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absorpfw.f
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c ********************** absorpfw*********************
c * ----- *
c * this subroutine calculates the imaginary part *
c * of refractive index using a formula from: *
c * S.C.Chiu,V.S.Chan,R.W.Harvey,M.Porkolab *
c * Theory of fast wave current drive for tokamak *
c * plasma, *
c * Nuclear fusion,1989,vol.29,No.12, p.2175-2186 *
c * *
c * Smirnov021018: Two corrections are introduced: *
c * Eq. (6) for eps23 has "-" sign *
c * Substitute Z_0(zeta)|Stix for all Z(zeta_e) *
c ****************************************************
c it uses the real*4 accuracy in the modified Bessel function
c which gives the zero ions damping (not good. See absorpf1, below).
c input parameters: z,r,phi (m,m,radian)
c cnpar -N_parallel (to magnetic field)
c cnper -N_perpendicular (real part)
c tempe-electron temperature (keV)
c dense-electron density (10*13/cm**3
c tempiar(2:nbulka) ions temperature(kev)
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c
c output parameter: cnprim_e -imaginary part of N_perp
c (electron absorption)
c cnprim_i -imaginary part of N_perp
c (ion absorption)
c The input parameter nb (the max order of the modified Bessel
c functions) is set inside absorpfw using operator 'parameter'.
c-----------------------------------------------------------------------
subroutine absorpfw(z,r,phi,cnpar,cnper,
1tempe,dense,tempiar,
1nbulk,bmod,cnprim_e,cnprim_i)
implicit integer (i-n), real*8 (a-h,o-z)
include 'param.i'
include 'ions.i'
dimension tempiar(nbulka)
double precision mu,mu2
parameter (nb=100) ! the max order of the modifed Bessel function
real br,bi
dimension br(nb),bi(nb)
complex argz,zf,zfp
real rpr,rpim
c write(*,*)'begin absorpfw '
c write(*,*)'cnpar=',cnpar,'cnper=',cnper
c write(*,*)'tempe=',tempe,'dense=',dense
c write(*,*)'bmod=',bmod
c********************************************************************
c electron absorption:
c Imag(N_perp)=abs(N_perp)*sqrt(pi)/4*beta_e*ksi_e*exp(-ksi_e**2)*G
c--------------------------------------------------------------------
pi=4.d0*datan(1.d0)
spi=dsqrt(pi)
c----------------------------------------
c cvac - light velocity in (cm/sec)
cvac=2.997930d+10
c ve=(sqrt(2Te/me)), ve in (cm/sec),Te(keV)
ve=1.87d9*dsqrt(tempe) !tempe keV
c----------------------------------------
c cksi_e=omega/(k_par*ve)=cvac/(N_par*ve)
cksi_e=cvac/(cnpar*ve)
c cksi_e=dabs(cksi_e)
c----------------------------------------
c beta_e=p_e/(btot**2/(8pi)),p_e electron pressure
c p_e=dense*tempe
c bmod ! tl
btot=bmod*1.d4 ! gauss
p_e=tempe*dense*1.6d+4 !(dyne/cm)
p_b=btot**2/(8.d0*pi) !magnetic pressure (dyne/cm)
beta_e=p_e/p_b
mu=510.94d0/tempe
mu2=mu*mu
c----------------------------------------
c G=(N_par**2-S)/A2+
c {1+omeg_pe**2*Z_r/(omega_e**2*abs(Z)**2*(N_par**2-S)}*
c (m_e*c**2/T_e)**2*(omega_e*D/omega*abs(eps33))**2/(A1*A2)
c----------------------------------------
c p_=P,d_=D,s_=S, P,D,S are like in the article
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
s_=1.d0+xe/(ye*ye)
d_=0.d0
do i=2,nbulk
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
p=1.d0/(1.d0-yi*yi)
s_=s_-xi*p
c d_=d_+xi*yi*p
d_=d_+xi*p/yi
enddo
p_=-xe
write(*,*)'xe,xi',xe,xi
write(*,*)'ye,yi',ye,yi
write(*,*)'s_,d_,p_',s_,d_,p_
c---------------------------------------
rpr=real(cksi_e)
argz=cmplx(rpr,0.)
