void PIC::Boris_uxy(Grid2D& Bx, Grid2D& By, double dt)
{
long j;
double tx, ty, tabs2, Bxj, Byj, Babs, u2, gamma, ux0, uy0, uz0;
for(j=0; j<part.size(); j++)
{
Bxj=Bx.Grid2PIC(part[j].x,part[j].y);
Byj=By.Grid2PIC(part[j].x,part[j].y);
Babs=sqrt(pow(Bxj,2)+pow(Byj,2));
u2=pow(part[j].uy,2)+pow(part[j].ux,2)+pow(part[j].uz,2);
gamma=sqrt(1.0+u2/pow(clight,2));
ux0=part[j].ux;uy0=part[j].uy;uz0=part[j].uz;
if (Babs > 0.0) {
tx=Bxj/Babs*tan(charge_p*dt*Babs/(2.0*gamma*mass_p));
ty=Byj/Babs*tan(charge_p*dt*Babs/(2.0*gamma*mass_p)); }
else {tx=0.0; ty=0.0;}
tabs2=pow(tx,2)+pow(ty,2);
part[j].ux+=-part[j].uz*ty;
part[j].uy+=part[j].uz*tx;
part[j].uz+=part[j].ux*ty-part[j].uy*tx;
part[j].ux=ux0-part[j].uz*ty*2.0/(1.0+tabs2);
part[j].uy=uy0+part[j].uz*tx*2.0/(1.0+tabs2);
part[j].uz=uz0+part[j].ux*ty*2.0/(1.0+tabs2)-part[j].uy*tx*2.0/(1.0+tabs2);
}
}
void Pic::kick(Grid2D& Ex, Grid2D& Ey, double ds){
double beta0 = SP->beta0, gamma0 = SP->gamma0, A = SP->A, Z = SP->Z;
double temp = qe*Z/(mp*A*pow(gamma0, 3)*pow(beta0*clight, 2))*ds;
double ex, ey;
for(long j=0; j < pics.size(); ++j){
ex = temp*Ex.Grid2PIC(pics[j].x, pics[j].y);
ey = temp*Ey.Grid2PIC(pics[j].x, pics[j].y);
//momenta:
pics[j].xs += ex;
pics[j].ys += ey;
}
}
double PIC::total_energy(Grid2D& pot)
{
long j, n=part.size();
double ekin=total_kinetic_energy();
double epot=0.0;
for(j=0; j<n; j++)
epot+=macroN*pot.Grid2PIC(part[j].x,part[j].y);
return ekin+epot;
}