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emission.for_DM
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emission.for_DM
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subroutine emiss_coef(aK,fluctcur,ce,flux,v_group,omega,nr,
+iabsorp_collisional,coll_mult,tempe,dense,zeff,
+al_emis,j_emis)
c al_emis (1/cm)
c j_emis (erg*sec/cm**3)
c
c-----calculates the emission coefficient j_emis(erg*sec/cm**3)
c and absorption al_emis (1/cm)
c
c see the article
c R.W.Harvey at al., Phys.Fluids B 5(2),Febrary 1993, page 446
c j_emis is the power radiated by the plasma
c per unit volume-radian frequency-steradian,
c
c formula (3)
c j_emis=pi*Nr**2(omega/clight)**2*vectorE^*tensorG*vectorE/S
c
c vector S(omega,k) is the flux energy density per frequency and
c per unit volume of k space,
c
c formula(4)
c S=vectorVgroup*U
c
c vectorVgroup is the wave group velocity
c
c U is the spectral energy density
c
c formula (5)
c U=1/(8*pi)(vectorB^*vectorB+
c +vectorE^*d(omega*eps_hermitian)/domega*vectorE)
c
c al_emis is absorption coefficient, the inverse damping length
c along the ray of rf wave energy
c
c formula (2)
c al_emis=(omega/(4*pi))vectorE^*eps_anti-herm*vectorE/abs(S)
c
c G is the correlation tensor formula(7)
c
c if iabsorp_collisional=1 it will add the collisional absorption
c al_emis_collisional=nu_ei/(Vgroup) (1/cm)
c in the absorption coeficient
c nu_ei is the electron-ion collision frequency
c coll_mult = multiplier for coll absorption expression (default=1.0)
c------------------------------------------------------------------
implicit none
c-----input
double complex aK(3,3) ! anti-hermitian relativistic tensor
double complex fluctcur(3,3)! correltion tensor G for the fluctuating current(erg)
double complex ce(3) ! wave (normalized) electric field in Stix frame
c wave energy flux for the normalized field |E|=1
c flux=(vectorB*vector_B^*+vector_E*d(omega*tensor_eps_herm)/dw*vector_E)
double complex flux ! wave energy flux for the normalized field |E|=1
double precision omega ! wave angle frequency (1/sec) =2*pi*f
double precision v_group ! wave group velocity [cm/sec]
double precision nr ! ray refructive index
integer iabsorp_collisional ! =0 do not calculate collisional absorption
! =1 to calculte collisonal absorption
double precision coll_mult ! multiplier for coll absorption
double precision tempe, !electron temperature (keV)
& dense, !electron density (10*13/cm**3
& zeff !plasma charge
c-----output
double precision al_emis !(1/sm)
double precision j_emis !(erg*sec/sm**3)
c-----local
double complex cec(3),cal_emis,cj_emis
integer i,j
double precision s,pi,clight,absflux,p
double precision arg,cln,r_nu_ei,al_emis_collisional
pi=4*datan(1.d0)
clight=2.99792458d10 !cm/sec
c--------------------------------------------------------------
c ce - wave electric field
c cec- comlex conjugate wave electric field
c----------------------------------------------------------
do i=1,3
cec(i)=dconjg(ce(i))
enddo
p=flux*dconjg(flux)
absflux=dsqrt(p)
c write(*,*)'emiss_coeff flux,absflux',flux,absflux
c s is the energy flux density per frequency and per unit volume in k space
s=dabs(v_group*absflux/(8.d0*pi))
s=s*4.d0*pi
c write(*,*)'emiss_coeff v_group,absflux,s',v_group,absflux,s
cal_emis=dcmplx(0.0d00,0.0d00)
cj_emis=dcmplx(0.0d00,0.0d00)
c write(*,*)'emiss_coef aK(i,j)',aK(1,1),aK(1,2),aK(1,3)
c write(*,*)aK(2,1),aK(2,2),aK(2,3)
c write(*,*)aK(3,1),aK(3,2),aK(3,3)
c write(*,*)'emiss_coef fluctcur',fluctcur(1,1)*omega,
c +fluctcur(1,2)*omega,fluctcur(1,3)*omega
c write(*,*)fluctcur(2,1)*omega,
c +fluctcur(2,2)*omega,fluctcur(2,3)*omega
c write(*,*)fluctcur(3,1)*omega,
