Absolute and relative cavity entry phases
There are three ways to define the phase of a cavity: by its relative entry phase \(\phi_{0,\,\mathrm{rel}}\), its absolute entry phase \(\phi_{0,\,\mathrm{abs}}\) or its synchronous phase \(\phi_s\) (still under implementation).
The relation between relative and entry phases is: \begin{equation} E_0\cos{\phi_{0,\,\mathrm{abs}}} = E_0\cos{(\phi_{0,\,\mathrm{rel}} + \phi_\mathrm{in})} \end{equation} where \(\phi_\mathrm{in}\) is the phase at which the synchronous particle enters the cavity, \(E_0\) is the amplitude of the electric field.
Preparation
Load libraries
[1]:
from pathlib import Path
import matplotlib.pyplot as plt
from lightwin.config_manager import process_config
from lightwin.beam_calculation.beam_calculator import BeamCalculator
from lightwin.beam_calculation.factory import BeamCalculatorsFactory
from lightwin.beam_calculation.simulation_output.simulation_output import SimulationOutput
from lightwin.core.accelerator.accelerator import Accelerator
from lightwin.core.accelerator.factory import NoFault, WithFaults
from lightwin.failures.fault_scenario import FaultScenario, fault_scenario_factory
from lightwin.visualization import plot
plt.rcParams["figure.figsize"] = (15, 5)
/home/placais/LightWin/venv/lib/python3.12/site-packages/pymoo/core/decision_making.py:2: DeprecationWarning: Please import `cKDTree` from the `scipy.spatial` namespace; the `scipy.spatial.ckdtree` namespace is deprecated and will be removed in SciPy 2.0.0.
from scipy.spatial.ckdtree import cKDTree
Set configuration dicts
[2]:
LW_DIR = Path("..", "..", "..").absolute().resolve()
DATA_DIR = LW_DIR / "data" / "example"
OUT_DIR = DATA_DIR / "results"
CONFIG_PATH = DATA_DIR / "lightwin.toml"
CONFIG_KEYS = {
'files': 'files',
'beam_calculator': 'generic_envelope1d',
'beam': 'beam',
'plots': 'plots_minimal',
'wtf': 'generic_wtf',
'design_space': 'generic_design_space',
}
override = {'beam_calculator': {'flag_phi_abs': True}, 'plots': {'energy': False}}
config_abs = process_config(CONFIG_PATH, CONFIG_KEYS, warn_mismatch=True, override=override)
plots_phase = config_abs['plots']
[INFO ] [files.py ] Setting project_path = PosixPath('/home/placais/LightWin/data/example/results_tests')
Setting log_file = PosixPath('/home/placais/LightWin/data/example/results_tests/lightwin.log')
[INFO ] [config_manager.py ] Config dict files successfully tested. After potential modifications, it looks like:
dat_file = /home/placais/LightWin/data/example/example.dat
project_folder = /home/placais/LightWin/data/example/results_tests
[INFO ] [config_manager.py ] Config dict beam_calculator successfully tested. After potential modifications, it looks like:
flag_cython = False
flag_phi_abs = True
method = RK4
n_steps_per_cell = 40
tool = Envelope1D
[INFO ] [config_manager.py ] Config dict beam successfully tested. After potential modifications, it looks like:
e_mev = 20.0
e_rest_mev = 938.27203
f_bunch_mhz = 100.0
i_milli_a = 0.0
q_adim = 1.0
sigma = [[ 8.409896e-06 3.548736e-06 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00]
[ 3.548736e-06 1.607857e-06 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 2.941564e-06 6.094860e-07 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 6.094860e-07 4.418911e-07 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.593136e-06
-2.552518e-07]
[ 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -2.552518e-07
5.994771e-07]]
inv_e_rest_mev = 0.0010657889908537506
gamma_init = 1.021315779817075
omega_0_bunch = 628318530.7179586
lambda_bunch = 2997924.58
q_over_m = 0.0010657889908537506
m_over_q = 938.27203
[WARNING ] [plots.py ] Some plots were not recognized: plots_kw = {'config_folder': PosixPath('/home/placais/LightWin/data/example')}.They probably will not do anything.