call zfunc(argz,zf,zfp)
rpr=real(zf)
zf_r=dble(rpr) !real(Z(cksi_e))
rpim=aimag(zf)
zf_im=dble(rpim) !imag(Z(cksi_e))
cksi_e2=cksi_e*cksi_e
z_r=2.d0*cksi_e2*(1.d0+cksi_e*zf_r) ! article formula (18)
z_im=2.d0*cksi_e2*cksi_e*zf_im ! article formula (18)
cmodez_2=z_r*z_r+z_im*z_im
eps33_r=xe*z_r ! article formula (5)
eps33_im=xe*z_im ! article formula (5)
eps33_2=eps33_r*eps33_r+eps33_im*eps33_im
cnpar2=cnpar*cnpar
p1=cnpar2-s_ ! for (15),(16),(17)
dp1=1.d0/p1 ! for (15),(16),(17)
z_rdz2=z_r/(cmodez_2)
p2=xe*z_rdz2*dp1/(ye*ye)
a1_=p1+p2*cnpar2 ! (16)
a2_=p1+p2*(cnpar2+s_) ! (17)
g_=p1/a2_+(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
cnprim_e=0.25d0*spi*cnper*beta_e*cksi_e*dexp(-cksi_e2)*g_ !(13)
cn1=p1/a2_ !(15)
cn2=(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
cnpert2=(p1*p1-d_*d_)/(-p1+d_*d_*eps33_r*cnpar2/
1(-eps33_2*p1)) !(13)
cnpert=dsqrt(dabs(cnpert2)) !(13)
c end of the electron absorption calculations
c***********************************************************************
c ion absorption:
c-----------------------------------------------------------------
c cksi_il=(1-l*yi)/(N_par*Vi/cvac)
c eps11_i, eps22_i, eps12_r, - only with ion contributions
eps11_i=0.d0
eps22_i=0.d0
eps12_r=0.d0
do i=2,nbulk
c vi=(sqrt(2Te/me)), vi in (cm/sec),Ti(keV)
vi=1.87d9*dsqrt(tempiar(i)/dmas(i))
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
cmui=0.5d0*(cnper*vi/(yi*cvac))**2
expmui=dexp(-cmui)
cksi_0=cvac/(cnpar*vi)
cksi_0=dabs(cksi_0)
p22=xi*cksi_0*expmui ! for (2),(3),(4)
p11=p22/cmui ! for (2)
rpr=cmui
c nb=100
c------------------------------------------
c izi=1 to calculate modified Bessel functions
c BESSEL FUNCTIONS AND ARGUMENTS ARE REAL
ize=1
call beslci(rpr,0.,nb,ize,br,bi,ncalc)
p=10.d0*dabs(cnpar)*vi/cvac
l0=1/yi
l1=(1-p)/yi
l2=(1+p)/yi+1
if(l2.gt.(nb-2)) then
WRITE(*,*)'in absorpwf l2>(nb-2) Increase
1 parameter nb in the subroutine absorpwf'
STOP
endif !l2=(nb-2)
if(l1.gt.(nb-2)) then
WRITE(*,*)'in absorpwf l1>(nb-2) Increase
1 parameter nb in the subroutine absorpwf'
STOP
endif ! l1=(nb-2)
if(l1.lt.-(nb-2)) then
WRITE(*,*)'in absorpwf l1<-(nb-2) Increase
1 parameter nb in the subroutine absorpwf'
STOP
endif !l1=-(nb-2)
do l=l1,l2
c cksi_l=(1-l*yi)/(N_par*Vi/cvac)
if(l.ge.0) then
lmode=l
else
lmode=-l
endif
besm_l=br(lmode+1) ! |l| order modified Bessel function
besm_lp=br(lmode+2)
if (l.eq.0)then
cksi_l=cksi_0
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
c besmp_l is a derivative from modified Bessel function I_0
c by argument cmui :I_0 prime=I_1
besmp_l=besm_lp
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
else
cksi_l=(1.d0-l*yi)*cvac/(cnpar*vi)
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
eps11_i=eps11_i+p11*l*l*besm_l*zfi_l !(2)
c besmp_l is a derivative from modified Bessel function I_l
c by argument cmui :I_l prime=0.5*(I_(l-1)+I_(l+1))
besm_lm=br(lmode)
besmp_l=0.5d0*(besm_lp+besm_lm)
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
eps12_r=eps12_r+p22*l*(besm_l-besmp_l)*zfi_l !(4)
endif
enddo !l
enddo !i
eps22_i=eps22_i+eps11_i !(3)
cnprim_i=0.5d0*cnper*(
1 (eps11_i-2.d0*d_*eps33_r*eps12_r/eps33_2)/a2_+
1 (-p1*(eps22_i+eps11_i)-2.d0*d_*eps12_r)*a1_/((p1*p1-d_*d_)*a2_))
c write(*,*)'after cnprim_i',cnprim_i
c end of the ion absorption calculations
c***********************************************************************
return
end
c ********************** absorpf1**********************
c * ----- *
c * this subroutine calculates imaginary part *
c * of refractive index using formula from: *
c * S.C.Chiu,V.S.Chan,R.W.Harvey,M.Porkolab *
c * Theory of fast wave current drive for tokamak *
c * plasma, *
c * Nuclear fusion,1989,vol.29,No.12, p.2175-2186 *
c !!the differens with absorpwf in the modified bessel function
c !!the real*8 bessel function it gives the good ions absorption
c * *
c * Smirnov021018: Two corrections are introduced: *
c * Eq. (6) for eps23 has "-" sign *
c * Substitute Z_0(zeta)|Stix for all Z(zeta_e) *
c ****************************************************
c input parameters: z,r,phi (m,m,radian)
c cnpar -N_parallel (to magnetic field)
c cnper -N_perpendicular (real part)
c tempe- electron temperature (keV)
c dense- electron density (10*13/cm**3
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c tempiar(2:nbulka) ions temperature(kev)
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c The input parameter nb (the max number of the modified Bessel
c functions) is set inside absorpfw using operator 'parameter'.
