ebisim package¶
This is the top level module of ebisim.
The ebisim package offers a number of tools to perform and evaluate simulations of the charge breeding process in an Electron Beam Ion Source / Trap.
For easier access a number of submodule members are available at this level, such that they can be referred to as ebisim.[member] without resolving the submodule in the call. The module level documentation lists these members with more granularity.
- class ebisim.AdvancedModel(device, targets, bg_gases, options, lb, ub, nq, q, a, eixs, rrxs, drxs, cxxs_bggas, cxxs_trgts)[source]¶
Bases:
tuple
The advanced model class is the base for ebisim.simulation.advanced_simulation. It acts as a fast datacontainer for the underlying rhs function which represents the right hand side of the differential equation system. Since it is jitcompiled using numba, care is required during instatiation.
- Parameters
device (ebisim.simulation.Device) – Container describing the EBIS/T and specifically the electron beam.
targets (numba.typed.List[ebisim.simulation.Target]) – List of ebisim.simulation.Target for which charge breeding is simulated.
bg_gases (numba.typed.List[ebisim.simulation.BackgroundGas], optional) – List of ebisim.simulation.BackgroundGas which act as CX partners, by default None.
options (ebisim.simulation.ModelOptions, optional) – Switches for effects considered in the simulation, see default values of ebisim.simulation.ModelOptions.
lb (ndarray) –
ub (ndarray) –
nq (int) –
q (ndarray) –
a (ndarray) –
eixs (ndarray) –
rrxs (ndarray) –
drxs (ndarray) –
cxxs_bggas (Any) –
cxxs_trgts (Any) –
Create new instance of AdvancedModel(device, targets, bg_gases, options, lb, ub, nq, q, a, eixs, rrxs, drxs, cxxs_bggas, cxxs_trgts)
- count(value, /)¶
Return number of occurrences of value.
- classmethod get(device, targets, bg_gases=None, options=ModelOptions(EI=True, RR=True, CX=True, DR=False, SPITZER_HEATING=True, COLLISIONAL_THERMALISATION=True, ESCAPE_AXIAL=True, ESCAPE_RADIAL=True, RECOMPUTE_CROSS_SECTIONS=False, RADIAL_DYNAMICS=False, IONISATION_HEATING=True, OVERRIDE_FWHM=False, RADIAL_SOLVER_MAX_STEPS=500, RADIAL_SOLVER_REL_DIFF=0.001))[source]¶
- Parameters
device (Device) –
targets (List[Element]) –
bg_gases (Optional[List[BackgroundGas]]) –
options (ModelOptions) –
- Return type
- index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
- property a¶
Alias for field number 8
- property bg_gases¶
Alias for field number 2
- property cxxs_bggas¶
Alias for field number 12
- property cxxs_trgts¶
Alias for field number 13
- property device¶
Alias for field number 0
- property drxs¶
Alias for field number 11
- property eixs¶
Alias for field number 9
- property lb¶
Alias for field number 4
- property nq¶
Alias for field number 6
- property options¶
Alias for field number 3
- property q¶
Alias for field number 7
- property rrxs¶
Alias for field number 10
- property targets¶
Alias for field number 1
- property ub¶
Alias for field number 5
- class ebisim.AdvancedResult(*, t, N, device, target, kbT, model, id_, res=None, rates=None)[source]¶
Bases:
BasicResult
[Device
]Instances of this class are containers for the results of ebisim advanced_simulations and contain a variety of convenience methods for simple plot generation etc.
- Parameters
t – An array holding the time step coordinates.
N – An array holding the occupancy of each charge state at a given time.
device – If coming from advanced_simulation, this is the machine / electron beam description.
target – If coming from advanced_simulation, this is the target represented by this Result.
kbT – An array holding the temperature of each charge state at a given time.
model – The AdvancedModel instance that was underlying the advanced_simulation
id – The position of this target in the list of all simulated targets.
res – The result object returned by scipy.integrate.solve_ivp. This can contain useful information about the solver performance etc. Refer to scipy documentation for details.
rates – A dictionary containing the different breeding rates in arrays shaped like N.
- abundance_at_time(t)¶
Yields the abundance of each charge state at a given time
- Parameters
t (float) – <s> Point of time to evaluate.
- Returns
Abundance of each charge state, array index corresponds to charge state.
- Return type
ndarray
- plot(relative=False, **kwargs)¶
Plot the charge state evolution of this result object.
- Parameters
relative (bool) – Flags whether the absolute numbers or a relative fraction should be plotted at each timestep, by default False.
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot.
- Raises
ValueError – If the required data (self.t, self.N) is not available, i.e. corresponding attributes of this Result instance have not been set correctly.
- Return type
Figure
- plot_charge_states(relative=False, **kwargs)¶
Plot the charge state evolution of this result object.
