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D_xx.cc
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//**.****|****.****|****.****|****.****|****.****|****.****|****.****|****.****|
// * D_xx.cc * galprop package * 02/13/2003
//**"****!****"****!****"****!****"****!****"****!****"****!****"****!****"****|
//**.****|****.****|****.****|****.****|****.****|****.****|****.****|****.****|
// Wave damping formalism is described in:
//
// Ptuskin, V.S., et al. 2006, ApJ 642, 902
// Ptuskin, V.S., et al. 2005, Adv. Space Res. 35, 162
//**.****|****.****|****.****|****.****|****.****|****.****|****.****|****.****|
using namespace std;//AWS20050624
#include<cstdio>
#include<cstdlib>
#include"galprop_classes.h"
#include"galprop_internal.h"
int iprotons,ir,ix,iy,iz,ip;
int damping_min_ip; // IMOS20060330
//this is to avoid problems of using Galprop class members in static function "fu" IMOS20060322
Particle *protons;
double damping_p0;
int n_spatial_dimensions, diff_reacc;
#pragma omp threadprivate(iprotons,ir,ix,iy,iz,ip,damping_min_ip,protons,damping_p0,n_spatial_dimensions,diff_reacc)
int Galprop::D_xx(Particle &particle,int iprotons_,int ir_,int ix_,int iy_,int iz_,int ip_)
{
iprotons=iprotons_; ir=ir_; ix=ix_; iy=iy_; iz=iz_; ip=ip_;
double L_cm, Lp_cm, tmp;
// integration parameters
double a=particle.rigidity[ip],ai(0);
//this is to avoid problems of using Galprop class members in static function "fu" IMOS20060322
protons=&gcr[iprotons];
damping_p0=galdef.damping_p0;
n_spatial_dimensions=galdef.n_spatial_dimensions;
diff_reacc=galdef.diff_reacc;
// STANDARD DIFFUSION COEFFICIENT (galdef.diff_reacc =0, 1, 2, -n==beta^n Dxx)
if(galdef.diff_reacc < 3)
{
// test of electron propagation vs analytical calculations IMOS20061030
if(abs(galdef.DM_int0)==99)
particle.Dxx.d2[ir][iz].s[ip]=galdef.D0_xx *pow(particle.Ekin[ip]/galdef.D_rigid_br, galdef.D_g_1);
// end of the test area
else //IMOS20070110
{
if(n_spatial_dimensions==2)
{
particle.Dxx.d2[ir][iz].s[ip] = particle.beta[ip] *galdef.D0_xx;
if(galdef.diff_reacc<0) particle.Dxx.d2[ir][iz].s[ip] = pow(particle.beta[ip],galdef.diff_reacc) *galdef.D0_xx;
if(particle.rigidity[ip]< galdef.D_rigid_br)
particle.Dxx.d2[ir][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_1);
if(particle.rigidity[ip]>=galdef.D_rigid_br)
particle.Dxx.d2[ir][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_2);
}
if(n_spatial_dimensions==3)
{
particle.Dxx.d3[ix][iy][iz].s[ip] = particle.beta[ip] *galdef.D0_xx;
if(galdef.diff_reacc<0) particle.Dxx.d3[ix][iy][iz].s[ip] = pow(particle.beta[ip],galdef.diff_reacc) *galdef.D0_xx;
if(particle.rigidity[ip]< galdef.D_rigid_br)
particle.Dxx.d3[ix][iy][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_1);
if(particle.rigidity[ip]>=galdef.D_rigid_br)
particle.Dxx.d3[ix][iy][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_2);
}
}
// assign Dzz: for isotropic diffusion set equal to Dxx. NB not done for wave damping AWS20131015
if(galdef.Diffusion_aniso==0) //AWS20131016
{
if(n_spatial_dimensions==2)particle.Dzz.d2[ir] [iz].s[ip] = particle.Dxx.d2[ir] [iz].s[ip]; //AWS20131015