c output parameter: cnprim_e -imaginary part of N_perp
c (electron absorption)
c cnprim_i -imaginary part of N_perp
c (ion absorption)
c-----------------------------------------------------------------*
c it uses beslci1 modified double precision Bessel functions *
c------------------------------------------------------------------
subroutine absorpf1(z,r,phi,cnpar,cnper,
1tempe,dense,tempiar,
1nbulk,bmod,cnprim_e,cnprim_i)
implicit integer (i-n), real*8 (a-h,o-z)
include 'param.i'
include 'ions.i'
dimension tempiar(nbulka)
double precision mu,mu2
parameter (nb=100) ! the max order of the modifed Bessel function
dimension br(nb),bi(nb)
complex argz,zf,zfp
real rpr,rpim
c********************************************************************
c electron absorption:
c Imag(N_perp)=abs(N_perp)*sqrt(pi)/4*beta_e*ksi_e*exp(-ksi_e**2)*G
c--------------------------------------------------------------------
pi=4.d0*datan(1.d0)
spi=dsqrt(pi)
c----------------------------------------
c cvac - light velocity in (cm/sec)
cvac=2.997930d+10
c ve=(sqrt(2Te/me)), ve in (cm/sec),Te(keV)
ve=1.87d9*dsqrt(tempe) !tempe keV
c----------------------------------------
c cksi_e=omega/(k_par*ve)=cvac/(N_par*ve)
cksi_e=cvac/(cnpar*ve)
cksi_e=dabs(cksi_e)
c----------------------------------------
c beta_e=p_e/(btot**2/(8pi)),p_e electron pressure
c p_e=dense*tempe
c bmod ! tl
btot=bmod*1.d4 ! gauss
p_e=tempe*dense*1.6d+4 !(dyne/cm)
p_b=btot**2/(8.d0*pi) !magnetic pressure (dyne/cm)
beta_e=p_e/p_b
mu=510.94d0/tempe
mu2=mu*mu
c----------------------------------------
c G=(N_par**2-S)/A2+
c {1+omeg_pe**2*Z_r/(omega_e**2*abs(Z)**2*(N_par**2-S)}*
c (m_e*c**2/T_e)**2*(omega_e*D/omega*abs(eps33))**2/(A1*A2)
c----------------------------------------
c p_=P,d_=D,s_=S, P,D,S are like in the article
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
s_=1.d0+xe/(ye*ye)
d_=0.d0
do i=2,nbulk
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
p=1.d0/(1.d0-yi*yi)
s_=s_-xi*p
d_=d_+xi*p/yi
enddo
p_=-xe
c---------------------------------------
rpr=real(cksi_e)
argz=cmplx(rpr,0.)
call zfunc(argz,zf,zfp)
rpr=real(zf)
zf_r=dble(rpr) !real(Z(cksi_e))
rpim=aimag(zf)
zf_im=dble(rpim) !imag(Z(cksi_e))
cksi_e2=cksi_e*cksi_e
z_r=2.d0*cksi_e2*(1.d0+cksi_e*zf_r) ! article formula (18)
z_im=2.d0*cksi_e2*cksi_e*zf_im ! article formula (18)
cmodez_2=z_r*z_r+z_im*z_im
eps33_r=xe*z_r ! article formula (5)
eps33_im=xe*z_im ! article formula (5)
eps33_2=eps33_r*eps33_r+eps33_im*eps33_im
cnpar2=cnpar*cnpar
p1=cnpar2-s_ ! for (15),(16),(17)
dp1=1.d0/p1 ! for (15),(16),(17)
z_rdz2=z_r/(cmodez_2)
p2=xe*z_rdz2*dp1/(ye*ye)
a1_=p1+p2*cnpar2 ! (16)
a2_=p1+p2*(cnpar2+s_) ! (17)
g_=p1/a2_+(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
cnprim_e=0.25d0*spi*cnper*beta_e*cksi_e*dexp(-cksi_e2)*g_ !(13)
cn1=p1/a2_ !(15)
cn2=(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
c end of the electron absorption calculations
c***********************************************************************
c ion absorption:
c-----------------------------------------------------------------------
c cksi_il=(1-l*yi)/(N_par*Vi/cvac)
c eps11_i, eps22_i, eps12_r, - only with ion contributions
eps11_i=0.d0
eps22_i=0.d0
eps12_r=0.d0