- Parameters
relative (bool) – Flags whether the absolute numbers or a relative fraction should be plotted at each timestep, by default False.
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot.
- Raises
ValueError – If the required data (self.t, self.N) is not available, i.e. corresponding attributes of this Result instance have not been set correctly.
- Return type
Figure
- plot_energy_density(**kwargs)[source]¶
Plot the energy density evolution of this result object.
- Parameters
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot.
- Raises
ValueError – If the required data (self.t, self.kbT) is not available, i.e. corresponding attributes of this Result instance have not been set correctly.
- Return type
Figure
- plot_radial_distribution_at_time(t, **kwargs)[source]¶
Plot the radial ion distribution at time t.
- Parameters
t (float) – <s> Point of time to evaluate.
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_radial_distribution and ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot.
- Return type
Figure
- plot_rate(rate_key, dens_threshold=0.001, **kwargs)[source]¶
Plots the requested ionisation- or energy flow rates.
- Parameters
rate_key (Rate) – The key identifying the rate to be plotted. See ebisim.simulation.Rate for valid values.
dens_threshold (float) – If given temperatures are only plotted where the particle denisty is larger than the threshold value.
kwargs – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot
- Raises
ValueError – If the required data (self.rates) is not available, or an invalid key is requested.
- Return type
Figure
- plot_temperature(dens_threshold=0.001, **kwargs)[source]¶
Plot the temperature evolution of this result object.
- Parameters
dens_threshold (float) – If given temperatures are only plotted where the particle denisty is larger than the threshold value.
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot
- Raises
ValueError – If the required data (self.t, self.kbT) is not available, i.e. corresponding attributes of this Result instance have not been set correctly.
- Return type
Figure
- radial_distribution_at_time(t)[source]¶
Yields the radial distribution information at time
- Parameters
t (float) – <s> Point of time to evaluate.
- Returns
phi – Radial potential
n3d – On axis 3D density for each charge state.
shapes – The Boltzmann shape factors for each charge state.
- Return type
Tuple[ndarray, ndarray, ndarray]
- temperature_at_time(t)[source]¶
Yields the temperature of each charge state at a given time
- Parameters
t (float) – <s> Point of time to evaluate.
- Returns
<eV>
Temperature of each charge state, array index corresponds to charge state.
- Return type
ndarray
- times_of_highest_abundance()¶
Yields the point of time with the highest abundance for each charge state
- Returns
<s>
Array of times.
- Return type
ndarray
- class ebisim.BackgroundGas(name, ip, n0)[source]¶
Bases:
tuple
Use the static get() factory methods to create instances of this class.
Simple datacontainer for a background gas for advanced simulations. A background gas only acts as a charge exchange partner to the Targets in the simulation.
See also
Create new instance of BackgroundGas(name, ip, n0)
- Parameters
name (str) –
ip (float) –
n0 (float) –
- count(value, /)¶
Return number of occurrences of value.
- classmethod get(element, p, T=300.0)[source]¶
Factory method for defining a background gas.
- Parameters
element (Union[Element, str, int]) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
p (float) – <mbar> Gas pressure.
T (float) – <K> Gas temperature, by default 300 K (Room temperature)
- Returns
ebisim.simulation.BackgroundGas – Ready to use BackgroundGas specification.
- Return type
- index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
- property ip¶
<eV> Ionisation potential of this Gas.
- property n0¶
<1/m^3> Gas number density.
- property name¶
Name of the element.
- class ebisim.BasicResult(*, t, N, device, target, res=None)[source]¶
Bases:
Generic
[GenericDevice
]Instances of this class are containers for the results of ebisim basic_simulations and contain a variety of convenience methods for simple plot generation etc.
- Parameters
t – An array holding the time step coordinates.
N – An array holding the occupancy of each charge state at a given time.
device – If coming from advanced_simulation, this is the machine / electron beam description.
target – If coming from advanced_simulation, this is the target represented by this Result.
res – The result object returned by scipy.integrate.solve_ivp. This can contain useful information about the solver performance etc. Refer to scipy documentation for details.
- abundance_at_time(t)[source]¶
Yields the abundance of each charge state at a given time
- Parameters
t (float) – <s> Point of time to evaluate.
- Returns
Abundance of each charge state, array index corresponds to charge state.
- Return type
ndarray
- plot(relative=False, **kwargs)¶
Alias for plot_charge_states
- Parameters
relative (bool) –
kwargs (Any) –
- Return type
Figure
- plot_charge_states(relative=False, **kwargs)[source]¶
Plot the charge state evolution of this result object.
- Parameters
relative (bool) – Flags whether the absolute numbers or a relative fraction should be plotted at each timestep, by default False.
kwargs (Any) – Keyword arguments are handed down to ebisim.plotting.plot_generic_evolution, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
Figure handle of the generated plot.
