const double rms_beam_size(ParticleState const &ps, unsigned axis)
{
if (ps.particle_count == 0)
return 0;
double result = 0;
for (particle_number pn = 0; pn < ps.particle_count; pn++)
result += square(ps.positions[pn*ps.xdim() + axis]);
return sqrt(result/ps.particle_count);
}
const double rms_beam_emittance(ParticleState const &ps, unsigned axis, unsigned beam_axis)
{
if (ps.particle_count == 0)
return 0;
double mean_x = 0;
double mean_xp = 0;
double mean_x_squared = 0;
double mean_xp_squared = 0;
double mean_xxp = 0;
// see doc/notes.tm
for (particle_number pn = 0; pn < ps.particle_count; pn++)
{
const double x = ps.positions[pn*ps.xdim() + axis];
mean_x += x;
mean_x_squared += square(x);
const double px = ps.momenta[pn*ps.vdim() + axis];
const double pz = ps.momenta[pn*ps.vdim() + beam_axis];
const double xprime = pz ? px/pz : 0;
mean_xp += xprime;
mean_xp_squared += square(xprime);
mean_xxp += x*xprime;
}
mean_x /= ps.particle_count;
mean_xp /= ps.particle_count;
mean_x_squared /= ps.particle_count;
mean_xp_squared /= ps.particle_count;
mean_xxp /= ps.particle_count;
return sqrt(
mean_x_squared*mean_xp_squared
- square(mean_x)*mean_xp_squared
- mean_x_squared*square(mean_xp)
- (
square(mean_xxp)
-2*mean_xxp*mean_x*mean_xp
)
);
}