do i=2,nbulk
c vi=(sqrt(2Te/me)), vi in (cm/sec),Ti(keV)
vi=1.87d9*dsqrt(tempiar(i)/dmas(i))
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
cmui=0.5d0*(cnper*vi/(yi*cvac))**2
expmui=dexp(-cmui)
cksi_0=cvac/(cnpar*vi)
cksi_0=dabs(cksi_0)
p22=xi*cksi_0*expmui ! for (2),(3),(4)
p11=p22/cmui ! for (2)
c nb=100
c------------------------------------------
c izi=1 to calculate modified Bessel functions
c BESSEL FUNCTIONS AND ARGUMENTS ARE REAL
ize=1
call beslci1(cmui,0.d0,nb,ize,br,bi,ncalc)
p=10.d0*dabs(cnpar)*vi/cvac
l0=1/yi
l1=(1-p)/yi
l2=(1+p)/yi+1
if(l2.gt.(nb-2)) then
WRITE(*,*)'in absorpf1 l2>(nb-2) Increase
1 parameter nb in the subroutine absorpf1'
STOP
endif
if(l1.gt.(nb-2)) then
WRITE(*,*)'in absorpf1 l1>(nb-2) Increase
1 parameter nb in the subroutine absorpf1'
STOP
endif
if(l1.lt.-(nb-2)) then
WRITE(*,*)'in absorpf1 l1<-(nb-2) Increase
1 parameter nb in the subroutine absorpf1'
STOP
endif
do l=l1,l2
c cksi_l=(1-l*yi)/(N_par*Vi/cvac)
if(l.ge.0) then
lmode=l
else
lmode=-l
endif
besm_l=br(lmode+1) ! |l| order modified Bessel function
besm_lp=br(lmode+2)
if (l.eq.0)then
cksi_l=cksi_0
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
c besmp_l is a derivative from modified Bessel function I_0
c by argument cmui :I_0 prime=I_1
besmp_l=besm_lp
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
else
cksi_l=(1.d0-l*yi)*cvac/(cnpar*vi)
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
eps11_i=eps11_i+p11*l*l*besm_l*zfi_l !(2)
c besmp_l is a derivative from modified Bessel function I_l
c by argument cmui :I_l prime=0.5*(I_(l-1)+I_(l+1))
besm_lm=br(lmode)
besmp_l=0.5d0*(besm_lp+besm_lm)
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
eps12_r=eps12_r+p22*l*(besm_l-besmp_l)*zfi_l !(4)
endif
enddo !l
enddo !i
eps22_i=eps22_i+eps11_i !(3)
cnprim_i=0.5d0*cnper*(
1 (eps11_i-2.d0*d_*eps33_r*eps12_r/eps33_2)/a2_+
1 (-p1*(eps22_i+eps11_i)-2.d0*d_*eps12_r)*a1_/((p1*p1-d_*d_)*a2_))
c write(*,*)'after cnprim_i',cnprim_i
c end of the ion absorption calculations
c***********************************************************************
return
end
c ********************** absorpfd**********************
c * ----- *
c * this subroutine calculates imaginary part *
c * of refractive index using formula from: *
c * S.C.Chiu,V.S.Chan,R.W.Harvey,M.Porkolab *
c * Theory of fast wave current drive for tokamak *
c * plasma, *
c * Nuclear fusion,1989,vol.29,No.12, p.2175-2186 *
c !!the differens with absorpwf in the modified bessel function
c !!the real*8 bessel function it gives the good ions absorption
c * *
c * Smirnov021018: Two corrections are introduced: *
c * Eq. (6) for eps23 has "-" sign *
c * Substitute Z_0(zeta)|Stix for all Z(zeta_e) *
c ****************************************************
c input parameters: z,r,phi (m,m,radian)
c cnpar -N_parallel (to magnetic field)
c cnper -N_perpendicular (real part)
c tempe- electron temperature (keV)
c dense- electron density (10*13/cm**3
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c tempiar(2:nbulka) ions temperature(kev)
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c The input parameter nb (the max number of the modified Bessel
c functions) is set inside absorpfw using operator 'parameter'.