if(n_spatial_dimensions==3)particle.Dzz.d3[ix][iy][iz].s[ip] = particle.Dxx.d3[ix][iy][iz].s[ip]; //AWS20131015
}
if(galdef.Diffusion_aniso==1)
{
if(n_spatial_dimensions==2)
{
particle.Dzz.d2[ir][iz].s[ip] = particle.beta[ip] *galdef.D0_zz;
if(galdef.diff_reacc<0) particle.Dzz.d2[ir][iz].s[ip] = pow(particle.beta[ip],galdef.diff_reacc) *galdef.D0_zz;
if(particle.rigidity[ip]< galdef.D_rigid_br)
particle.Dzz.d2[ir][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_1);
if(particle.rigidity[ip]>=galdef.D_rigid_br)
particle.Dzz.d2[ir][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_2);
}
if(n_spatial_dimensions==3)
{
particle.Dzz.d3[ix][iy][iz].s[ip] = particle.beta[ip] *galdef.D0_zz;
if(galdef.diff_reacc<0) particle.Dzz.d3[ix][iy][iz].s[ip] = pow(particle.beta[ip],galdef.diff_reacc) *galdef.D0_zz;
if(particle.rigidity[ip]< galdef.D_rigid_br)
particle.Dzz.d3[ix][iy][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_1);
if(particle.rigidity[ip]>=galdef.D_rigid_br)
particle.Dzz.d3[ix][iy][iz].s[ip]*= pow(particle.rigidity[ip]/galdef.D_rigid_br, galdef.D_g_2);
}
}
return 0;
}
// WAVE DAMPING (see Ptuskin et al. astro-ph/0301420)
if(ip==particle.n_pgrid-1) damping_min_ip=0; // IMOS20060330
L_cm = galdef.damping_max_path_L; // max free path
if(ip<damping_min_ip) // IMOS20060330
{
if(n_spatial_dimensions==2) particle.Dxx.d2[ir] [iz].s[ip] = particle.beta[ip] *C*L_cm/3.;
if(n_spatial_dimensions==3) particle.Dxx.d3[ix][iy][iz].s[ip] = particle.beta[ip] *C*L_cm/3.;
// printout at the solar system position
if(iz==particle.n_zgrid/2+1 && ir==9) cout<<" D_xx>>>> "<<particle.rigidity[ip]<<" "<<particle.Ekin[ip]<<" "<<particle.beta[ip] *C*L_cm/3.<<" "<<-ai<<endl;
return 0;
}
Lp_cm = 3./C *galdef.D0_xx*pow(particle.rigidity[ip]/galdef.D_rigid_br,galdef.D_g_1);
for(int i=1;i<gcr[iprotons].n_pgrid;i++)
if(gcr[iprotons].rigidity[i]> galdef.damping_p0)
{
damping_p0 = gcr[iprotons].rigidity[i]; // re-definition of galdef.damping_p0
break;
}
/*******************TEST
ir=0; iz=0;
for(int i=0; i<particle.n_pgrid; i++)
{
gcr[iprotons].cr_density.d2[0][0].s[i] = pow(gcr[iprotons].p[i],-2.);
cout<<" p= "<<gcr[iprotons].p[i]<<" y= "<<gcr[iprotons].cr_density.d2[0][0].s[i]<<endl;
}
double xxx=0.001;
fu(xxx);
*******************/
// static double (*fuPtr)(double);
// fuPtr = &Galprop::fu;
ai = 0.;
if(n_spatial_dimensions==2)
if(iz>0 && iz<particle.n_zgrid-1 && ir<particle.n_rgrid-1)
if(a<damping_p0) ai=sim(damping_p0,a,a/100.,0.01,1.e-30,&Galprop::fu); //IMOS20060330
if(n_spatial_dimensions==3)
if(iz>0 && iz<particle.n_zgrid-1 && ix>0 && ix<particle.n_xgrid-1 && iy>0 && iy<particle.n_ygrid-1)
if(a<damping_p0) ai=sim(damping_p0,a,a/100.,0.01,1.e-10,&Galprop::fu); //IMOS20060330
// if(a<damping_p0) ai=sim(damping_p0,a,h,reps,aeps,&fu); //IMOS20060330
// cout<<" Dxx------>"<<damping_p0<<" "<<a<<" "<<ai<<endl;
// Kolmogorov diffusion with wave damping ##
if(galdef.diff_reacc==11)
{
tmp = 1. -galdef.damping_const_G*(-ai); // /pow(particle.Z, 5./3.)
if(tmp>0.) L_cm = Lp_cm/pow(tmp, 2);
}
// Kraichnan diffusion with wave damping ##
if(galdef.diff_reacc==12)
{
tmp = 1. -galdef.damping_const_G*(-ai); // /pow(particle.Z, 3./2.)