c +fluctcur(3,2)*omega,fluctcur(3,3)*omega
c write(*,*)'emiss_coef ce',ce
do i=1,3
do j=1,3
cal_emis=cal_emis+cec(i)*aK(i,j)*ce(j)
cj_emis =cj_emis +cec(i)*fluctcur(i,j)*ce(j)
c write(*,*)'emiss_coef i,j',i,j
c write(*,*)'cec(i),ce(j),aK(i,j)',cec(i),ce(j),aK(i,j)
c write(*,*)'cec(i)*aK(i,j)*ce(j)',cec(i)*aK(i,j)*ce(j)
c write(*,*)'fluctcur(i,j)',fluctcur(i,j)
c write(*,*)'cj_emis',cj_emis
enddo
enddo
c write(*,*)'emiss_coef 0 cal_emis',cal_emis
c write(*,*)'emiss_coef 0 cj_emis',cj_emis
cal_emis=cal_emis*omega/(4.d0*pi)/s
cj_emis=cj_emis*pi*(nr*omega/clight)**2/s
c write(*,*)'omega,s,omega/(4.d0*pi)/s',omega,s,omega/(4.d0*pi)/s
c write(*,*)'nr,clight,pi*(nr*omega/clight)**2/s',
c +nr,clight,pi*(nr*omega/clight)**2/s
c write(*,*)'emiss_coef cal_emis',cal_emis
c write(*,*)'emiss_coef cj_emis',cj_emis
p=cal_emis*dconjg(cal_emis)
al_emis=dsqrt(p)
al_emis=al_emis*4.d0*pi
c write(*,*)'emiss_coeff cal_emis,al_emis',cal_emis,al_emis
p=cj_emis*dconjg(cj_emis)
j_emis=dsqrt(p)*omega
j_emis=j_emis*4.d0*pi
c write(*,*)'emiss_coeff nr,cj_emis,j_emis',nr,cj_emis,j_emis
if (iabsorp_collisional.eq.0) then
al_emis_collisional=0.d0
endif
if (iabsorp_collisional.eq.1) then
c-------------------------------------------------------------------------------------
c collisional absorption calculations
c-------------------------------------------------------------------------------------
c--------Coulomb Logarithm = cln
arg=(1.d3/tempe)*dsqrt(10.d0*dense) !tempe KeV,
!dense 10**13/sm**3
cln=24.d0-dlog(arg)
c--------electron-ion collision rate =r_nu_ei [1/sec]
r_nu_ei=dense/(tempe*dsqrt(tempe))*zeff*cln*0.919d3 ![1/sec]
al_emis_collisional=2.d0*r_nu_ei/(v_group)*coll_mult
endif
c write(*,*)'al_emis,al_emis_collisional',
c &al_emis,al_emis_collisional
c-----total absorption
al_emis= al_emis+al_emis_collisional
return
end
subroutine emis_tens(X,Y,T_kev,nll_in,np_in,
+n_relt_harm1,n_relt_harm2,n_relt_intgr,
+i_resonance_curve_integration_method,epsi,
+i_fkin,r,z,phi,
+aK,fluctcur)
c-----calulates the anti-hermitian relativistic dielectric tensor aK
c for electron plasma
c and the correlation tensor fluctcur=G for the fluctuating current density
c
c see the article
c R.W.Harvey at all Phys.Fluids B 5(2),Febrary 1993, page 446
c G is the correlation tensor formula(7)
c aK formula (6)
c
c INPUTS:
c
c X = (fpe/f)**2
c Y = fce/f
c T_kev - electron temperature
c nll_in - parallel index of refraction N.
c np_in - perpendicular refractive index N
c n_relt_harm1 - min number of used cyclotron jn harmonics,
c n_relt_harm2 - max number of used cyclotron jn harmonics,
c n_relt_harm1 <= jn <= n_relt_harm2
c n_relt_intgr - the number of points for the integration over p_perp
c i_fkin =0 the usage of the analytic relativistic distribution
c =1 the usage of the numerical 3D distribution from diskf or netcdfnm.nc
c written be CQL3D code or created analytically at mesh points
c r - the major radius (it is used for i_fkin=1)
c z - the vertical coordinate (it is used for i_fkin=1)
c phi - toroidal angle
c----------------------------------------------------------------------
c i_resonance_curve_interation_method
c
c i_resonance_curve_integration_method=1 angle integration
c now it works for ellipse case only c
c
c i_resonance_curve_integration_method=2 rectangle formula
c for p_perp integration
c
c i_resonance_curve_integration_method=3 trapezoidal formula
c for p_perp integration
c
c i_resonance_curve_integration_method=4 !adaptive Simpson
c for p_perp integration
c
c epsi is the accuracy used in integration by adaptive Simpson
c------------------------------------------------------------
c OUTPUT:
