def calc_emittance_coupling(accelerator):
# I copied the code below from:
# http://nicky.vanforeest.com/misc/fitEllipse/fitEllipse.html
def fitEllipse(x,y):
x = x[:,_np.newaxis]
y = y[:,_np.newaxis]
D = _np.hstack((x*x, x*y, y*y, x, y, _np.ones_like(x)))
S = _np.dot(D.T,D)
C = _np.zeros([6,6])
C[0,2] = C[2,0] = 2; C[1,1] = -1
E, V = _np.linalg.eig(_np.linalg.solve(S, C))
n = _np.argmax(_np.abs(E))
a = V[:,n]
b,c,d,f,g,a = a[1]/2, a[2], a[3]/2, a[4]/2, a[5], a[0]
up = 2*(a*f*f+c*d*d+g*b*b-2*b*d*f-a*c*g)
down1 = (b*b-a*c)*( (c-a)*_np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
down2 = (b*b-a*c)*( (a-c)*_np.sqrt(1+4*b*b/((a-c)*(a-c)))-(c+a))
res1 = _np.sqrt(up/down1)
res2 = _np.sqrt(up/down2)
return _np.array([res1, res2]) #returns the axes of the ellipse
acc = accelerator[:]
acc.cavity_on = False
acc.radiation_on = False
orb = _tracking.findorbit4(acc)
rin = _np.array([2e-5+orb[0],0+orb[1],1e-8+orb[2],0+orb[3],0,0],dtype=float)
rout, *_ = _tracking.ringpass(acc, rin, nr_turns=100, turn_by_turn='closed',element_offset = 0)
r = _np.dstack([rin[None,:,None],rout])
ax,bx = fitEllipse(r[0][0],r[0][1])
ay,by = fitEllipse(r[0][2],r[0][3])
return (ay*by) / (ax*bx) # ey/ex
def get_mcf(accelerator, order=1, energy_offset=None):
"""Return momentum compaction factor of the accelerator"""
if energy_offset is None:
energy_offset = _np.linspace(-1e-3,1e-3,11)
accel=accelerator[:]
_tracking.set4dtracking(accel)
ring_length = _lattice.length(accel)
dl = _np.zeros(_np.size(energy_offset))
for i in range(len(energy_offset)):
fp = _tracking.findorbit4(accel,energy_offset[i])
X0 = _np.concatenate([fp,[energy_offset[i],0]]).tolist()
T = _tracking.ringpass(accel,X0)
dl[i] = T[0][5]/ring_length
polynom = _np.polyfit(energy_offset,dl,order)
a = _np.fliplr([polynom])[0].tolist()
a = a[1:]
if len(a) == 1:
a=a[0]
return a