def outline_from_length(self, target_length, nPts=1000):
self.smooth_well()
if target_length > self.length:
raise excpt.BunchSizeError("target_length longer than bucket")
def len_func(potential):
try:
lTime, rTime = self._interp_time_from_potential(potential[0])
except excpt.InputError:
return self.time[-1] - self.time[0]
return np.abs(target_length - (rTime - lTime))
result = opt.minimize(len_func,
np.max(self.well) / 2,
method='Nelder-Mead')
interpTime = self._interp_time_from_potential(result['x'][0], nPts)
interpWell = self._well_smooth_func(interpTime)
interpWell[interpWell > interpWell[0]] = interpWell[0]
energyContour = np.sqrt(
pot.potential_to_hamiltonian(interpTime, interpWell, self.beta,
self.energy, self.eta))
outlineTime = interpTime.tolist() + interpTime[::-1].tolist()
outlineEnergy = energyContour.tolist() \
+ (-energyContour[::-1]).tolist()
return np.array([outlineTime, outlineEnergy])
def calc_separatrix(self):
hamil = pot.potential_to_hamiltonian(self.time, self.well, self.beta,
self.energy, self.eta)
self.upper_energy_bound = np.sqrt(hamil)
sepTime = self.time.tolist() + self.time[::-1].tolist()
sepEnergy = self.upper_energy_bound.tolist() \
+ (-self.upper_energy_bound[::-1]).tolist()
self.separatrix = np.array([sepTime, sepEnergy])
def inner_buckets(self):
self.inner_separatrices = []
for t, w in zip(self.inner_times, self.inner_wells):
hamil = pot.potential_to_hamiltonian(t, w, self.beta, self.energy,
self.eta)
upper_energy_bound = np.sqrt(hamil)
sepTime = t.tolist() + t[::-1].tolist()
sepEnergy = upper_energy_bound.tolist() \
+ (-upper_energy_bound[::-1]).tolist()
self.inner_separatrices.append(np.array([sepTime, sepEnergy]))
def outline_from_emittance(self, target_emittance, nPts=1000):
self.smooth_well()
if target_emittance > self.area:
raise excpt.BunchSizeError("target_emittance exceeds bucket area")
def emit_func(potential, *args):
nPts = args[0]
try:
interpTime = self._interp_time_from_potential(
potential[0], nPts)
except excpt.InputError:
return self.area
interpWell = self._well_smooth_func(interpTime)
interpWell[interpWell > interpWell[0]] = interpWell[0]
energyContour = np.sqrt(
pot.potential_to_hamiltonian(interpTime, interpWell, self.beta,
self.energy, self.eta))
emittance = 2 * np.trapz(energyContour, interpTime)
return np.abs(target_emittance - emittance)
result = opt.minimize(emit_func,
np.max(self.well) / 2,
method='Nelder-Mead',
args=(nPts, ))
try:
interpTime = self._interp_time_from_potential(result['x'][0], nPts)
except excpt.InputError:
interpTime = self.time.copy()
interpWell = self.well.copy()
else:
interpWell = self._well_smooth_func(interpTime)
interpWell[interpWell > interpWell[0]] = interpWell[0]
energyContour = np.sqrt(
pot.potential_to_hamiltonian(interpTime, interpWell, self.beta,
self.energy, self.eta))
outlineTime = interpTime.tolist() + interpTime[::-1].tolist()
outlineEnergy = energyContour.tolist() \
+ (-energyContour[::-1]).tolist()
return np.array([outlineTime, outlineEnergy])
def emit_func(potential, *args):
nPts = args[0]
try:
interpTime = self._interp_time_from_potential(
potential[0], nPts)
except excpt.InputError:
return self.area
interpWell = self._well_smooth_func(interpTime)
interpWell[interpWell > interpWell[0]] = interpWell[0]
energyContour = np.sqrt(
pot.potential_to_hamiltonian(interpTime, interpWell, self.beta,
self.energy, self.eta))
emittance = 2 * np.trapz(energyContour, interpTime)
return np.abs(target_emittance - emittance)
def outline_from_dE(self, target_height):
self.smooth_well()
if target_height > self.half_height:
raise excpt.BunchSizeError("target_height higher than bucket")
potential = target_height**2 * self.eta / (2 * self.beta**2 *
self.energy)
interpTime = self._interp_time_from_potential(potential, 1000)
interpWell = self._well_smooth_func(interpTime)
interpWell[interpWell > interpWell[0]] = interpWell[0]
energyContour = np.sqrt(
pot.potential_to_hamiltonian(interpTime, interpWell, self.beta,
self.energy, self.eta))
outlineTime = interpTime.tolist() + interpTime[::-1].tolist()
outlineEnergy = energyContour.tolist() \
+ (-energyContour[::-1]).tolist()
return np.array([outlineTime, outlineEnergy])