c aK(3,3): the nine components of the anti-hermition
c part dielectric relativistic tensor
c evaluated at (X,Y,Te,nll,np,n)
c
c fluctcur(3,3) the correlation tensor fluctcur=G (egr)
c for the fluctuating current density
c
implicit none
c input
double precision X,Y,T_kev,nll_in,np_in,epsi
integer n_relt_harm1,n_relt_harm2,n_relt_intgr,i_fkin,
&i_resonance_curve_integration_method
double precision r,z,phi
c output
double complex aK(3,3),fluctcur(3,3)
c local
double precision c,mass_e,k_1_kev,nll,np,nlls,p_perp0,theta,pi,
.dens,xpidens,xpidensmcs,p,psi,rho
double complex integral(3,3)
double complex fluctcur_n(3,3)
integer jn,ires,jn_negative
c external zeroK, npnllmin, ec_cond, intgr_rl,fdens_fdist
double precision fdens_fdist,fpsi,rhopsi,densrho
c =2.99792458d10 !speed of light (cm/sec)
mass_e=9.1094d-28 !electron rest mass (g)
k_1_kev=1.6022d-9 !egrs in 1 KeV (erg)
theta=mass_e*c**2/(k_1_kev*T_kev)
pi=4.d0*datan(1.d0)
call npnllmin(nll_in,np_in,nll,np)
nlls = nll**2
c-----initialization aK=0
call zeroK(aK)
call zeroK(fluctcur)
c-----the loop over the cyclotron harmonics
write(*,*)'emission.f in emis_tens'
do jn=n_relt_harm1,n_relt_harm2
jn_negative=-jn
c-------control the EC resonance condition
cSm060315
c call ec_cond(jn,Y,nll,ires,p_perp0)
call ec_cond(jn_negative,Y,nll,ires,p_perp0)
c write(*,*)'emission.f emis_tens jn,ires,p_perp0',jn,ires,p_perp0
if(ires.eq.0) then
c---------no resonace
goto 10
endif
cSm060315
c call intgr_emis(jn,nll,np,Y,theta,ires,p_perp0,n_relt_intgr,
call intgr_emis(jn_negative,nll,np,Y,theta,ires,p_perp0,
+ n_relt_intgr,i_resonance_curve_integration_method,epsi,
+ i_fkin,r,z,phi,
+ integral,fluctcur_n)
c write(*,*)'emis_tens after integr_emis integral',integral
c write(*,*)'emis_tens after integr_emis fluctcur_n',fluctcur_n
aK(1,1)=aK(1,1)+integral(1,1)
aK(1,2)=aK(1,2)+integral(1,2)
aK(1,3)=aK(1,3)+integral(1,3)
aK(2,2)=aK(2,2)+integral(2,2)
aK(2,3)=aK(2,3)+integral(2,3)
aK(3,3)=aK(3,3)+integral(3,3)
fluctcur(1,1)=fluctcur(1,1)+fluctcur_n(1,1)
fluctcur(1,2)=fluctcur(1,2)+fluctcur_n(1,2)
fluctcur(1,3)=fluctcur(1,3)+fluctcur_n(1,3)
fluctcur(2,2)=fluctcur(2,2)+fluctcur_n(2,2)
fluctcur(2,3)=fluctcur(2,3)+fluctcur_n(2,3)
fluctcur(3,3)=fluctcur(3,3)+fluctcur_n(3,3)
10 continue
enddo !jn
if (i_fkin.eq.0) then
dens=1.d0
else
c dens=fdens_fdist(r,z,phi)
cSm011228 call the density of the bulk plasma to reduce the CPU time
psi=fpsi(r,z)
rho=rhopsi(psi)
dens=densrho(rho,1)
c write(*,*)'emision_tens dens',dens
c dens=1.d0
endif
c-----normalization for the unit electron density
xpidens=X*pi/dens
aK(1,1)=-xpidens*aK(1,1)
aK(1,2)=-xpidens*aK(1,2)
aK(1,3)=-xpidens*aK(1,3)
aK(2,2)=-xpidens*aK(2,2)
aK(2,3)=-xpidens*aK(2,3)
aK(3,3)=-xpidens*aK(3,3)
c aK(2,1)=-aK(1,2)
c aK(3,1)= aK(1,3)
c aK(3,2)=-aK(2,3)
cSm060705
aK(2,1)=conjg(aK(1,2))
aK(3,1)=conjg(aK(1,3))
aK(3,2)=conjg(aK(2,3))
xpidensmcs=X*pi/(2.d0*pi)**5*(mass_e*c**2)/dens
fluctcur(1,1)=fluctcur(1,1)*xpidensmcs
fluctcur(1,2)=fluctcur(1,2)*xpidensmcs
fluctcur(1,3)=fluctcur(1,3)*xpidensmcs
fluctcur(2,2)=fluctcur(2,2)*xpidensmcs
fluctcur(2,3)=fluctcur(2,3)*xpidensmcs
fluctcur(3,3)=fluctcur(3,3)*xpidensmcs
fluctcur(2,1)=-fluctcur(1,2)
fluctcur(3,1)= fluctcur(1,3)
fluctcur(3,2)=-fluctcur(2,3)
return
end
subroutine intgr_emis(n,nll,np,Y,theta,ires,p_perp0,
+n_relt_intgr,i_resonance_curve_integration_method,epsi,
+i_fkin,r,z,phi,
+integral,fluctcur_n)
c-----------------------------------------------------------------
c calculates the matrix: double complex integrals
c for the relativistic electron plasma
c I(n)^=integral(0<=p_perp<=p_perp0)g_n, g_n={sum_k=1,2,G_nk(p_perp)
c fluctcar(n)^=integral(0<=p_perp<=p_perp0)g_fluctcur_n.