- Raises
ValueError – If the required data (self.t, self.N) is not available, i.e. corresponding attributes of this Result instance have not been set correctly.
- Return type
Figure
- class ebisim.Device(current, e_kin, r_e, length, j, v_ax, v_ax_sc, v_ra, b_ax, r_dt, r_dt_bar, fwhm, rad_grid, rad_fd_l, rad_fd_d, rad_fd_u, rad_phi_uncomp, rad_phi_ax_barr, rad_re_idx)[source]¶
Bases:
tuple
Use the static get() factory methods to create instances of this class.
Objects of this class are used to pass important EBIS/T parameters into the simulation.
Create new instance of Device(current, e_kin, r_e, length, j, v_ax, v_ax_sc, v_ra, b_ax, r_dt, r_dt_bar, fwhm, rad_grid, rad_fd_l, rad_fd_d, rad_fd_u, rad_phi_uncomp, rad_phi_ax_barr, rad_re_idx)
- Parameters
current (float) –
e_kin (float) –
r_e (float) –
length (Optional[float]) –
j (float) –
v_ax (float) –
v_ax_sc (float) –
v_ra (float) –
b_ax (float) –
r_dt (float) –
r_dt_bar (float) –
fwhm (float) –
rad_grid (ndarray) –
rad_fd_l (ndarray) –
rad_fd_d (ndarray) –
rad_fd_u (ndarray) –
rad_phi_uncomp (ndarray) –
rad_phi_ax_barr (ndarray) –
rad_re_idx (int) –
- count(value, /)¶
Return number of occurrences of value.
- classmethod get(*, current, e_kin, r_e, v_ax, b_ax, r_dt, length=None, v_ra=None, j=None, fwhm=None, n_grid=400, r_dt_bar=None)[source]¶
Factory method for defining a device. All arguments are keyword only to reduce the chance of mixing them up.
- Parameters
current (float) – <A> Electron beam current.
e_kin (float) – <eV> Uncorrected electron beam energy.
r_e (float) – <m> Electron beam radius.
v_ax (float) – <V> Axial barrier bias.
b_ax (float) – <T> Axial magnetic flux density in the trap.
r_dt (float) – <m> Drift tube radius.
length (Optional[float]) – <m> Trap length -> Currently not used in simulations.
v_ra (Optional[float]) – <V> Override for radial trap depth. Only effective if ModelOptions.RADIAL_DYNAMICS=False.
j (Optional[float]) – <A/cm^2> Override for current density.
fwhm (Optional[float]) – <eV> Override for the electron beam energy spread. Only effective if ModelOptions.RADIAL_DYNAMICS=False.
n_grid (int) – Approximate number of nodes for the radial mesh.
r_dt_bar (Optional[float]) – Radius of the barrier drift tubes. If not passed, assuming equal radius as trap drift tube.
- Returns
ebisim.simulation.Device – The populated device object.
- Return type
- index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
- property b_ax¶
<T> Axial magnetic field density.
- property current¶
<A> Beam current.
- property e_kin¶
<eV> Uncorrected beam energy.
- property fwhm¶
<eV> Electron beam energy spread.
- property j¶
<A/cm^2> Current density.
- property length¶
<m> Trap length.
- property r_dt¶
<m> Drift tube radius.
- property r_dt_bar¶
<m> Drift tube radius of the barrier drift tubes.
- property r_e¶
<m> Beam radius.
- property rad_fd_d¶
Diagonal vector of finite difference scheme.
- property rad_fd_l¶
Lower diagonal vector of finite difference scheme.
- property rad_fd_u¶
Upper diagonal vector of finite difference scheme.
- property rad_grid¶
<m> Radial grid for finite difference computations.
- property rad_phi_ax_barr¶
<V> Radial potential of the electron beam in the barrier tube
- property rad_phi_uncomp¶
<V> Radial potential of the electron beam.
- property rad_re_idx¶
Index of the radial grid point closest to r_e
- property v_ax¶
<V> Axial barrier voltage.
- property v_ax_sc¶
<V> Axial barrier space charge correction.
- property v_ra¶
<V> Radial barrier voltage.
- class ebisim.Element(z, symbol, name, a, ip, e_cfg, e_bind, rr_z_eff, rr_n_0_eff, dr_cs, dr_e_res, dr_strength, ei_lotz_a, ei_lotz_b, ei_lotz_c, n=None, kT=None, cx=True)[source]¶
Bases:
tuple
The Element class is one of the main data structures in ebisim. Virtually any function relies on information provided in this data structure. The leading fields of the underlying tuple contain physcial properties, whereas the n kT and cx fields are optional and only required for advanced simulations.
Instead of populating the fields manually, the user should choose one of the factory functions that meets their needs best.