if(tmp>0.) L_cm = Lp_cm/tmp;
}
if (L_cm>galdef.damping_max_path_L && gcr[iprotons].rigidity[ip]<1.e4) // IMOS20050907
{
L_cm = galdef.damping_max_path_L;
damping_min_ip=ip;
}
if(n_spatial_dimensions==2) particle.Dxx.d2[ir] [iz].s[ip] = particle.beta[ip] *C*L_cm/3.;
if(n_spatial_dimensions==3) particle.Dxx.d3[ix][iy][iz].s[ip] = particle.beta[ip] *C*L_cm/3.;
if(iz==particle.n_zgrid/2+1 && ir==9)
cout<<" D_xx>>>> "<<particle.rigidity[ip]<<" "<<particle.Ekin[ip]
<<" "<<particle.beta[ip] *C*L_cm/3.<<" "<<-ai<<endl;
return 0;
}
//**"****!****"****!****"****!****"****!****"****!****"****!****"****!****"****|
double Galprop::fu(double x)
{
int i,n,m;
double int_psi=0., y;
// cout<<" ir,iz,ip,iprotons,x= "<<ir<<" "<<iz<<" "<<ip<<" "<<iprotons<<" "<<x<<endl;
// for(int i=0; i<protons->n_pgrid; i++) cout<<" "<<protons->cr_density.d2[ir][iz-1].s[i];
// cout<<endl;
// search in the grid
for(n=1;n<protons->n_pgrid;n++) if(protons->p[n]> x) break;
for(m=1;m<protons->n_pgrid;m++) if(protons->p[m]> damping_p0) break;
// cout<<">>>> x,n= "<<x<<" "<<n<<" gcr[iprotons].p[n]= "<<gcr[iprotons].p[n]<<endl;
// integration over rigidity (= momentum for protons)
if(n_spatial_dimensions==2)
{
// fit each interval with power-law and integrate analytically
for(int_psi=0., i=n-1; i<m; i++)
{
if ( protons->cr_density.d2[ir] [iz].s[i] > 0 && protons->cr_density.d2[ir] [iz].s[i+1] > 0 )
{
// derive y (= power-law index)
y =log(protons->cr_density.d2[ir] [iz].s[i]/protons->cr_density.d2[ir] [iz].s[i+1])
/log(protons-> p[i]/protons-> p[i+1]);
// integrate (psi/p) dp
if(i>n-1) int_psi +=protons->cr_density.d2[ir][iz].s[i ] // fit norm.
*pow(protons-> p[i ],-y)/y
*(pow(protons-> p[i+1], y)
-pow(protons-> p[i ], y));
else int_psi +=protons->cr_density.d2[ir][iz].s[i ] // fit norm.
*pow(protons-> p[i ],-y)/y
*(pow(protons-> p[i+1], y)
-pow(x, y));
}
}
}
if(n_spatial_dimensions==3)
{
// fit each interval with power-law and integrate analytically
for(int_psi=0., i=n-1; i<m; i++)
{
// derive y (= power-law index)
if ( protons->cr_density.d3[ix][iy][iz].s[i] > 0 && protons->cr_density.d3[ix][iy][iz].s[i+1] > 0 )
{
y =log(protons->cr_density.d3[ix][iy][iz].s[i]/protons->cr_density.d3[ix][iy][iz].s[i+1])
/log(protons-> p[i]/protons-> p[i+1]);
// integrate (psi/p) dp
if(i>n-1) int_psi +=protons->cr_density.d3[ix][iy][iz].s[i ] // fit norm.
*pow(protons-> p[i ],-y)/y
*(pow(protons-> p[i+1], y)
-pow(protons-> p[i ], y));
else int_psi +=protons->cr_density.d3[ix][iy][iz].s[i ] // fit norm.
*pow(protons-> p[i ],-y)/y
*(pow(protons-> p[i+1], y)
-pow(x, y));
}
}
}
//if(ir==0 && iz==80 && ip==40) cout<<" integral = "<<n<<" "<<y<<" "<<int_psi<<" "<<protons->p[n]<<" "<<x<<" "<<damping_p0 <<endl; //exit(1);
if(diff_reacc==11) return ( pow(x,2./3.)*int_psi ); // Kolmogorov
if(diff_reacc==12) return (sqrt(x) *int_psi ); // Kraichnan
return 0; // in case of an error return 0.
}