c g_fluctcur_n={sum_k=1,2,g_fluctcur_nk(p_perp)
c for the EC harmonic with number 'n'
c-----------------------------------------------------------------
c input
c n - EC harmonic number
c nll - N_parallel
c np - N_perpendicular
c Y = omega_ce/omega for the electron rest mass
c theta = mc**2/T
c ires =0 no resonance,=1 ellipse,=2 parabola,=3 hyperbole
c n_relt_intgr - the number of points for the integration over p_perp
c p_perp0 - max value of the perpendicular momentum divided by mc
c on the resonanse ellipse
c i_fkin =0 the usage of the analytic relativistic distribution
c =1 the usage of the numerical 3D distribution from diskf
c written be CQL3D code
c r - the major radius (it is used for i_fkin=1)
c z - the vertical coordinate (it is used for i_fkin=1)
c phi - toroidal angle (it is used for i_fkin=1)
c i_resonance_curve_interation_method
c
c i_resonance_curve_integration_method=1 angle integration
c now it works for ellipse case only c
c
c i_resonance_curve_integration_method=2 rectangle formula
c for p_perp integration
c
c i_resonance_curve_integration_method=3 trapezoidal formula
c for p_perp integration
c
c i_resonance_curve_integration_method=4 !adaptive Simpson
c for p_perp integration
c
c epsi is the accuracy used in integration by adaptive Simpson
c
c------------------------------------------------------------
c output
c integral(3,3) double complex integral from G_nk over 0<=p_perp=<p_perpmax
c fluctcur(3,3) double complec integral from fluct_cur_nk over 0<=p_perp=<p_perpmax
c----------------------------------------------------------------
c The integration method is specified by the variable
c i_resonance_curve_integration_method.
c Now this variable is set inside this subroutine.
c----------------------------------------------------------------
implicit none
c input
double precision nll,np,Y,theta,p_perp0,epsi
integer n,ires,n_relt_intgr,i_fkin,
&i_resonance_curve_integration_method
double precision r,z,phi
double precision vnormloc,massloc ! cm/sec, g
COMMON /dskin1/vnormloc,massloc
c output
double complex integral(3,3)
double complex fluctcur_n(3,3)
c local
cSm060725
double precision eps,p_permax,h,p_perp,p,p_t,clight,p_int,
c double precision eps,p_permax,h,p_perp,p,p_t,jmax,clight,p_int,
&vmax_d_vt
double complex i,g_n(3,3),g_fluctcur_n(3,3)
cSm060725
integer j,jmax
c-----for integration along ellipse by angle
double precision rme,rtem0,vper,xint,cs,sn,thet1,thet2,p_par,
& p_par_min,p_par_pl,p_perp_min,p_perp_pl,v0dc,vmax1dc,vpar0dc,
+vpar1dc,vpar2dc,dth,vt0,cdvt,tem0,dvper,vmaxdt
c external
c ec_cond, zeroK, g_n
double precision temperho
i = ( 0.0d0,1.0d0) !imaginary number
jmax=n_relt_intgr
cSm060310
if(ires.eq.0)goto10 ! no resonance
vmax_d_vt=10.d0
call p_perp_max_calc(i_fkin,theta,n,Y,nll,vmax_d_vt,
&vnormloc,p_permax,ires)
if(ires.eq.4) then
c--------the resonance curve is outside the grid
call zeroK(integral)
call zeroK(fluctcur_n)
goto 10
else
h=p_permax/(n_relt_intgr) ! step of integration over p_perp
endif
c calculations of the integrals over p_perp
call zeroK(integral)
call zeroK(fluctcur_n)
c----------------------------------------------------------
c i_resonance_curve_interation_method
c
c i_resonance_curve_interation_method=1 angle integration
c now it works for ellipse case only c
c i_resonance_curve_interation_method=2 rectangle formula
c for p_perp integraion
c
c i_resonance_curve_interation_method=3 trapezoidal formula
c for p_perp integraion
c
c i_resonance_curve_integration_method=4 !adaptive Simpson
c for p_perp integration
c------------------------------------------------------------
goto (1,2,3,4) i_resonance_curve_integration_method
1 continue
cSm060327
if(dabs(nll).ge.1.d0) goto 3 !to trapezoidal formula
