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etrans.f90
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etrans.f90
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! Subroutine ETRANS
! This software is part of the glow model. Use is governed by the open source
! academic research license agreement contained in the file glowlicense.txt.
! For more information see the file glow.txt.
! Banks & Nagy 2-stream electron transport code
! Adapted by Stan Solomon, 1986, 1988
! Uses variable altitude and energy grids
! Updated comments and removed artifacts, scs, 2005
! Moved common blocks into use-associated variables defined in cglow.f90, btf, 2015
! Changed input to subroutine impit to argument list, scs, 2015
! Modernized to remove upper case and numbered line statements, scs, 2016
! Refactored for f90, scs, 2016
! Subroutine EXSECT called first time only to calculate electron impact cross sections.
! Definitions:
! Use-associated variables (formerly in common blocks): See glow.f90, cglow.f90, and exsect.f
! psi first term of parabolic d.e., = 1
! alpha second term "; cm-1
! beta third term "; cm-2
! gamma forth term "; cm-4 s-1 ev-1
! delz altitude increments; cm
! del2 sum of altitude increment and next higher increment; cm
! dela average of "
! delp product of dela and next higher delz
! delm product of dela and delz
! dels product of delz and next higer delz
! den dummy array for transfer of calculated downward flux
! fac factor for extrapolating production rate, = 0
! prod sum of photoelectron production and secondary electrons from protons; cm-3 s-1 ev-1
! eprod energy of "; ev cm-3
! t1 elastic collision term; cm-1
! t2 elastic + inelastic collision term; cm-1
! tsa total energy loss cross section for each species; cm2
! produp upward cascade + secondary production; cm-3 s-1 ev-1
! prodwn downward "
! phiup upward flux; cm-2 s-1 ev-1
! phidwn downward "
! tsigne thermal electron collision term; cm-1
! secion total ionization rate; cm-3 s-1
! secp secondary electron production; cm-3 s-1 ev-1
! r1 ratio term for calculating upward flux; cm-2 s-1 ev-1
! expt2 exponential term for calculating upward flux
! produa collection array for calculating produp; cm-3 s-1 ev-1
! prodda " prodwn
! phiinf downward flux at top of atmos., divided by avmu; cm-2 s-1 ev-1
! potion ionizaition potential for each species; ev
! avmu cosine of the average pitch angle
! Array dimensions:
! jmax number of altitude levels
! nbins number of energetic electron energy bins
! nmaj number of major species
! nei number of states produced by electron impact
subroutine etrans
use cglow,only: nmaj,nbins,jmax,nei,ierr,jlocal, &
dip,ener,del,aglw,eheat,sion,phitop,zz,pespec, &
sespec,zte,ze,zmaj,uflx,dflx,tez,efrac ! formerly /cglow/
use cglow,only: siga,sigs,pe,sigex,sec,iimaxx,pin ! formerly /cxsect/
use cglow,only: ww ! formerly /cxpars/
implicit none
integer,save :: ifirst=1
integer :: ii,ib,ibb,i,n,jj,j,k,jjj4,iv,ll,kk,im,iq
real :: prod(jmax), eprod(jmax), t1(jmax), t2(jmax), tsa(nmaj), &
produp(jmax,nbins), prodwn(jmax,nbins), &
phiup(jmax), phidwn(jmax), tsigne(jmax), taue(jmax), &
secion(jmax), secp(nmaj,jmax), r1(jmax), expt2(jmax), &
produa(jmax), prodda(jmax), phiinf(nbins), potion(nmaj), &
alpha(jmax),beta(jmax),gamma(jmax),psi(jmax),del2(jmax), &
delp(jmax),delm(jmax),dels(jmax),den(jmax), &
delz(jmax),dela(jmax)
real :: sindip,rmusin,phiout,dag,et,eet,fluxj,edep,epe,ephi,aprod,ein,eout,fac
real,parameter :: avmu=0.5
potion = (/16.,16.,18./)
ierr = 0
fac = 0.
sindip = sin(dip)
rmusin = 1. / sindip / avmu
psi(1) = 1.
!
! First call only: calculate cross-sectons:
!
if (ifirst == 1) then
call exsect (ener, del)
ifirst = 0
endif
!
! Zero variables:
!
alpha(1) = 0.
beta(1) = 0.
gamma(1) = 0.
phiout = 0.0
eheat(:) = 0.0
eprod(:) = 0.0
secion(:) = 0.0
sion(:,:) = 0.0
aglw(:,:,:) = 0.0
produp(:,:) = 1.0e-20
prodwn(:,:) = 1.0e-20
!
! Divide downward flux at top of atmos. by average pitch angle cosine:
!
phiinf(:) = phitop(:) / avmu
!