[INFO ] [config_manager.py ] Config dict plots successfully tested. After potential modifications, it looks like:
cav = True
emittance = False
energy = False
envelopes = False
phase = True
transfer_matrices = False
twiss = False
[INFO ] [config_manager.py ] Config dict wtf successfully tested. After potential modifications, it looks like:
failed = [['FM11']]
id_nature = name
k = 3
objective_preset = simple_ADS
optimisation_algorithm = downhill_simplex
optimisation_algorithm_kwargs = {'options': {'disp': False, 'adaptive': True}}
strategy = k out of n
[INFO ] [config_manager.py ] Config dict design_space successfully tested. After potential modifications, it looks like:
design_space_preset = abs_phase_amplitude
from_file = False
max_absolute_sync_phase_in_deg = 0.0
max_decrease_k_e_in_percent = 20.0
max_increase_k_e_in_percent = 180.0
max_increase_sync_phase_in_percent = 40.0
maximum_k_e_is_calculated_wrt_maximum_k_e_of_section = True
min_absolute_sync_phase_in_deg = -90.0
[3]:
override = {
'beam_calculator':
{
'flag_phi_abs': False
},
'plots': {
'cav': True
},
'wtf': {
'objective_preset': 'rephased_ADS',
}
}
config_rel = process_config(CONFIG_PATH, CONFIG_KEYS, warn_mismatch=True, override=override)
plots_complete = config_rel['plots']
[INFO ] [files.py ] Setting project_path = PosixPath('/home/placais/LightWin/data/example/results_tests')
Setting log_file = PosixPath('/home/placais/LightWin/data/example/results_tests/lightwin.log')
[INFO ] [config_manager.py ] Config dict files successfully tested. After potential modifications, it looks like:
dat_file = /home/placais/LightWin/data/example/example.dat
project_folder = /home/placais/LightWin/data/example/results_tests
[INFO ] [config_manager.py ] Config dict beam_calculator successfully tested. After potential modifications, it looks like:
flag_cython = False
flag_phi_abs = False
method = RK4
n_steps_per_cell = 40
tool = Envelope1D
[INFO ] [config_manager.py ] Config dict beam successfully tested. After potential modifications, it looks like:
e_mev = 20.0
e_rest_mev = 938.27203
f_bunch_mhz = 100.0
i_milli_a = 0.0
q_adim = 1.0
sigma = [[ 8.409896e-06 3.548736e-06 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00]
[ 3.548736e-06 1.607857e-06 0.000000e+00 0.000000e+00 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 2.941564e-06 6.094860e-07 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 6.094860e-07 4.418911e-07 0.000000e+00
0.000000e+00]
[ 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.593136e-06
-2.552518e-07]
[ 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 -2.552518e-07
5.994771e-07]]
inv_e_rest_mev = 0.0010657889908537506
gamma_init = 1.021315779817075
omega_0_bunch = 628318530.7179586
lambda_bunch = 2997924.58
q_over_m = 0.0010657889908537506
m_over_q = 938.27203
[WARNING ] [plots.py ] Some plots were not recognized: plots_kw = {'config_folder': PosixPath('/home/placais/LightWin/data/example')}.They probably will not do anything.
[INFO ] [config_manager.py ] Config dict plots successfully tested. After potential modifications, it looks like:
cav = True
emittance = False
energy = True
envelopes = False
phase = True
transfer_matrices = False
twiss = False
[INFO ] [config_manager.py ] Config dict wtf successfully tested. After potential modifications, it looks like:
failed = [['FM11']]
id_nature = name
k = 3
objective_preset = rephased_ADS
optimisation_algorithm = downhill_simplex
optimisation_algorithm_kwargs = {'options': {'disp': False, 'adaptive': True}}
strategy = k out of n
[INFO ] [config_manager.py ] Config dict design_space successfully tested. After potential modifications, it looks like:
design_space_preset = abs_phase_amplitude
from_file = False
max_absolute_sync_phase_in_deg = 0.0
max_decrease_k_e_in_percent = 20.0
max_increase_k_e_in_percent = 180.0
max_increase_sync_phase_in_percent = 40.0
maximum_k_e_is_calculated_wrt_maximum_k_e_of_section = True
min_absolute_sync_phase_in_deg = -90.0
/home/placais/LightWin/src/lightwin/util/log_manager.py:66: ResourceWarning: unclosed file <_io.TextIOWrapper name='/home/placais/LightWin/data/example/results_tests/lightwin.log' mode='a' encoding='UTF-8'>
del logging.root.handlers[:]
ResourceWarning: Enable tracemalloc to get the object allocation traceback
Set BeamCalculator objects
[4]:
factory = BeamCalculatorsFactory(beam_calculator=config_abs['beam_calculator'],
files=config_abs['files'])
solver_abs = factory.run_all()[0]
factory = BeamCalculatorsFactory(beam_calculator=config_rel['beam_calculator'],
files=config_rel['files'])
solver_rel = factory.run_all()[0]
Set Accelerator objects
[5]:
factory = WithFaults(beam_calculators=solver_abs, **config_abs['files'], **config_abs['wtf'])
accelerators_abs = factory.run_all()
for acc in accelerators_abs:
acc.name += r' (absolute $\phi_0$)'
working_abs = accelerators_abs[0]
broken_abs = accelerators_abs[1]
factory = WithFaults(beam_calculators=solver_rel, **config_rel['files'], **config_rel['wtf'])
accelerators_rel = factory.run_all()
for acc in accelerators_rel:
acc.name += r' (relative $\phi_0$)'
working_rel = accelerators_rel[0]
broken_rel = accelerators_rel[1]
working = (working_abs, working_rel)
broken = (broken_abs, broken_rel)
[INFO ] [factory.py ] First initialisation of ListOfElements, ecompassing all linac. Created with dat_file = PosixPath('/home/placais/LightWin/data/example/example.dat')
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 20.0 MeV and self.phi_abs_in = 0.0 rad.