c--------------------------------------------------------------------
c integration along the resonance curve using angle (thet)
c thet1<thet<thet2
c begin
c--------------------------------------------------------------------
clight=2.99792458d10
rme=9.1094d-28
call get_rtem0_from_one(rtem0)
tem0=temperho(0.d0,1)*rtem0
vt0=dsqrt(2.d0*tem0*1.6022d-9/rme) !(cm/sec)the central
!thermal velocity
cdvt=clight/vt0
vmaxdt=dsqrt(rtem0)
call ec_condh(n,Y,nll,vmaxdt/cdvt,ires,v0dc,vmax1dc,vpar0dc,
+vpar1dc,vpar2dc,thet1,thet2)
c write(8,*)'theta integration boundaries: thet1,thet2',
c thet1,thet2
c-----Subdivide theta range of integration
dth=(thet2-thet1)/(jmax-1)
do j=1,jmax
xint=thet1+(j-1)*dth
cs=dcos(xint)
sn=dsin(xint)
p_par=(vpar0dc-dabs(v0dc)*cs) !vper/Vt
p_perp=vmax1dc*sn !vpar/Vt
if(p_perp.lt.1.d-3) p_perp=1.d-3 !to avoid singularity
call g_n_emis_theta(p_perp,p_par,y,nll,np,theta,n,i_fkin,
& r,z,phi,g_n,g_fluctcur_n)
if((j.ne.jmax).and.(j.ne.1)) then
sn=dsin(xint+dth)
p_perp_pl=vmax1dc*sn !vper/c
sn=dsin(xint-dth)
p_perp_min=vmax1dc*sn
h=0.5d0*(dabs(p_perp_pl-p_perp)+dabs(p_perp-p_perp_min))
else
if(j.eq.1) then
sn=dsin(xint+dth)
p_perp_pl=vmax1dc*sn !vper/c
h=0.5d0*dabs(p_perp_pl-p_perp)
else
!j=jmax
sn=dsin(xint-dth)
p_perp_min=vmax1dc*sn !vper/c
h=0.5d0*dabs(p_perp-p_perp_min)
endif
endif
integral(1,1)=integral(1,1)+h*g_n(1,1)
integral(1,2)=integral(1,2)+h*g_n(1,2)
integral(1,3)=integral(1,3)+h*g_n(1,3)
integral(2,2)=integral(2,2)+h*g_n(2,2)
integral(2,3)=integral(2,3)+h*g_n(2,3)
integral(3,3)=integral(3,3)+h*g_n(3,3)
fluctcur_n(1,1)=fluctcur_n(1,1)+h*g_fluctcur_n(1,1)
fluctcur_n(1,2)=fluctcur_n(1,2)+h*g_fluctcur_n(1,2)
fluctcur_n(1,3)=fluctcur_n(1,3)+h*g_fluctcur_n(1,3)
fluctcur_n(2,2)=fluctcur_n(2,2)+h*g_fluctcur_n(2,2)
fluctcur_n(2,3)=fluctcur_n(2,3)+h*g_fluctcur_n(2,3)
fluctcur_n(3,3)=fluctcur_n(3,3)+h*g_fluctcur_n(3,3)
enddo
goto 20
c--------------------------------------------------------------------
c integration along the resonance curve using angle (thet)
c thet1<thet<thet2
c end
c--------------------------------------------------------------------
2 continue
c --------------------------------------------------------------------
c integration along the resonance curve using rectangle
c formula
c begin
c--------------------------------------------------------------------
cSm060306
do j=1,jmax
p_perp=h*(j-0.5)
call g_n_emis(p_perp,y,nll,np,theta,n,i_fkin,r,z,phi,
. g_n,g_fluctcur_n)
integral(1,1)=integral(1,1)+g_n(1,1)
integral(1,2)=integral(1,2)+g_n(1,2)
integral(1,3)=integral(1,3)+g_n(1,3)
integral(2,2)=integral(2,2)+g_n(2,2)
integral(2,3)=integral(2,3)+g_n(2,3)
integral(3,3)=integral(3,3)+g_n(3,3)
fluctcur_n(1,1)=fluctcur_n(1,1)+g_fluctcur_n(1,1)
fluctcur_n(1,2)=fluctcur_n(1,2)+g_fluctcur_n(1,2)
fluctcur_n(1,3)=fluctcur_n(1,3)+g_fluctcur_n(1,3)
fluctcur_n(2,2)=fluctcur_n(2,2)+g_fluctcur_n(2,2)
fluctcur_n(2,3)=fluctcur_n(2,3)+g_fluctcur_n(2,3)
fluctcur_n(3,3)=fluctcur_n(3,3)+g_fluctcur_n(3,3)
enddo
integral(1,1)=integral(1,1)*h
integral(1,2)=integral(1,2)*h
integral(1,3)=integral(1,3)*h
integral(2,2)=integral(2,2)*h
integral(2,3)=integral(2,3)*h
integral(3,3)=integral(3,3)*h
fluctcur_n(1,1)=fluctcur_n(1,1)*h
fluctcur_n(1,2)=fluctcur_n(1,2)*h
fluctcur_n(1,3)=fluctcur_n(1,3)*h
fluctcur_n(2,2)=fluctcur_n(2,2)*h
fluctcur_n(2,3)=fluctcur_n(2,3)*h
fluctcur_n(3,3)=fluctcur_n(3,3)*h
goto 20
c --------------------------------------------------------------------
c integration along the resonance curve using rectangle
c formula
c end
c--------------------------------------------------------------------
3 continue
cSm060306
c --------------------------------------------------------------------
c integration along the resonance curve using trapezoidal