c output parameter: cnprim_e -imaginary part of N_perp
c (electron absorption)
c cnprim_i -imaginary part of N_perp
c (ion absorption)
c
cBH041009: Added breakdown of ion damping into components, cnprim_s(2:nbulk)
c
c-----------------------------------------------------------------*
c it uses beslci1 modified double precision Bessel functions *
c------------------------------------------------------------------
subroutine absorpfd(z,r,phi,cnpar,cnper,
1tempe,dense,tempiar,
1nbulk,bmod,cnprim_e,cnprim_i,cnprim_s)
implicit integer (i-n), real*8 (a-h,o-z)
include 'param.i'
include 'ions.i'
include 'eps.i'
dimension cnprim_s(*) !BH041009, for separate ion contributions
!cnprim_s(1:nbulk), cnprim_s(1)=cnprim_e
dimension tempiar(nbulka)
double precision mu,mu2
cSAP091015
c parameter (nb=100) ! the max order of the modifed Bessel function
cyup parameter (nb=200) ! the max order of the modifed Bessel function
parameter (nb=500) ! the max order of the modifed Bessel function
dimension br(nb),bi(nb)
c complex argz,zf,zfp
c real rpr,rpim
double complex argz,zf,zfp
double precision rpr,rpim
double complex ci,ckappae2,czero
czero=dcmplx(0.d0,0.d0)
c********************************************************************
c electron absorption:
c Imag(N_perp)=abs(N_perp)*sqrt(pi)/4*beta_e*ksi_e*exp(-ksi_e**2)*G
c--------------------------------------------------------------------
pi=4.d0*datan(1.d0)
spi=dsqrt(pi)
c----------------------------------------
c cvac - light velocity in (cm/sec)
cvac=2.997930d+10
c ve=(sqrt(2Te/me)), ve in (cm/sec),Te(keV)
ve=1.87d9*dsqrt(tempe) !tempe keV
c----------------------------------------
c cksi_e=omega/(k_par*ve)=cvac/(N_par*ve)
cksi_e=cvac/(cnpar*ve)
cSm021022
c cksi_e=dabs(cksi_e)
c----------------------------------------
c beta_e=p_e/(btot**2/(8pi)),p_e electron pressure
c p_e=dense*tempe
c bmod ! tl
btot=bmod*1.d4 ! gauss
p_e=tempe*dense*1.6d+4 !(dyne/cm)
p_b=btot**2/(8.d0*pi) !magnetic pressure (dyne/cm)
beta_e=p_e/p_b
mu=510.94d0/tempe
mu2=mu*mu
c----------------------------------------
c G=(N_par**2-S)/A2+
c {1+omeg_pe**2*Z_r/(omega_e**2*abs(Z)**2*(N_par**2-S)}*
c (m_e*c**2/T_e)**2*(omega_e*D/omega*abs(eps33))**2/(A1*A2)
c----------------------------------------
c p_=P,d_=D,s_=S, P,D,S are like in the article
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
s_=1.d0+xe/(ye*ye)
d_=0.d0
do i=2,nbulk
xi=x(z,r,phi,i)
write(*,*)'absorpfd i,xi',i,xi
yi=y(z,r,phi,i)
p=1.d0/(1.d0-yi*yi)
s_=s_-xi*p
d_=d_+xi*p/yi
enddo
p_=-xe
c---------------------------------------
c rpr=real(cksi_e)
c argz=cmplx(rpr,0.)
argz=dcmplx(cksi_e,0.d0)
c call zfunc(argz,zf,zfp)
cSm021022
c call czeta(argz,zf,zfp,ierror)
call CZETA0(cnpar,argz,zf,zfp,ierror)
c rpr=real(zf)
c rpr=dble(zf)
rpr=dreal(zf)
zf_r=dble(rpr) !real(Z(cksi_e))
c rpim=aimag(zf)
rpim=dimag(zf)
zf_im=dble(rpim) !imag(Z(cksi_e))
cksi_e2=cksi_e*cksi_e
z_r=2.d0*cksi_e2*(1.d0+cksi_e*zf_r) ! article formula (18)
z_im=2.d0*cksi_e2*cksi_e*zf_im ! article formula (18)
cmodez_2=z_r*z_r+z_im*z_im
eps33_r=xe*z_r ! article formula (5)
eps33_im=xe*z_im ! article formula (5)
eps33_2=eps33_r*eps33_r+eps33_im*eps33_im
cnpar2=cnpar*cnpar
p1=cnpar2-s_ ! for (15),(16),(17)
dp1=1.d0/p1 ! for (15),(16),(17)
z_rdz2=z_r/(cmodez_2)
p2=xe*z_rdz2*dp1/(ye*ye)
a1_=p1+p2*cnpar2 ! (16)
a2_=p1+p2*(cnpar2+s_) ! (17)
g_=p1/a2_+(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