! Calcualte delta z's:
!
delz(1) = zz(2)-zz(1)
do i=2,jmax
delz(i) = zz(i)-zz(i-1)
enddo
do i=1,jmax-1
del2(i) = delz(i)+delz(i+1)
dela(i) = del2(i)/2.
delp(i) = dela(i)*delz(i+1)
delm(i) = dela(i)*delz(i)
dels(i) = delz(i)*delz(i+1)
enddo
del2(jmax) = del2(jmax-1)
dela(jmax) = dela(jmax-1)
delp(jmax) = delp(jmax-1)
delm(jmax) = delp(jmax-1)
dels(jmax) = dels(jmax-1)
!
! Top of energy loop:
!
do j=nbins,1,-1
!
! Calculate production:
!
do i = 1, jmax
prod(i) = (pespec(j,i)+sespec(j,i)) * rmusin / del(j)
eprod(i) = eprod(i) + prod(i) * ener(j) * del(j) / rmusin
enddo
!
! Total energy loss cross section for each species:
!
tsa(:) = 0.0
if (j > 1) then
do k = 1, j-1
do i = 1, nmaj
tsa(i) = tsa(i) + siga(i,k,j) * (del(j-k)/del(j))
enddo
enddo
else
do i=1,nmaj
tsa(i) = tsa(i) + siga(i,1,j) + 1.e-18
enddo
endif
!
! Thermal electron energy loss:
!
jjj4 = j - 1
if (j == 1) jjj4 = 1
dag = ener(j) - ener(jjj4)
if (dag <= 0.0) dag = del(1)
!
do i = 1, jmax
et = 8.618e-5 * zte(i)
eet = ener(j) - et
if (eet <= 0.0) then
tsigne(i) = 0.0
else
tsigne(i) = ((3.37e-12*ze(i)**0.97)/(ener(j)**0.94)) &
* ((eet)/(ener(j) - (0.53*et))) ** 2.36
endif
tsigne(i) = tsigne(i) * rmusin / dag
enddo
!
! Collision terms:
!
do i = 1, jmax
t1(i) = 0.0
t2(i) = 0.0
do iv = 1, nmaj
t1(i) = t1(i) + zmaj(iv,i) * sigs(iv,j) * pe(iv,j)
t2(i) = t2(i) + zmaj(iv,i) * (sigs(iv,j)*pe(iv,j) + tsa(iv))
enddo
t1(i) = t1(i) * rmusin
t2(i) = t2(i) * rmusin + tsigne(i)
enddo
!
! Bypass next section if local calculation was specified:
!
if (jlocal /= 1) then
!
! Solve parabolic d.e. by Crank-Nicholson method to find downward flux:
!
do i = 2, jmax-1
psi(i) = 1.
alpha(i) = (t1(i-1) - t1(i+1)) / (del2(i) * t1(i))
beta(i) = t2(i) * (t1(i+1) - t1(i-1)) / (t1(i) * del2(i)) &
- (t2(i+1) - t2(i-1)) / del2(i) - t2(i)**2 + t1(i)**2
if (prod(i) < 1.e-30) prod(i) = 1.e-30
if (prodwn(i,j) < 1.e-30) prodwn(i,j) = 1.e-30
gamma(i) = (prod(i)/2.0) * (-t1(i) - t2(i) - alpha(i) &
- (prod(i+1) - prod(i-1))/prod(i)/del2(i)) &
+ prodwn(i,j) * (-alpha(i) - t2(i) &
- (prodwn(i+1,j)-prodwn(i-1,j))/prodwn(i,j)/del2(i)) &
- produp(i,j) * t1(i)
enddo
if (abs(beta(2)) < 1.e-20) then
beta(2) = 1.e-20
ierr = 2
endif
phidwn(2) = gamma(2) / beta(2)
den(1) = phidwn(2)
fluxj = phiinf(j)
call impit(jmax,fluxj,fac,alpha,beta,gamma,psi,del2,delp,delm,dels,den)
phidwn(:) = den(:)
!
! Apply lower boundary condition: phiup=phidwn. Should be nearly zero.
!
phiup(1) = phidwn(1)
!
! Integrate back upward to calculate upward flux:
!
do i = 2, jmax
r1(i) = (t1(i)*phidwn(i) + (prod(i)+2.*produp(i,j))/2.) / t2(i)
taue(i) = t2(i)*delz(i)
if (taue(i) > 60.) taue(i)=60.
expt2(i) = exp(-taue(i))
enddo
do i=2,jmax
phiup(i) = r1(i) + (phiup(i-1)-r1(i)) * expt2(i)
enddo
else
!
! Local calculation only:
!
do i = 1, jmax
if (t2(i) <= t1(i)) then
ierr = 1
t2(i) = t1(i) * 1.0001
endif
phiup(i) = (prod(i)/2.0 + produp(i,j)) / (t2(i) - t1(i))
phidwn(i) = (prod(i)/2.0 + prodwn(i,j)) / (t2(i) - t1(i))
enddo
endif
!
! Multiply fluxes by average pitch angle cosine and put in arrays:
!
do i=1,jmax
uflx(j,i) = phiup(i) * avmu
dflx(j,i) = phidwn(i) * avmu
enddo
!
! Calculate outgoing electron energy flux for conservation check:
!
phiout = phiout + phiup(jmax) * del(j) * ener(j)
!