c formula
c begin
c--------------------------------------------------------------------
do j=0,jmax
p_int=1.d0
if((j.eq.1).or.(j.eq.jmax)) p_int=0.5d0
p_perp=h*j
if(p_perp.lt.1.d-3) p_perp=1.d-3
if(j.eq.jmax) p_perp=p_perp-1.d-3
call g_n_emis(p_perp,y,nll,np,theta,n,i_fkin,r,z,phi,
. g_n,g_fluctcur_n)
integral(1,1)=integral(1,1)+p_int*g_n(1,1)
integral(1,2)=integral(1,2)+p_int*g_n(1,2)
integral(1,3)=integral(1,3)+p_int*g_n(1,3)
integral(2,2)=integral(2,2)+p_int*g_n(2,2)
integral(2,3)=integral(2,3)+p_int*g_n(2,3)
integral(3,3)=integral(3,3)+p_int*g_n(3,3)
fluctcur_n(1,1)=fluctcur_n(1,1)+p_int*g_fluctcur_n(1,1)
fluctcur_n(1,2)=fluctcur_n(1,2)+p_int*g_fluctcur_n(1,2)
fluctcur_n(1,3)=fluctcur_n(1,3)+p_int*g_fluctcur_n(1,3)
fluctcur_n(2,2)=fluctcur_n(2,2)+p_int*g_fluctcur_n(2,2)
fluctcur_n(2,3)=fluctcur_n(2,3)+p_int*g_fluctcur_n(2,3)
fluctcur_n(3,3)=fluctcur_n(3,3)+p_int*g_fluctcur_n(3,3)
enddo
integral(1,1)=integral(1,1)*h
integral(1,2)=integral(1,2)*h
integral(1,3)=integral(1,3)*h
integral(2,2)=integral(2,2)*h
integral(2,3)=integral(2,3)*h
integral(3,3)=integral(3,3)*h
fluctcur_n(1,1)=fluctcur_n(1,1)*h
fluctcur_n(1,2)=fluctcur_n(1,2)*h
fluctcur_n(1,3)=fluctcur_n(1,3)*h
fluctcur_n(2,2)=fluctcur_n(2,2)*h
fluctcur_n(2,3)=fluctcur_n(2,3)*h
fluctcur_n(3,3)=fluctcur_n(3,3)*h
goto20
c --------------------------------------------------------------------
c end integration along the resonance curve using trapezoidal
c formula
c end
c--------------------------------------------------------------------
4 continue
cSm070417
c -------------------------------------------------------------------
c integration along the resonance curve using
c the adaptive Simpson function
c--------------------------------------------------------------------
c write(*,*)'emission.f intgr_emis before adaptive_simpson'
call calc_emission_integral_array_by_adaptive_simpson
&(y,nll,np,theta,n,i_fkin,r,z,phi,p_permax,epsi,
&integral,fluctcur_n)
c write(*,*)'intgr_emis after adaptive_simpson'
c write(*,*)'integral',integral
c write(*,*)'fluctcur_n',fluctcur_n
c--------------------------------------------------------------------
20 continue
integral(2,1)=-integral(2,1)
integral(3,1)= integral(3,1)
integral(3,2)=-integral(3,2)
fluctcur_n(2,1)=-fluctcur_n(2,1)
fluctcur_n(3,1)= fluctcur_n(3,1)
fluctcur_n(3,2)=-fluctcur_n(3,2)
10 continue
return
end
subroutine g_n_emis(p_perp,y,nll,np,theta,n,i_fkin,r,z,phi,
.g_n,g_fluctcur_n)
c calculates under integral complex marix functions
c g_n(3,3)=sum{k}g_nk and g_fluctcur_n(3,3)=sum{k}g_fluctcur_nk
c input
c p_perp - momentum divided by (mc)
c y = omega_ce/omega for the electron rest mass
c nll - N_parallel
c np - N_perpendicular
c theta - mc**2/T
c n - n number of the given resonance harmonic
c i_fkin =0 the usage of the analytical relativistic distributin
c =1 the usage of the numerical 3D distribution from diskf
c written be CQL3D code
c r - the major radius (it is used for i_fkin=1)
c z - the vertical coordinate (it is used for i_fkin=1)
c phi - toroidal angle(it is used for i_fkin=1)
c output
c g_n(3,3) under integral matrix double complex function
c g_fluctcur_n(3,3)
c-------------------------------------------------------
implicit none
c-----input
double precision p_perp,y,nll,np,theta,r,z,phi
integer n,i_fkin
c-----external root_res, s_calcn, zeroK, unde_intgr
double precision u_n,u_flcur_n
c-----output
double complex g_n(3,3), g_fluctcur_n(3,3)
c-----local
double complex sn_k(3,3),g_nk(3,3),g_fluctcur_nk(3,3)
double precision gamma, p_par_rl(2),coeff,eps,ps,ps_max,pi,
+dgdp_par,u_nk,u_flcur_nk,coeff_fc
integer k,kmax,i,j
c kmax - total number of the resonace condition root p_perp_k(p_perp)
pi=4.d0*datan(1.d0)