[WARNING ] [factory.py ] You asked LW a simulation in absolute phase, while there is at least one cavity in relative phase in the .dat file used by TW. You can expect a phase difference between LightWin results and TraceWin results for the same input .dat, after the first failed cavity. No difference should appear with the output .dat, or when using TraceWin solver within LightWin.
[INFO ] [factory.py ] First initialisation of ListOfElements, ecompassing all linac. Created with dat_file = PosixPath('/home/placais/LightWin/data/example/example.dat')
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 20.0 MeV and self.phi_abs_in = 0.0 rad.
[WARNING ] [factory.py ] You asked LW a simulation in absolute phase, while there is at least one cavity in relative phase in the .dat file used by TW. You can expect a phase difference between LightWin results and TraceWin results for the same input .dat, after the first failed cavity. No difference should appear with the output .dat, or when using TraceWin solver within LightWin.
[INFO ] [factory.py ] First initialisation of ListOfElements, ecompassing all linac. Created with dat_file = PosixPath('/home/placais/LightWin/data/example/example.dat')
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 20.0 MeV and self.phi_abs_in = 0.0 rad.
[INFO ] [factory.py ] First initialisation of ListOfElements, ecompassing all linac. Created with dat_file = PosixPath('/home/placais/LightWin/data/example/example.dat')
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 20.0 MeV and self.phi_abs_in = 0.0 rad.
Propagate the beam
Nominal linac
[6]:
_ = solver_abs.compute(working_abs)
_ = solver_rel.compute(working_rel)
figs = plot.factory(working, plots_phase, save_fig=False, clean_fig=False)
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000000_ref/0_Envelope1D/example.dat.
[INFO ] [beam_calculator.py ] Elapsed time in beam calculation: 0:00:01.886844
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000000_ref/0_Envelope1D/example.dat.
[INFO ] [beam_calculator.py ] Elapsed time in beam calculation: 0:00:01.802594
The reference \(\phi_0\) that is used is the one defined in the .dat. As a matter of a fact, we need to propagate the beam a first time to know the entry phase of the synchronous particle in every cavity. This quantity is necessary to link \(\phi_{0,\,\mathrm{abs}}\) with \(\phi_{0,\,\mathrm{rel}}\).
Linac with one broken cavity
[7]:
fault_scenarios_abs = fault_scenario_factory(accelerators_abs, solver_abs, config_abs['wtf'], config_abs['design_space'])
[INFO ] [design_space.py ] Created variables:
====================================================================================================
Variable | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
$\phi_{0, abs}$ [deg] | FM10 | 55.649 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM12 | 101.288 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM9 | 272.279 | -360.000 | 360.000
$k_e$ [1] | FM10 | 1.649 | 1.319 | 4.756
$k_e$ [1] | FM12 | 1.698 | 1.359 | 4.756
$k_e$ [1] | FM9 | 1.649 | 1.319 | 4.756
====================================================================================================
Created constraints:
====================================================================================================
Constraint | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
====================================================================================================
[INFO ] [factory.py ] Created variables:
====================================================================================================
Variable | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
$\phi_{0, abs}$ [deg] | FM10 | 55.649 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM12 | 101.288 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM9 | 272.279 | -360.000 | 360.000
$k_e$ [1] | FM10 | 1.649 | 1.319 | 4.756
$k_e$ [1] | FM12 | 1.698 | 1.359 | 4.756
$k_e$ [1] | FM9 | 1.649 | 1.319 | 4.756
====================================================================================================
Created constraints:
====================================================================================================
Constraint | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
====================================================================================================
[INFO ] [factory.py ] Created objectives:
====================================================================================================
What, where, etc | wgt. | ideal val
----------------------------------------------------------------------------------------------------
w_kin @elt DR36 (out) | 1.0 | 25.771551199731583
phi_abs @elt DR36 (out) | 1.0 | 177.9905075357864
$M_{z\delta}$ @elt DR36 (out) | 1.0 | 0.0
====================================================================================================
[INFO ] [factory.py ] Initalisation of ListOfElements from already initialized elements: FM9 to DR36.