For basic simulations and cross sections calculations only the physical / chemical properties of and element are needed. In these cases use the generic get() method to create instances of this class.
Advanced simulations require additional information about the initial particle densities, temperature and participation in charge exchange. The user will likely want to chose between the get_ions() and get_gas() methods, which offer a convenient interface for generating this data based on simple parameters. If these functions are not flexible enough, the get() method can be used to populate the required fields manually.
This class is derived from collections.namedtuple which facilitates use with numba-compiled functions.
See also
ebisim.elements.Element.get
,ebisim.elements.Element.get_ions
,ebisim.elements.Element.get_gas
Create new instance of Element(z, symbol, name, a, ip, e_cfg, e_bind, rr_z_eff, rr_n_0_eff, dr_cs, dr_e_res, dr_strength, ei_lotz_a, ei_lotz_b, ei_lotz_c, n, kT, cx)
- Parameters
z (int) –
symbol (str) –
name (str) –
a (float) –
ip (float) –
e_cfg (ndarray) –
e_bind (ndarray) –
rr_z_eff (ndarray) –
rr_n_0_eff (ndarray) –
dr_cs (ndarray) –
dr_e_res (ndarray) –
dr_strength (ndarray) –
ei_lotz_a (ndarray) –
ei_lotz_b (ndarray) –
ei_lotz_c (ndarray) –
n (Optional[ndarray]) –
kT (Optional[ndarray]) –
cx (bool) –
- classmethod as_element(element)[source]¶
If element is already an instance of Element it is returned. If element is a string or int identyfying an element an appropriate Element instance is returned.
- count(value, /)¶
Return number of occurrences of value.
- classmethod get(element_id, a=None, n=None, kT=None, cx=True)[source]¶
Factory method to create instances of the Element class.
- Parameters
element_id (Union[str, int]) – The full name, abbreviated symbol, or proton number of the element of interest.
a (Optional[float]) – If provided sets the mass number of the Element object otherwise a reasonable value is chosen automatically.
n (Optional[ndarray]) – <1/m> Only needed for advanced simulations! Array holding the initial ion line densities of each charge state. If provided, has to be an array of length Z+1, where Z is the nuclear charge.
kT (Optional[ndarray]) – <eV> Only needed for advanced simulations! Array holding the initial ion line densities of each charge state. If provided, has to be an array of length Z+1, where Z is the nuclear charge.
cx (bool) – Only needed for advanced simulations! Boolean flag determining whether the neutral particles of this element contribute to charge exchange with ions.
- Returns
An instance of Element with the user-supplied and generated data.
- Raises
ValueError – If the Element could not be identified or a meaningless mass number is provided.
ValueError – If the passed arrays for n or kT have the wrong shape.
- Return type
- classmethod get_gas(element_id, p, r_dt, T=300.0, cx=True, a=None)[source]¶
Factory method for defining a neutral gas injection target. A gas target is a target with constant density in charge state 0.
- Parameters
element_id (Union[str, int]) – The full name, abbreviated symbol, or proton number of the element of interest.
p (float) – <mbar> Gas pressure.
r_dt (float) – <m> Drift tube radius, required to compute linear density from volumetric density.
T (float) – <K> Gas temperature, by default 300 K (approx. room temperature)
cx (bool) – Boolean flag determining whether the neutral particles of this element contribute to charge exchange with ions.
a (Optional[float]) – If provided sets the mass number of the Element object otherwise a reasonable value is chosen automatically.
- Returns
Element instance with automatically populated n and kT fields.
- Raises
ValueError – If the density resulting from the pressure and temperature is smaller than the internal minimal value.
- Return type
- classmethod get_ions(element_id, nl, kT=10.0, q=1, cx=True, a=None)[source]¶
Factory method for defining a pulsed ion injection target. An ion target has a given density in the charge state of choice q.
- Parameters
element_id (Union[str, int]) – The full name, abbreviated symbol, or proton number of the element of interest.
nl (float) – <1/m> Linear density of the initial charge state (ions per unit length).
kT (float) – <eV> Temperature / kinetic energy of the injected ions.
q (int) – Initial charge state.
cx (bool) – Boolean flag determining whether the neutral particles of this element contribute to charge exchange with ions.
a (Optional[float]) – If provided sets the mass number of the Element object otherwise a reasonable value is chosen automatically.
- Returns
Element instance with automatically populated n and kT fields.
- Raises
ValueError – If the requested density is smaller than the internal minimal value.
- Return type
- index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
- latex_isotope()[source]¶
Returns the isotope as a LaTeX formatted string.
- Returns
str – LaTeX formatted string describing the isotope.
- Return type
str
- property a¶
Mass number / approx. mass in proton masses
- property cx¶
Boolean flag determining whether neutral particles of this target are considered as charge exchange partners.