c-----calculations ot the roots p_par_rl of the resonace condition
c-----gamma=N_par*p_par_rl+nY
call root_res(p_perp,nll,n,Y,kmax,p_par_rl)
c write(*,*)'g_n_emis number of roots p_par_rl(p_perp) kmax',kmax
c-----initialize g_n
call zeroK(g_n)
call zeroK(g_fluctcur_n)
if (kmax.eq.0) goto 20
c eps=1.d-9 ! the min value of Maxwell exponent
c ps_max=(1.d0-dlog(eps)/theta)**2-1.d0
do k=1,kmax
ps=p_perp*p_perp+p_par_rl(k)*p_par_rl(k)
gamma=dsqrt(1.d0+ps)
c if(ps.gt.ps_max) then
c write(*,*)'emission.f g_n_emis k,ps,ps_max',k,ps,ps_max
c goto 10
c endif
c write(*,*)'g_n_emis k,p_perp,p_par_rl(k),ps',
c . k,p_perp,p_par_rl(k),ps
call s_calcn(n,p_perp,p_par_rl(k),np,y,sn_k)
c write(*,*)'g_n_emis k,sn_k',k,sn_k
c--------resonance condition uses the delta function with argument
c g_delta=gamma-nll*p_par-n*y
c the derivative from this argument d(g_delta)/dp_par=dgdp_par
dgdp_par=dabs((p_par_rl(k)-nll*gamma)/gamma)
cSm030415
c if(dgdp_par.lt.1.d-3)then
c write(*,*)'dgdp_par k,p_par_rl(k),nll,p_perp,gamma',
c + k,p_par_rl(k),nll,p_perp,gamma
c endif
call unde_intgr(p_perp,p_par_rl(k),y,nll,theta,n,i_fkin,
+ r,z,phi,u_nk,u_flcur_nk)
c write(*,*)'in g_n_emis after unde_integr u_nk,u_flcur_nk',
c + u_nk,u_flcur_nk
coeff=2.d0*pi*u_nk/dgdp_par
coeff_fc=2.d0*pi*u_flcur_nk/dgdp_par
c write(*,*)'in g_n_emis u_nk,u_flcur_nk',u_nk,u_flcur_nk
c write(*,*)'in g_n_emis coeff,coeff_fc',coeff,coeff_fc
g_nk(1,1)=coeff*sn_k(1,1)
g_nk(1,2)=coeff*sn_k(1,2)
g_nk(1,3)=coeff*sn_k(1,3)
g_nk(2,2)=coeff*sn_k(2,2)
g_nk(2,3)=coeff*sn_k(2,3)
g_nk(3,3)=coeff*sn_k(3,3)
g_nk(2,1)=-g_nk(1,2)
g_nk(3,1)= g_nk(1,3)
g_nk(3,2)=-g_nk(2,3)
g_fluctcur_nk(1,1)=coeff_fc*sn_k(1,1)
g_fluctcur_nk(1,2)=coeff_fc*sn_k(1,2)
g_fluctcur_nk(1,3)=coeff_fc*sn_k(1,3)
g_fluctcur_nk(2,2)=coeff_fc*sn_k(2,2)
g_fluctcur_nk(2,3)=coeff_fc*sn_k(2,3)
g_fluctcur_nk(3,3)=coeff_fc*sn_k(3,3)
do i=1,3
do j=1,3
g_n(i,j)=g_n(i,j)+g_nk(i,j)
g_fluctcur_n(i,j)=g_fluctcur_n(i,j)+g_fluctcur_nk(i,j)
enddo
enddo
10 continue
enddo !kmax
20 continue
return
end
subroutine unde_intgr(p_perp,p_par,y,nll,
+theta,n,i_fkin,r,z,phi,u_n,u_flcur_n)
c calculates under integral functions
c u_n=U_n(np=p_per,p_perp=p_parallel)=(1/gamma)*
c (n*Y*df/dp^_perpendicular+N_parallel*p^_perpendicular*df/dp^_parallel)
c u_n is used in under integral complex marix function G_nk(3,3)
c
c u_flcur_n=f*p^perp/gamma
c u_flcur_n is used in under integral complex matrix fluct_car_nk(3,3)
c Here p^=p/mc
c input
c p_perp - perpendicular momentum divided by (mc)
c p_par parallel momentum/mc
c y = omega_ce/omega for the electron rest mass
c nll - N_parallel
c theta - mc**2/T
c n - n number of the given resonance harmonic
c i_fkin =0 the usage of the analytical relativistic Maxwellian distributin
c =1 the usage of the numerical 3D distribution from diskf or
c netcdfnm.nc files or the mesh distribution given analytically
c written be CQL3D code
c r - the major radius (it is used for i_fkin=1)
c z - the vertical coordinate (it is used for i_fkin=1)
c phi - toroidal angle
c-------------------------------------------------------
implicit none
c input
double precision p_perp,p_par,y,nll,theta
double precision r,z,phi
integer n,i_fkin
c external besk2as, root_res,psif,rhopsi,bmin_psi,b
double precision psif,rhopsi,bmin_psi,b,fdens_fdist
c output
double precision u_n,u_flcur_n
c_for test
double precision vnormloc,massloc
COMMON /dskin1/vnormloc,massloc !v (cm/sec),m( g)
cendtest
c local
double precision gamma, bk2,f_maxw,ps,p,ps_max,eps,pi,d_maxw_dp,
+ m_e,clight,energy,psi,rho,pitch,pitch0,bmin,btotal,
+ c_pitch,s_pitch,s_pitch0,c_pitch0,
+ dptc0dpt, !d(pitch0)/d(pitch)
+ dens,u_np,u_flcur_np
c distributin function and its derivatives
double precision fdist0,dfdx,dfdpitch,dfdpitc0,dfdp
integer initial
c-----!