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/tmp/tmp.dat.
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 23.496060468989743 MeV and self.phi_abs_in = 133.38246030585947 rad.
[WARNING ] [fault_scenario.py ] Not storing elements in dat
[8]:
fault_scenarios_rel = fault_scenario_factory(accelerators_rel, solver_rel, config_rel['wtf'], config_rel['design_space'])
[INFO ] [design_space.py ] Created variables:
====================================================================================================
Variable | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
$\phi_{0, abs}$ [deg] | FM10 | 55.649 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM12 | 101.288 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM9 | 272.279 | -360.000 | 360.000
$k_e$ [1] | FM10 | 1.649 | 1.319 | 4.756
$k_e$ [1] | FM12 | 1.698 | 1.359 | 4.756
$k_e$ [1] | FM9 | 1.649 | 1.319 | 4.756
====================================================================================================
Created constraints:
====================================================================================================
Constraint | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
====================================================================================================
[INFO ] [factory.py ] Created variables:
====================================================================================================
Variable | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
$\phi_{0, abs}$ [deg] | FM10 | 55.649 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM12 | 101.288 | -360.000 | 360.000
$\phi_{0, abs}$ [deg] | FM9 | 272.279 | -360.000 | 360.000
$k_e$ [1] | FM10 | 1.649 | 1.319 | 4.756
$k_e$ [1] | FM12 | 1.698 | 1.359 | 4.756
$k_e$ [1] | FM9 | 1.649 | 1.319 | 4.756
====================================================================================================
Created constraints:
====================================================================================================
Constraint | Element | x_0 | Lower lim | Upper lim
----------------------------------------------------------------------------------------------------
====================================================================================================
[INFO ] [factory.py ] Created objectives:
====================================================================================================
What, where, etc | wgt. | ideal val
----------------------------------------------------------------------------------------------------
w_kin @elt DR36 (out) | 1.0 | 25.771551199731583
$M_{z\delta}$ @elt DR36 (out) | 1.0 | 0.0
====================================================================================================
[INFO ] [factory.py ] Initalisation of ListOfElements from already initialized elements: FM9 to DR36.
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/tmp/tmp.dat.
[INFO ] [list_of_elements.py ] Successfully created a ListOfElements with self.w_kin_in = 23.496060468989743 MeV and self.phi_abs_in = 133.38246030585947 rad.
[WARNING ] [fault_scenario.py ] The phases in the broken linac are relative. It may be more relatable to use absolute phases, as it would avoid the rephasing of the linac at each cavity.
[WARNING ] [fault_scenario.py ] Not storing elements in dat
[9]:
_ = solver_abs.compute(broken_abs)
figs = plot.factory(accelerators_abs, plots_phase, save_fig=False, clean_fig=False)
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/0_Envelope1D/example.dat.
[INFO ] [beam_calculator.py ] Elapsed time in beam calculation: 0:00:01.765818
[10]:
_ = solver_rel.compute(broken_rel)
figs = plot.factory(accelerators_rel, plots_phase, save_fig=False, clean_fig=False)
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/0_Envelope1D/example.dat.
[INFO ] [beam_calculator.py ] Elapsed time in beam calculation: 0:00:01.801515
After a cavity failure, the definition of the reference \(\phi_0\) becomes important. With \(\phi_\mathrm{ref} = \phi_{0,\,\mathrm{abs}}\), the cavities after the failure keep their absolute entry phase. With \(\phi_\mathrm{ref} = \phi_{0,\,\mathrm{rel}}\), the cavities after the failure (olive color) are rephased, so that they keep their relative entry phase.