- property dr_cs¶
Numpy array of charge states for DR cross sections.
- property dr_e_res¶
Numpy array of resonance energies for DR cross sections.
- property dr_strength¶
Numpy array of transition strengths for DR cross sections.
- property e_bind¶
Numpy array of binding energies associated with electron subshells. The index of each row corresponds to the charge state. The columns are the subshells sorted as in (‘1s’, ‘2s’, ‘2p-’, ‘2p+’, ‘3s’, ‘3p-’, ‘3p+’, ‘3d-’, ‘3d+’, ‘4s’, ‘4p-’, ‘4p+’, ‘4d-’, ‘4d+’, ‘4f-’, ‘4f+’, ‘5s’, ‘5p-’, ‘5p+’, ‘5d-’, ‘5d+’, ‘5f-’, ‘5f+’, ‘6s’, ‘6p-’, ‘6p+’, ‘6d-’, ‘6d+’, ‘7s’, ‘7p-‘).
- property e_cfg¶
Numpy array of electron configuration in different charge states. The index of each row corresponds to the charge state. The columns are the subshells sorted as in (‘1s’, ‘2s’, ‘2p-’, ‘2p+’, ‘3s’, ‘3p-’, ‘3p+’, ‘3d-’, ‘3d+’, ‘4s’, ‘4p-’, ‘4p+’, ‘4d-’, ‘4d+’, ‘4f-’, ‘4f+’, ‘5s’, ‘5p-’, ‘5p+’, ‘5d-’, ‘5d+’, ‘5f-’, ‘5f+’, ‘6s’, ‘6p-’, ‘6p+’, ‘6d-’, ‘6d+’, ‘7s’, ‘7p-‘).
- property ei_lotz_a¶
Numpy array of precomputed Lotz factor ‘a’ for each entry of ‘e_cfg’.
- property ei_lotz_b¶
Numpy array of precomputed Lotz factor ‘b’ for each entry of ‘e_cfg’.
- property ei_lotz_c¶
Numpy array of precomputed Lotz factor ‘c’ for each entry of ‘e_cfg’.
- property ip¶
Ionisation potential
- property kT¶
<eV> Array holding the initial temperature of each charge state.
- property n¶
<1/m> Array holding the initial linear density of each charge state.
- property name¶
Element name
- property rr_n_0_eff¶
Numpy array of effective valence shell numbers for RR cross sections.
- property rr_z_eff¶
Numpy array of effective nuclear charges for RR cross sections.
- property symbol¶
Element symbol e.g. H, He, Li
- property z¶
Atomic number
- class ebisim.EnergyScanResult(sim_kwargs, energies, results)[source]¶
Bases:
object
This class provides a convenient interface to access and evaluate the the results of the ebisim.simulation.energy_scan function. Abundances at arbitrary times are provided by performing linear interpolations of the solutions of the rate equation.
- Parameters
sim_kwargs (dict) – The sim_kwargs dictionary as provided during the call to ebisim.simulation.energy_scan.
energies (numpy.array) – <eV> A sorted array containing the energies at which the energy scan has been evaluated.
results (list of ebisim.simulation.Result) – A list of Result objects holding the results of each individual simulation
- abundance_at_time(t)[source]¶
Provides information about the charge state distribution at a given time for all energies.
- Parameters
t (float) – <s> Point of time to evaluate.
- Returns
energies (numpy.array) – The evaluated energies.
abundance (numpy.array) – Contains the abundance of each charge state (rows) for each energy (columns).
- Raises
ValueError – If ‘t’ is not part of the simulated time domain
- abundance_of_cs(cs)[source]¶
Provides information about the abundance of a single charge states at all simulated times and energies.
- Parameters
cs (int) – The charge state to evaluate.
- Returns
energies (numpy.array) – The evaluated energies.
times (numpy.array) – The evaluated timesteps.
abundance (numpy.array) – Abundance of charge state ‘cs’ at given times (rows) and energies (columns).
- Raises
ValueError – If ‘cs’ is not a sensible charge state for the performed simulation.
- get_result(e_kin)[source]¶
Returns the result object corresponding to the simulation at a given energy
- Parameters
e_kin (float) – <eV> The energy of the simulation one wishes to retrieve.
- Returns
ebisim.simulation.Result – The Result object for the polled scan step.
- Raises
ValueError – If the polled energy is not available.
- plot_abundance_at_time(t, cs=None, **kwargs)[source]¶
Produces a plot of the charge state abundance for different energies at a given time.
- Parameters
t (float) – <s> Point of time to evaluate.
cs (list or None, optional) – If None, all charge states are plotted. By supplying a list of int it is possible to filter the charge states that should be plotted. By default None.
**kwargs – Keyword arguments are handed down to ebisim.plotting.plot_energy_scan, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- plot_abundance_of_cs(cs, **kwargs)[source]¶
Produces a 2D contour plot of the charge state abundance for all simulated energies and times.
