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
def old_calc_twiss(accelerator=None, init_twiss=None, fixed_point=None, indices = 'open'):
"""Return Twiss parameters of uncoupled dynamics.
Keyword arguments:
accelerator -- Accelerator object
init_twiss -- Twiss parameters at the start of first element
fixed_point -- 6D position at the start of first element
indices -- Open or closed
Returns:
tw -- list of Twiss objects
m66
transfer_matrices
closed_orbit
"""
if indices == 'open':
length = len(accelerator)
elif indices == 'closed':
length = len(accelerator)+1
else:
raise OpticsException("invalid value for 'indices' in calc_twiss")
if init_twiss is not None:
''' as a transport line: uses init_twiss '''
if fixed_point is None:
fixed_point = init_twiss.fixed_point
else:
raise OpticsException('arguments init_twiss and fixed_orbit are mutually exclusive')
closed_orbit, *_ = _tracking.linepass(accelerator, particles=list(fixed_point), indices='open')
m66, cumul_trans_matrices = _tracking.findm66(accelerator, closed_orbit=closed_orbit)
if indices == 'closed':
orb, *_ = _tracking.linepass(accelerator[-1:], particles=closed_orbit[:,-1])
closed_orbit = _np.append(closed_orbit,orb.transpose(),axis=1)
mx, my = m66[0:2, 0:2], m66[2:4, 2:4]
t = init_twiss
t.etax = _np.array([[t.etax], [t.etapx]])
t.etay = _np.array([[t.etay], [t.etapy]])
else:
''' as a periodic system: try to find periodic solution '''
if accelerator.harmonic_number == 0:
raise OpticsException('Either harmonic number was not set or calc_twiss was'
'invoked for transport line without initial twiss')
if fixed_point is None:
if not accelerator.cavity_on and not accelerator.radiation_on:
closed_orbit = _np.zeros((6,length))
closed_orbit[:4,:] = _tracking.findorbit4(accelerator, indices=indices)
elif not accelerator.cavity_on and accelerator.radiation_on:
raise OpticsException('The radiation is on but the cavity is off')
else:
closed_orbit = _tracking.findorbit6(accelerator, indices=indices)
else:
closed_orbit, *_ = _tracking.linepass(accelerator, particles=list(fixed_point), indices=indices)
''' calcs twiss at first element '''
orbit = closed_orbit[:,:-1] if indices == 'closed' else closed_orbit
m66, cumul_trans_matrices, *_ = _tracking.findm66(accelerator, closed_orbit=orbit)
mx, my = m66[0:2,0:2], m66[2:4,2:4] # decoupled transfer matrices
trace_x, trace_y, *_ = get_traces(accelerator, m66 = m66, closed_orbit=closed_orbit)
if not (-2.0 < trace_x < 2.0):
raise OpticsException('horizontal dynamics is unstable')
if not (-2.0 < trace_y < 2.0):
raise OpticsException('vertical dynamics is unstable')
sin_nux = _math.copysign(1,mx[0,1]) * _math.sqrt(-mx[0,1] * mx[1,0] - ((mx[0,0] - mx[1,1])**2)/4);
sin_nuy = _math.copysign(1,my[0,1]) * _math.sqrt(-my[0,1] * my[1,0] - ((my[0,0] - my[1,1])**2)/4);
fp = closed_orbit[:,0]
t = Twiss()
t.spos = 0
t.rx, t.px = fixed_point[0], fixed_point[1]
t.ry, t.py = fixed_point[2], fixed_point[3]
t.de, t.dl = fixed_point[4], fixed_point[5]
t.alphax = (mx[0,0] - mx[1,1]) / 2 / sin_nux
t.betax = mx[0,1] / sin_nux
t.alphay = (my[0,0] - my[1,1]) / 2 / sin_nuy
t.betay = my[0,1] / sin_nuy
''' dispersion function based on eta = (1 - M)^(-1) D '''
Dx = _np.array([[m66[0,4]],[m66[1,4]]])
Dy = _np.array([[m66[2,4]],[m66[3,4]]])
t.etax = _np.linalg.solve(_np.eye(2,2) - mx, Dx)
t.etay = _np.linalg.solve(_np.eye(2,2) - my, Dy)
''' get transfer matrices from cumulative transfer matrices '''
transfer_matrices = []
m66_prev = _np.eye(6,6)
cumul_trans_matrices.append(m66)
for m66_this in cumul_trans_matrices[1:]: # Matrices at start of elements
inv_m66_prev = _np.linalg.inv(m66_prev)
tm = _np.dot(m66_this, inv_m66_prev)
#tm = _np.linalg.solve(m66_prev.T, m66_this.T).T # Fernando, you may uncomment this line when running YOUR code! aushuashuahs
m66_prev = m66_this
transfer_matrices.append(tm)
''' propagates twiss through line '''
tw = [t]
m_previous = _np.eye(6,6)
for i in range(1, length):
m = transfer_matrices[i-1]
mx, my = m[0:2,0:2], m[2:4,2:4] # decoupled transfer matrices
Dx = _np.array([[m[0,4]],[m[1,4]]])
Dy = _np.array([[m[2,4]],[m[3,4]]])
n = Twiss()
n.spos = t.spos + accelerator[i-1].length
fp = closed_orbit[:,i]
n.rx, n.px = fixed_point[0], fixed_point[1]
n.ry, n.py = fixed_point[2], fixed_point[3]
n.de, n.dl = fixed_point[4], fixed_point[5]
n.betax = ((mx[0,0] * t.betax - mx[0,1] * t.alphax)**2 + mx[0,1]**2) / t.betax
n.alphax = -((mx[0,0] * t.betax - mx[0,1] * t.alphax) * (mx[1,0] * t.betax - mx[1,1] * t.alphax) + mx[0,1] * mx[1,1]) / t.betax
n.betay = ((my[0,0] * t.betay - my[0,1] * t.alphay)**2 + my[0,1]**2) / t.betay
n.alphay = -((my[0,0] * t.betay - my[0,1] * t.alphay) * (my[1,0] * t.betay - my[1,1] * t.alphay) + my[0,1] * my[1,1]) / t.betay
''' calcs phase advance based on R(mu) = U(2) M(2|1) U^-1(1) '''
sint = mx[0,1]/_math.sqrt(n.betax * t.betax)
cost = (mx[0,0] * t.betax - mx[0,1] * t.alphax)/_math.sqrt(n.betax * t.betax)
dmux = _math.atan2(sint, cost)
n.mux = t.mux + dmux
sint = my[0,1]/_math.sqrt(n.betay * t.betay)
cost = (my[0,0] * t.betay - my[0,1] * t.alphay)/_math.sqrt(n.betay * t.betay)
dmuy = _math.atan2(sint, cost)
n.muy = t.muy + dmuy
''' when phase advance in an element is over PI atan2 returns a
negative value that has to be corrected by adding 2*PI'''
if dmux < 0 and dmux < -10*_sys.float_info.epsilon:
n.mux += 2*_math.pi
if dmuy < 0 and dmuy < -10*_sys.float_info.epsilon:
n.muy += 2*_math.pi
''' dispersion function'''
n.etax = Dx + _np.dot(mx, t.etax)
n.etay = Dy + _np.dot(my, t.etay)
tw.append(n)
t = n.make_copy()
''' converts eta format '''
for t in tw:
t.etapx, t.etapy = (t.etax[1,0], t.etay[1,0])
t.etax, t.etay = (t.etax[0,0], t.etay[0,0])
return tw, m66, transfer_matrices, closed_orbit