Fixing the fault
In the absolute phase calculation, it is mandatory to retrieve the nominal energy and the nominal phase of the beam at the exit of the compensation zone. In the relative phase calculation, the phase no longer needs to be retrieved, as the integrity of the linac after the failure is rephased.
[11]:
for scenario in fault_scenarios_abs:
scenario.fix_all()
figs = plot.factory(accelerators_abs, plots_complete, save_fig=False, clean_fig=False)
[INFO ] [downhill_simplex.py ] Objective functions results:
0: | 3.525559733930095e-06
1: | 2.8023950449096446e-06
2: | 8.57188357339389e-06
Norm: 9.682983911019546e-06
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/0_Envelope1D/example.dat.
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/tmp/tmp.dat.
[INFO ] [debug.py ] Fixed (1 of 2)
----------------------------------------------------------------------------------------------------
name status k_e phi_0_abs phi_0_rel v_cav_mv phi_s
1 FM9 compensate (ok) 1.396623 5.304986 3.839113 0.613335 -0.186859
2 FM10 compensate (ok) 2.174922 0.823152 3.169552 0.971894 -0.924121
3 FM12 compensate (ok) 2.851343 1.889864 3.571021 1.327753 -0.611272
----------------------------------------------------------------------------------------------------
[INFO ] [list_of_simulation_output_evaluators.py] Fit quality:(FIXME: settings in FaultScenario, not config_manager)
----------------------------------------------------------------------------------------------------
end comp zone (DR36) end linac RMS [usual units]
Beam energy [MeV] 0.000% -0.000% 0.000
Beam phase [rad] 0.000% -0.000% 0.000
Norm. $\sigma_\phi$ @ $1\sigma$ [rad] -0.001% -0.002% 0.000
Norm. $\sigma_\phi$ @ $1\sigma$ [MeV] 0.000% 0.001% 0.000
$\epsilon_{\phi W}$ [$\pi$.rad.MeV] -0.001% -0.001% 0.000
$M_{z\delta}$ 0.000 0.000 nan
----------------------------------------------------------------------------------------------------
[INFO ] [fault_scenario.py ] Elapsed time in optimisation: 0:00:11.483819
[12]:
for scenario in fault_scenarios_rel:
scenario.fix_all()
figs = plot.factory(accelerators_rel, plots_complete, save_fig=False, clean_fig=False)
[INFO ] [downhill_simplex.py ] Objective functions results:
0: | -3.0456890556251892e-06
1: | 1.3755391933711891e-05
Norm: 1.4088542475131387e-05
[WARNING ] [simulation_output.py] data_in_tw_fashion is bugged
[WARNING ] [accelerator.py ] Manually set which_phase
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/0_Envelope1D/example.dat.
[INFO ] [dat_files.py ] New dat saved in /home/placais/LightWin/data/example/results_tests/000001/tmp/tmp.dat.
[INFO ] [debug.py ] Fixed (1 of 2)
----------------------------------------------------------------------------------------------------
name status k_e phi_0_abs phi_0_rel v_cav_mv phi_s
1 FM9 compensate (ok) 1.573024 5.464923 3.999051 0.693787 -0.030682
2 FM10 compensate (ok) 1.70301 0.549345 2.862516 0.758889 -1.24041
3 FM12 compensate (ok) 3.035455 1.742644 3.82891 1.412413 -0.330618
----------------------------------------------------------------------------------------------------
[INFO ] [list_of_simulation_output_evaluators.py] Fit quality:(FIXME: settings in FaultScenario, not config_manager)
----------------------------------------------------------------------------------------------------
end comp zone (DR36) end linac RMS [usual units]
Beam energy [MeV] -0.000% -0.000% 0.000
Beam phase [rad] 0.068% 0.010% 0.001
Norm. $\sigma_\phi$ @ $1\sigma$ [rad] -0.001% -0.002% 0.000
Norm. $\sigma_\phi$ @ $1\sigma$ [MeV] -0.000% 0.000% 0.000
$\epsilon_{\phi W}$ [$\pi$.rad.MeV] -0.001% -0.001% 0.000
$M_{z\delta}$ 0.000 0.000 nan
----------------------------------------------------------------------------------------------------
[INFO ] [fault_scenario.py ] Elapsed time in optimisation: 0:00:10.068008
The main advantage with the studies in relative phase is that we do not need to recover the absolute beam phase at the exit of the compensation zone. It is one less variable for the optimisation objective.