- Parameters
cs (int) – The charge state to plot.
**kwargs – Keyword arguments are handed down to ebisim.plotting.plot_energy_scan, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- class ebisim.ModelOptions(EI=True, RR=True, CX=True, DR=False, SPITZER_HEATING=True, COLLISIONAL_THERMALISATION=True, ESCAPE_AXIAL=True, ESCAPE_RADIAL=True, RECOMPUTE_CROSS_SECTIONS=False, RADIAL_DYNAMICS=False, IONISATION_HEATING=True, OVERRIDE_FWHM=False, RADIAL_SOLVER_MAX_STEPS=500, RADIAL_SOLVER_REL_DIFF=0.001)[source]¶
Bases:
tuple
An instance of ModelOptions can be used to turn on or off certain effects in an advanced simulation.
Create new instance of ModelOptions(EI, RR, CX, DR, SPITZER_HEATING, COLLISIONAL_THERMALISATION, ESCAPE_AXIAL, ESCAPE_RADIAL, RECOMPUTE_CROSS_SECTIONS, RADIAL_DYNAMICS, IONISATION_HEATING, OVERRIDE_FWHM, RADIAL_SOLVER_MAX_STEPS, RADIAL_SOLVER_REL_DIFF)
- Parameters
EI (bool) –
RR (bool) –
CX (bool) –
DR (bool) –
SPITZER_HEATING (bool) –
COLLISIONAL_THERMALISATION (bool) –
ESCAPE_AXIAL (bool) –
ESCAPE_RADIAL (bool) –
RECOMPUTE_CROSS_SECTIONS (bool) –
RADIAL_DYNAMICS (bool) –
IONISATION_HEATING (bool) –
OVERRIDE_FWHM (bool) –
RADIAL_SOLVER_MAX_STEPS (int) –
RADIAL_SOLVER_REL_DIFF (float) –
- count(value, /)¶
Return number of occurrences of value.
- index(value, start=0, stop=9223372036854775807, /)¶
Return first index of value.
Raises ValueError if the value is not present.
- property COLLISIONAL_THERMALISATION¶
Switch for ion-ion thermalisation, default True.
- property CX¶
Switch for charge exchange, default True.
- property DR¶
Switch for dielectronic recombination, default False.
- property EI¶
Switch for electron impact ionisation, default True.
- property ESCAPE_AXIAL¶
Switch for axial escape from the trap, default True.
- property ESCAPE_RADIAL¶
Switch for radial escape from the trap, default True.
- property IONISATION_HEATING¶
Switch for ionisation heating/recombination cooling
- property OVERRIDE_FWHM¶
If set use FWHM from device definition instead of computed value.
- property RADIAL_DYNAMICS¶
Switch for effects of radial ion cloud extent. May be computationally very intensive
- property RADIAL_SOLVER_MAX_STEPS¶
Alias for field number 12
- property RADIAL_SOLVER_REL_DIFF¶
Alias for field number 13
- property RECOMPUTE_CROSS_SECTIONS¶
Switch deciding whether EI, RR, and DR cross sections are recomputed on each call of the differential equation system. Advisable if electron beam energy changes over time and sharp transitions are expected, e.g. DR or ionisation thresholds for a given shell. Default False.
- property RR¶
Switch for radiative recombination, default True.
- property SPITZER_HEATING¶
Switch for Spitzer- or electron-heating, default True.
- class ebisim.Rate(value)[source]¶
Bases:
IntEnum
Enum for conveniently identifying rates produced in advanced simulations
- AX_CO = 105¶
- CHARGE_EXCHANGE = 104¶
- COLLISIONAL_THERMALISATION = 301¶
- COLLISION_RATE_SELF = 402¶
- COLLISION_RATE_TOTAL = 401¶
- CX = 104¶
- DIELECTRONIC_RECOMBINATION = 103¶
- DR = 103¶
- EI = 101¶
- ELECTRON_IONISATION = 101¶
- E_KIN_FWHM = 532¶
- E_KIN_MEAN = 531¶
- F_EI = 501¶
- IONISATION_HEAT = 303¶
- LOSSES_AXIAL_COLLISIONAL = 105¶
- LOSSES_RADIAL_COLLISIONAL = 107¶
- OVERLAP_FACTORS_EBEAM = 501¶
- RADIATIVE_RECOMBINATION = 102¶
- RA_CO = 107¶
- RR = 102¶
- SPITZER_HEATING = 302¶
- TRAPPING_PARAMETER_AXIAL = 521¶
- TRAPPING_PARAMETER_RADIAL = 522¶
- TRAP_DEPTH_AXIAL = 523¶
- TRAP_DEPTH_RADIAL = 524¶
- T_AX_CO = 205¶
- T_COLLISIONAL_THERMALISATION = 301¶
- T_CT = 301¶
- T_LOSSES_AXIAL_COLLISIONAL = 205¶
- T_LOSSES_RADIAL_COLLISIONAL = 207¶
- T_RA_CO = 207¶
- T_SH = 302¶
- T_SPITZER_HEATING = 302¶
- V_AX = 523¶
- V_RA = 524¶
- W_AX = 521¶
- W_RA = 522¶
- ebisim.advanced_simulation(device, targets, t_max, bg_gases=None, options=None, rates=False, solver_kwargs=None, verbose=True, n_threads=1)[source]¶
Interface for performing advanced charge breeding simulations.