cnprim_e=0.25d0*spi*cnper*beta_e*cksi_e*dexp(-cksi_e2)*g_ !(13)
cSm021021
cnprim_e=dabs(cnprim_e)
cn1=p1/a2_ !(15)
cn2=(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
c end of the electron absorption calculations
ci=dcmplx(0.d0,1.d0)
cmue=0.5d0*(cnper*ve/(ye*cvac))**2
ckappae2=xe*2.d0*cmue*cksi_e*(zf_r+ci*zf_im) ! formula (7)
c call tensrcld(z,r,phi)
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
cSm021018
c-----tensor for the electrons with the hot correction
c The hot correction is in eps(2,2),eps(3,3),eps(2,3)
c-----------------------------------------------------
do i=1,3
do j=1,3
reps(i,j)=czero
enddo
enddo
reps(1,1)=1.d0+xe/ye**2 !part of formula(2)
cSm021018
c reps(1,2)=-ci*xe/ye !part of formula(4)
cSm050207
c reps(1,2)=xe/ye !part of formula(4)
cSm080916
reps(1,2)=-ci*xe/ye !part of formula(4)
reps(2,2)=reps(1,1)+ckappae2 !part of formula (3)
reps(3,3)=xe*(z_r+ci*z_im) !formula (5)
c reps(2,3)=-ci*0.5*dsqrt(2.d0*cmue)*reps(3,3)/cksi_e !formula (6)
cSm021018
reps(2,3)=-ci*0.5*dsqrt(2.d0*cmue)*reps(3,3)/cksi_e
cSm021022
c if(cnpar.lt.0.d0) reps(2,3)=-reps(2,3)
cnprim_s(1)=cnprim_e
c do i=2,nbulk
c xi=x(z,r,phi,i)
c yi=y(z,r,phi,i)
c reps(1,1)=reps(1,1)+xi/(yi**2-1.d0)
c reps(2,2)=reps(2,2)+xi/(yi**2-1.d0)
c reps(1,2)=reps(1,2)-ci*yi*xi/(yi**2-1.d0)
c enddo
c***********************************************************************
c ion absorption:
c-----------------------------------------------------------------
c cksi_il=(1-l*yi)/(N_par*Vi/cvac)
c eps11_i, eps22_i, eps12_r, - only with ion contributions
cnprim_i=0.d0
do i=2,nbulk
eps11_i=0.d0
eps22_i=0.d0
eps12_r=0.d0
cSm050209 The elements eps11_r, eps22_r, eps12_i are used only
c in the dielectric tensor reps()
c They are not used in absorption (cnprim) calculations
eps11_r=0.d0
eps22_r=0.d0
eps12_i=0.d0
c vi=(sqrt(2Te/me)), vi in (cm/sec),Ti(keV)
vi=1.87d9*dsqrt(tempiar(i)/dmas(i))
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
cmui=0.5d0*(cnper*vi/(yi*cvac))**2
cSAP091015
write(*,*)'in absorpfd i,cnper,yi,vi/cvac,cmui',
& i,cnper,yi,vi/cvac,cmui
expmui=dexp(-cmui)
cksi_0=cvac/(cnpar*vi)
cSm050209
c cksi_0=dabs(cksi_0)
p22=xi*cksi_0*expmui ! for (2),(3),(4)
p11=p22/cmui ! for (2)
c nb=100
c------------------------------------------
c izi=1 to calculate modified Bessel functions
c BESSEL FUNCTIONS AND ARGUMENTS ARE REAL
ize=1
call beslci1(cmui,0.d0,nb,ize,br,bi,ncalc)
write(*,*)'in absorpfd cmui,nb,ncalc',cmui,nb,ncalc
c write(*,*)'br',br
c write(*,*)'bi',bi
do k=1,nb
write(*,*)'k,expmui,br(k)*expmui,br(k)',
& k,expmui,br(k)*expmui,br(k)
enddo
p=10.d0*dabs(cnpar)*vi/cvac
l0=1/yi
l1=(1-p)/yi
l2=(1+p)/yi+1
write(*,*)'l1,l2',l1,l2
cSAP091015
c if(l2.gt.98) then
if(l2.gt.(nb-2)) then
cSAP091015
write(*,*)'l2,l1,cnpar,vi/cvac,yi,p',
& l2,l1,cnpar,vi/cvac,yi,p
WRITE(*,*)'in absorpfd l2>nb-2 Increase
1 parameter nb in the subroutine absorpfd'
STOP
endif
if(l1.gt.nb-2) then
WRITE(*,*)'in absorpfd l1>nb-2 Increase
1 parameter nb in the subroutine absorpfd'
STOP
endif
if(l1.lt.-(nb-2)) then
WRITE(*,*)'in absorpfd l1<-(nb-2) Increase
1 parameter nb in the subroutine absorpfd'
STOP
endif
do l=l1,l2
c cksi_l=(1-l*yi)/(N_par*Vi/cvac)
if(l.ge.0) then
lmode=l
else
lmode=-l
endif
besm_l=br(lmode+1) ! |l| order modified Bessel function
besm_lp=br(lmode+2)
if (l.eq.0)then
cksi_l=cksi_0
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