pi=4*datan(1.d0)
ps=p_perp*p_perp+p_par*p_par
p=dsqrt(ps)
gamma=dsqrt(1.d0+ps)
if (i_fkin.eq.0) then
c--------usage of the analytical relativistic Maxwellian distribution
c calculation the Mackdonalds function bk2=K_2(theta)*EXP(theta)
call besk2as(theta,bk2)
eps=1.d-9 ! the min value of Maxwell exponent
ps_max=(1.d0-dlog(eps)/theta)**2-1.d0
c if(ps.gt.ps_max) then
c u_n=0.d0
c goto 10
c endif
f_maxw=theta*dexp(theta*(1.d0-gamma))/(4.d0*pi*bk2)
u_n=-p_perp*theta*f_maxw*(n*y+nll*p_par)/(gamma*gamma)
u_flcur_n=p_perp*f_maxw/gamma
cSm070126
c write(*,*)' emission unde_int'
c write(*,*)' old u_n, old f_maxw,u_n,u_flcur_n',
c & f_maxw,u_n,u_flcur_n
call analytical_distrib(theta,p,r,z,phi,
& f_maxw,d_maxw_dp)
u_n=p_perp*d_maxw_dp*(n*y+nll*p_par)/gamma/p
u_flcur_n=p_perp*f_maxw/gamma
c write(*,*)'unde_intgr new f_maxw,u_n u_flcur_n',
c & f_maxw,u_n,u_flcur_n
goto10
endif
if (i_fkin.eq.1)then
c--------usage of the numerical 3D relativistic distribution from diskf file
c written by CQL3D code
initial=0
c energy=p**2/(2m) ps=(p/mc)**2. energy should be in KeV
c pitch
c rho
m_e=9.1094d-28 !g
clight=2.99792458d10 !cm/sec
energy=0.5d0*ps*m_e*clight**2 !erg
energy=energy/1.6022d-9 !KeV
psi=psif(z,r) !poloidal flux
rho=rhopsi(psi)!small radius
if (p.ne.0.d0) then
pitch=dacos(p_par/p)
else
pitch=0.d0
endif
if (pitch.gt.pi) pitch=pi
if (pitch.lt.-pi) pitch=-pi
c------- pitch0 is pitch angle for the point with the minimal
c------- value of the magnetic field at the give flux surface with the poloidal flux=psi
pitch0=pitch
dptc0dpt=1.d0
cSm060227
c goto 100
bmin=bmin_psi(psi)
btotal=b(z,r,phi)
if (p.ne.0.d0) then
c_pitch=p_par/p !cos(pitch)
s_pitch=p_perp/p !sin(pitch)
else
c_pitch=1.d0 !cos(pitch)
s_pitch=0.d0 !sin(pitch)
endif
c--------s_pitch0=sin and c_pitch0=cos of the pitch angle for the minimal b
s_pitch0=s_pitch*dsqrt(bmin/btotal) !sin(pitch0)
c write(*,*)'bmin,btotal,s_pitch,s_pitch0',
c + bmin,btotal,s_pitch,s_pitch0
if (s_pitch0.gt.1.d0) then
s_pitch0=1.d0
c_pitch0=0.d0
else
c_pitch0=dsqrt(1.d0-s_pitch0**2) !dabs(cos(pitch0))
endif
if (c_pitch.lt.0.d0) then
c_pitch0=-c_pitch0
endif
pitch0=dacos(c_pitch0)
if (pitch0.gt.pi) pitch0=pi
if (pitch0.lt.-pi) pitch0=-pi
c write(*,*)'emission in u_n pitch,pitch0',pitch,pitch0
c--------d(pitch0)/d(pitch)
c dptc0dpt=(c_pitch/c_pitch0)*(s_pitch0/s_pitch)
cSm051206
if((dabs(c_pitch0).lt.1.d-12).or.(dabs(s_pitch).lt.1.d-12))
& then
dptc0dpt=1.d0
else
dptc0dpt=(c_pitch/c_pitch0)*(s_pitch0/s_pitch)
endif
c write(*,*)'c_pitch,c_pitch0',c_pitch,c_pitch0
c write(*,*)'s_pitch,s_pitch0',s_pitch,s_pitch0
100 continue
c--------calculations of the distribution function fdist0
c and its derivatives df/dx,df/dpitch0
c x = momentum-per-mass(nomalized to maximum 1.)
c vel=dsqrt(2.d0*energy*1.d3*1.6022d-12/fmass(1))
c at the point (rho,energy,pitch0). Here pitch0=pitch0(r,z,pitch)
c write(*,*)'unde_intgr initial,energy,pitch0,rho',
c + initial,energy,pitch0,rho
call dskin(initial,energy,pitch0,rho,fdist0,dfdx,dfdpitc0,