For a list of effects refer to ebisim.simulation.ModelOptions.
- Parameters
device (Device) – Container describing the EBIS/T and specifically the electron beam.
targets (Union[Element, List[Element]]) – Target(s) for which charge breeding is simulated.
t_max (float) – <s> Simulated breeding time
bg_gases (Optional[Union[BackgroundGas, List[BackgroundGas]]]) – Background gas(es) which act as CX partners.
rates (bool) – If true a ‘second run’ is performed to store the rates, this takes extra time and can create quite a bit of data.
options (Optional[ModelOptions]) – Switches for effects considered in the simulation, see default values of ebisim.simulation.ModelOptions.
solver_kwargs (Optional[Dict[str, Any]]) – If supplied these keyword arguments are unpacked in the solver call. Refer to the documentation of scipy.integrate.solve_ivp for more information. By default None.
verbose (bool) – Print a little progress indicator and some status messages, by default True.
n_threads (int) – How many threads to use (mostly for jacbion estimation which can evaluate the RHS in parallel with different inputs.)
- Returns
An instance of the AdvancedResult class, holding the simulation parameters, timesteps and
charge state distribution including the species temperature.
- Return type
Union[AdvancedResult, Tuple[AdvancedResult, …]]
- ebisim.basic_simulation(element, j, e_kin, t_max, dr_fwhm=None, N_initial=None, CNI=False, solver_kwargs=None)[source]¶
Interface for performing basic charge breeding simulations.
These simulations only include the most important effects, i.e. electron ionisation, radiative recombination and optionally dielectronic recombination (for those transitions whose data is available in the resource directory). All other effects are ignored.
Continuous Neutral Injection (CNI) can be activated on demand.
The results only represent the proportions of different charge states, not actual densities.
- Parameters
element (Union[Element, str, int]) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
j (float) – <A/cm^2> Current density
e_kin (float) – <eV> Electron beam energy
t_max (float) – <s> Simulated breeding time
dr_fwhm (Optional[float]) – <eV> If a value is given, determines the energy spread of the electron beam (in terms of Full Width Half Max) and hence the effective width of DR resonances. Otherwise DR is excluded from the simulation.
N_initial (Optional[ndarray]) – Determines the initial charge state distribution if given, must have Z + 1 entries, where the array index corresponds to the charge state. If no value is given the distribution defaults to 100% of 1+ ions at t = 0 s, or a small amount of neutral atoms in the case of CNI.
CNI (bool) – If Continuous Neutral Injection is activated, the neutrals are assumed to form an infinite reservoir. Their absolute number will not change over time and hence they act as a constant source of new singly charged ions. Therefore the absolute amount of ions increases over time.
solver_kwargs (Optional[Dict[str, Any]]) – If supplied these keyword arguments are unpacked in the solver call. Refer to the documentation of scipy.integrate.solve_ivp for more information.
- Returns
An instance of the BasicResult class, holding the simulation parameters, timesteps and
charge state distribution.
- Return type
- @numba.jitebisim.drxs_energyscan(element, fwhm, e_kin=None, n=1000)[source]¶
Creates an array of DR cross sections for varying electron energies.
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
fwhm (float) – <eV> Energy spread to apply for the resonance smearing, expressed in terms of full width at half maximum.
e_kin (None or numpy.ndarray, optional) – <eV> If e_kin is None, the range of sampling energies is chosen based on the binding enrgies of the element and energies are sampled on a logscale. If e_kin is an array with 2 elements, they are interpreted as the minimum and maximum sampling energy. If e_kin is an array with more than two values, the energies are taken as the sampling energies directly, by default None.
n (int, optional) – The number of energy sampling points, if the sampling locations are not supplied by the user, by default 1000.
- Returns
e_samp (numpy.ndarray) – <eV> Array holding the sampling energies
xs_scan (numpy.ndarray) – <m^2> Array holding the cross sections, where the row index corresponds to the charge state and the columns correspond to the different sampling energies
- @numba.jitebisim.drxs_mat(element, e_kin, fwhm)[source]¶
Dielectronic recombination cross section. The cross sections are estimated by weighing the strength of each transition with the profile of a normal Gaussian distribution. This simulates the effective spreading of the resonance peaks due to the energy spread of the electron beam
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
fwhm (float) – <eV> Energy spread to apply for the resonance smearing, expressed in terms of full width at half maximum.