c-------------------------------------------------------------------------
cSm050209 The calculatios for eps11_r,eps22_r,eps12_i
c They are not used in absorption calculations
argz=dcmplx(cksi_l,0.d0)
call CZETA0(cnpar,argz,zf,zfp,ierror)
write(*,*)'absorpfd i,l,argz,zfi_l,imag(zf)',
& i,l,argz,zfi_l,dimag(zf)
zfr_l=dreal(zf)
c-------------------------------------------------------------------------
c besmp_l is a derivative from modified Bessel function I_0
c by argument cmui :I_0 prime=I_1
besmp_l=besm_lp
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
cSm050209 The calculatios for eps22_r
c They are not used in absorption calculations
eps22_r=eps22_r+2.d0*p22*cmui*(besm_l-besmp_l)*zfr_l !(3)
else
cksi_l=(1.d0-l*yi)*cvac/(cnpar*vi)
cksi_l2=cksi_l*cksi_l
zfi_l=spi*dexp(-cksi_l2) !Im(Z_func(cksi_l))
c-------------------------------------------------------------------------
cSm050209 The calculatios for eps11_r,eps22_r,eps12_i
c They are not used in absorption calculations
argz=dcmplx(cksi_l,0.d0)
call CZETA0(cnpar,argz,zf,zfp,ierror)
write(*,*)'absorpfd i,l,argz,zfi_l,zf',
& i,l,argz,zfi_l,zf
zfr_l=dreal(zf)
zfi_l=dimag(zf)
c-------------------------------------------------------------------------
eps11_i=eps11_i+p11*l*l*besm_l*zfi_l !(2)
c besmp_l is a derivative from modified Bessel function I_l
c by argument cmui :I_l prime=0.5*(I_(l-1)+I_(l+1))
besm_lm=br(lmode)
besmp_l=0.5d0*(besm_lp+besm_lm)
eps22_i=eps22_i+2.d0*p22*cmui*(besm_l-besmp_l)*zfi_l !(3)
eps12_r=eps12_r+p22*l*(besm_l-besmp_l)*zfi_l !(4)
cSm050209 The calculatios for epss11_r,eps22_r,eps12_i
c They are not used in absorption calculations
eps11_r=eps11_r+p11*l*l*besm_l*zfr_l !(2)
eps22_r=eps22_r+2.d0*p22*cmui*(besm_l-besmp_l)*zfr_l !(3)
eps12_i=eps12_i-p22*l*(besm_l-besmp_l)*zfr_l !(4)
endif
enddo !l (bessel function order)
eps22_i=eps22_i+eps11_i !(3)
cnprim_s(i)=0.5d0*cnper*(
1 (eps11_i-2.d0*d_*eps33_r*eps12_r/eps33_2)/a2_+
1 (-p1*(eps22_i+eps11_i)-2.d0*d_*eps12_r)*a1_/((p1*p1-d_*d_)*a2_))
cnprim_i=cnprim_i+cnprim_s(i)
c end of the ion absorption calculations
c-----add the hot ions terms to the tensor
cSm050209
c reps(1,1)=reps(1,1)+eps11_i
c reps(2,2)=reps(2,2)+eps22_i
c reps(1,2)=reps(1,2)+ci*eps12_r
reps(1,1)=reps(1,1) + ci*eps11_i + eps11_r
reps(2,2)=reps(2,2) + ci*eps22_i + eps22_r
reps(1,2)=reps(1,2) + eps12_r + ci*eps12_i
enddo !i (ion species)
write(*,*)'subroutine absorpfd after cnprim_i',cnprim_i
reps(2,1)=-reps(1,2)
reps(3,1)=reps(1,3)
reps(3,2)=-reps(2,3)
c***********************************************************************
return
end
c ********************** absorpfw_pinsker ***********
c * ----- *
c * this subroutine calculates imaginary part *
c * of refractive index using formula from: *
c * R.i.Pinsker,M.Porkolab *
c * e-mail: [email protected] *
c * 05/02/10
c ****************************************************
c input parameters: z,r,phi (m,m,radian)
c cnpar -N_parallel (to magnetic field)
c cnper -N_perpendicular (real part)
c tempe- electron temperature (keV)
c dense- electron density (10*13/cm**3
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c tempiar(2:nbulka) ions temperature(kev)
c nbulk is the number of the plasma species
c bmod is the total magnetic field (Tl)
c The input parameter nb (the max number of the modified Bessel
c functions) is set inside absorpfw using operator 'parameter'.
