_emH2 ! - (w_em_new(:,j)- w_h0)*gamma_d/omega_emH_om**2 *dt
where (w_em_new(:,j) .le. w_h0) w_em_new(:,j) = w_h0
ENDDO
END SUBROUTINE harmonic
END MODULE NONLIN