! Cascade production:
!
if (j > 1) then
do k = 1, j-1
ll = j - k
produa(:)=0.
prodda(:)=0.
do n = 1, nmaj
do i=1,jmax
produa(i) = produa(i) &
+ zmaj(n,i) * (siga(n,k,j)*pin(n,j)*phidwn(i) &
+ (1. - pin(n,j))*siga(n,k,j)*phiup(i))
prodda(i) = prodda(i) &
+ zmaj(n,i) * (siga(n,k,j)*pin(n,j)*phiup(i) &
+ (1. - pin(n,j))*siga(n,k,j)*phidwn(i))
enddo
enddo
do i=1,jmax
produp(i,ll) = produp(i,ll) + produa(i) * rmusin
prodwn(i,ll) = prodwn(i,ll) + prodda(i) * rmusin
enddo
enddo
endif
kk = j - 1
if (kk > 0) then
do i = 1, jmax
produp(i,kk) = produp(i,kk)+tsigne(i)*phiup(i)*(del(j)/del(kk))
prodwn(i,kk) = prodwn(i,kk)+tsigne(i)*phidwn(i)*(del(j)/del(kk))
enddo
endif
!
! Electron heating rate:
!
dag = del(j)
do i = 1, jmax
eheat(i) = eheat(i) + tsigne(i) * (phiup(i)+phidwn(i)) * dag**2
enddo
!
! Electron impact excitation rates:
!
do ii = 1, jmax
do i = 1, nmaj
do ibb = 1, nei
aglw(ibb,i,ii) = aglw(ibb,i,ii) + (phiup(ii) + phidwn(ii)) &
* sigex(ibb,i,j) * del(j) * zmaj(i,ii)
enddo
enddo
enddo
!
! Calculate production of secondaries into k bin for energy j bin and add to production:
!
do k = 1, iimaxx(j)
do n = 1, nmaj
do i = 1, jmax
secp(n,i) = sec(n,k,j) * zmaj(n,i) * (phiup(i) + phidwn(i))
sion(n,i) = sion(n,i) + secp(n,i) * del(k)
secion(i) = secion(i) + secp(n,i) * del(k)
produp(i,k) = produp(i,k) + (secp(n,i)*.5*rmusin)
prodwn(i,k) = prodwn(i,k) + (secp(n,i)*.5*rmusin)
enddo
enddo
enddo
enddo ! bottom of energy loop
eheat(:) = eheat(:) / rmusin
!
! Calculate energy deposited as a function of altitude and total energy deposition:
!
edep = 0.
do im=1,jmax
tez(im) = eheat(im)
do ii=1,nmaj
tez(im) = tez(im) + sion(ii,im)*potion(ii)
do iq=1,nei
tez(im) = tez(im) + aglw(iq,ii,im)*ww(iq,ii)
enddo
enddo
edep = edep + tez(im) * dela(im)
enddo
!
! Calculate energy input, output, and fractional conservation:
!
epe = 0.0
ephi = 0.0
do i = 2, jmax
aprod = sqrt(eprod(i)*eprod(i-1))
epe = epe + aprod * delz(i)
enddo
do jj = 1, nbins
ephi = ephi + phiinf(jj) * ener(jj) * del(jj) / rmusin
enddo
ein = ephi + epe
phiout = phiout / rmusin
eout = edep + phiout
efrac = (eout - ein) / ein
return
end subroutine etrans
!-----------------------------------------------------------------------
! Subroutine impit solves parabolic differential equation by implicit Crank-Nicholson method
subroutine impit(jmax,fluxj,fac,alpha,beta,gamma,psi,del2,delp,delm,dels,den)
implicit none
integer,intent(in) :: jmax
real,intent(in) :: fluxj,fac,alpha(jmax),beta(jmax),gamma(jmax), &
psi(jmax),del2(jmax),delp(jmax),delm(jmax),dels(jmax)
real,intent(out) :: den(jmax)
integer :: i1,i,kk,jk
real :: dem,k(jmax),l(jmax),a(jmax),b(jmax),c(jmax),d(jmax)
i1 = jmax - 1
do i = 1, i1
a(i) = psi(i) / delp(i) + alpha(i) / del2(i)
b(i) = -2. * psi(i) / dels(i) + beta(i)
c(i) = psi(i) / delm(i) - alpha(i) / del2(i)
d(i) = gamma(i)
enddo
k(2) = (d(2) - c(2)*den(1)) / b(2)
l(2) = a(2) / b(2)
do i = 3, i1
dem = b(i) - c(i) * l(i-1)
k(i) = (d(i) - c(i)*k(i-1)) / dem
l(i) = a(i) / dem
enddo
den(i1) = (k(i1) - l(i1)*fluxj) / (1. + l(i1)*fac)
den(jmax) = den(i1)
do kk = 1, jmax-3
jk = i1 - kk
den(jk) = k(jk) - l(jk) * den(jk + 1)
enddo
return
end subroutine impit