c output parameter: cnprim_e -imaginary part of N_perp
c (electron absorption)
c cnprim_i -imaginary part of N_perp
c (ion absorption)
c
cBH041009: Added breakdown of ion damping into components, cnprim_s(2:nbulk)
c
c-----------------------------------------------------------------*
c it uses beslci1 modified double precision Bessel functions *
c------------------------------------------------------------------
subroutine absorpfw_pinsker(z,r,phi,cnpar,cnper,
1tempe,dense,tempiar,
1nbulk,bmod,cnprim_e,cnprim_i,cnprim_s)
implicit integer (i-n), real*8 (a-h,o-z)
include 'param.i'
include 'ions.i'
include 'eps.i'
dimension cnprim_s(1) !BH041009, for separate ion contributions
!cnprim_s(1:nbulk), cnprim_s(1)=cnprim_e
dimension tempiar(nbulka)
double precision mu,mu2
parameter (nb=100) ! the max order of the modifed Bessel function
dimension br(nb),bi(nb)
c complex argz,zf,zfp
c real rpr,rpim
double complex argz,zf,zfp
double precision rpr,rpim
double complex ci,ckappae2,czero
czero=dcmplx(0.d0,0.d0)
c********************************************************************
c electron absorption:
c Imag(N_perp)=abs(N_perp)*sqrt(pi)/4*beta_e*ksi_e*exp(-ksi_e**2)*G
c--------------------------------------------------------------------
pi=4.d0*datan(1.d0)
spi=dsqrt(pi)
c----------------------------------------
c cvac - light velocity in (cm/sec)
cvac=2.997930d+10
c ve=(sqrt(2Te/me)), ve in (cm/sec),Te(keV)
ve=1.87d9*dsqrt(tempe) !tempe keV
c----------------------------------------
c cksi_e=omega/(k_par*ve)=cvac/(N_par*ve)
cksi_e=cvac/(cnpar*ve)
cSm021022
c cksi_e=dabs(cksi_e)
c----------------------------------------
c beta_e=p_e/(btot**2/(8pi)),p_e electron pressure
c p_e=dense*tempe
c bmod ! tl
btot=bmod*1.d4 ! gauss
p_e=tempe*dense*1.6d+4 !(dyne/cm)
p_b=btot**2/(8.d0*pi) !magnetic pressure (dyne/cm)
beta_e=p_e/p_b
mu=510.94d0/tempe
mu2=mu*mu
c----------------------------------------
c G=(N_par**2-S)/A2+
c {1+omeg_pe**2*Z_r/(omega_e**2*abs(Z)**2*(N_par**2-S)}*
c (m_e*c**2/T_e)**2*(omega_e*D/omega*abs(eps33))**2/(A1*A2)
c----------------------------------------
c p_=P,d_=D,s_=S, P,D,S are like in the article
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
s_=1.d0+xe/(ye*ye)
d_=0.d0
do i=2,nbulk
xi=x(z,r,phi,i)
yi=y(z,r,phi,i)
p=1.d0/(1.d0-yi*yi)
s_=s_-xi*p
d_=d_+xi*p/yi
enddo
p_=-xe
c---------------------------------------
argz=dcmplx(cksi_e,0.d0)
call CZETA0(cnpar,argz,zf,zfp,ierror)
rpr=dreal(zf)
zf_r=dble(rpr) !real(Z(cksi_e))
rpim=dimag(zf)
zf_im=dble(rpim) !imag(Z(cksi_e))
cksi_e2=cksi_e*cksi_e
z_r=2.d0*cksi_e2*(1.d0+cksi_e*zf_r) ! article formula (18)
z_im=2.d0*cksi_e2*cksi_e*zf_im ! article formula (18)
cmodez_2=z_r*z_r+z_im*z_im
eps33_r=xe*z_r ! article formula (5)
eps33_im=xe*z_im ! article formula (5)
eps33_2=eps33_r*eps33_r+eps33_im*eps33_im
cnpar2=cnpar*cnpar
p1=cnpar2-s_ ! for (15),(16),(17)
dp1=1.d0/p1 ! for (15),(16),(17)
z_rdz2=z_r/(cmodez_2)
p2=xe*z_rdz2*dp1/(ye*ye)
a1_=p1+p2*cnpar2 ! (16)
a2_=p1+p2*(cnpar2+s_) ! (17)
g_=p1/a2_+(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
cnprim_e=0.25d0*spi*cnper*beta_e*cksi_e*dexp(-cksi_e2)*g_ !(13)
cnprim_e=dabs(cnprim_e)
cn1=p1/a2_ !(15)
cn2=(1.d0+p2)*mu2*ye*ye*d_*d_/(eps33_2*a1_*a2_) !(15)
c end of the electron absorption calculations
ci=dcmplx(0.d0,1.d0)
cmue=0.5d0*(cnper*ve/(ye*cvac))**2
ckappae2=xe*2.d0*cmue*cksi_e*(zf_r+ci*zf_im) ! formula (7)
c call tensrcld(z,r,phi)
xe=x(z,r,phi,1)
ye=y(z,r,phi,1)
cSm021018
c-----tensor for the electrons with the hot correction
c The hot correction is in eps(2,2),eps(3,3),eps(2,3)
c-----------------------------------------------------
do i=1,3
do j=1,3
reps(i,j)=czero
enddo
enddo
reps(1,1)=1.d0+xe/ye**2 !part of formula(2)
reps(1,2)=xe/ye !part of formula(4)
reps(2,2)=reps(1,1)+ckappae2 !part of formula (3)
reps(3,3)=xe*(z_r+ci*z_im) !formula (5)
reps(2,3)=-ci*0.5*dsqrt(2.d0*cmue)*reps(3,3)/cksi_e !formula (6)
cnprim_s(1)=cnprim_e
c do i=2,nbulk