- Returns
numpy.array – <m^2> The cross sections for each individual charge state, arranged in a matrix suitable for implementation of a rate equation like dN/dt = j * xs_matrix dot N. out[q, q] = - cross section of q+ ion out[q, q+1] = + cross section of (q+1)+ ion
See also
ebisim.xs.drxs_vec
Similar method with different output format.
- @numba.jitebisim.drxs_vec(element, e_kin, fwhm)[source]¶
Dielectronic recombination cross section. The cross sections are estimated by weighing the strength of each transition with the profile of a normal Gaussian distribution. This simulates the effective spreading of the resonance peaks due to the energy spread of the electron beam
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
fwhm (float) – <eV> Energy spread to apply for the resonance smearing, expressed in terms of full width at half maximum.
- Returns
numpy.ndarray – <m^2> The cross sections for each individual charge state, where the array-index corresponds to the charge state, i.e. out[q] ~ cross section of q+ ion.
See also
ebisim.xs.drxs_mat
Similar method with different output format.
- @numba.jitebisim.eixs_energyscan(element, e_kin=None, n=1000)[source]¶
Creates an array of EI cross sections for varying electron energies.
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (None or numpy.ndarray, optional) – <eV> If e_kin is None, the range of sampling energies is chosen based on the binding enrgies of the element and energies are sampled on a logscale. If e_kin is an array with 2 elements, they are interpreted as the minimum and maximum sampling energy. If e_kin is an array with more than two values, the energies are taken as the sampling energies directly, by default None.
n (int, optional) – The number of energy sampling points, if the sampling locations are not supplied by the user, by default 1000.
- Returns
e_samp (numpy.ndarray) – <eV> Array holding the sampling energies
xs_scan (numpy.ndarray) – <m^2> Array holding the cross sections, where the row index corresponds to the charge state and the columns correspond to the different sampling energies
- @numba.jitebisim.eixs_mat(element, e_kin)[source]¶
Electron ionisation cross section.
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
- Returns
numpy.array – <m^2> The cross sections for each individual charge state, arranged in a matrix suitable for implementation of a rate equation like dN/dt = j * xs_matrix dot N. out[q, q] = - cross section of q+ ion out[q+1, q] = + cross section of (q+1)+ ion
See also
ebisim.xs.eixs_vec
Similar method with different output format.
- @numba.jitebisim.eixs_vec(element, e_kin)[source]¶
Electron ionisation cross section according to a simplified version of the models given in [Lotz1967].
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
- Returns
numpy.ndarray – <m^2> The cross sections for each individual charge state, where the array-index corresponds to the charge state, i.e. out[q] ~ cross section of q+ ion.
References
- Lotz1967
“An empirical formula for the electron-impact ionization cross-section”, W. Lotz, Zeitschrift Für Physik, 206(2), 205–211 (1967), https://doi.org/10.1007/BF01325928
See also
ebisim.xs.eixs_mat
Similar method with different output format.
- ebisim.energy_scan(sim_func, sim_kwargs, energies, parallel=False)[source]¶
This function provides a convenient way to repeat the same simulation for a number of different electron beam energies. This can reveal variations in the charge state balance due to weakly energy dependent ionisation cross sections or even resonant phenomena like dielectronic recombination.
- Parameters
sim_func (callable) – The function handle for the simulation e.g. ebisim.simulation.basic_simulation.
sim_kwargs (dict) – A dictionary containing all the required and optional parameters of the simulations (except for the kinetic electron energy) as key value pairs. This is unpacked in the function call.
energies (list or numpy.array) – A list or array of the energies at which the simulation should be performed.
parallel (bool, optional) – Determine whether multiple simulations should be run in parallel using pythons multiprocessing.pool. This may accelerate the scan when performing a large number of simulations. By default False.
- Returns
ebisim.simulation.EnergyScanResult – An object providing convenient access to the generated scan data.
- ebisim.get_element(element_id, a=None)[source]¶
[LEGACY] Factory function to create instances of the Element class.
- Parameters
element_id (str or int) – The full name, abbreviated symbol, or proton number of the element of interest.
a (int or None, optional) – If provided sets the (isotopic) mass number of the Element object otherwise a reasonable value is chosen automatically, by default None.
- Returns
ebisim.elements.Element – An instance of Element with the physical data corresponding to the supplied element_id, and optionally mass number.
- Raises
ValueError – If the Element could not be identified or a meaningless mass number is provided.
- Return type
- ebisim.plot_combined_xs(element, fwhm, **kwargs)[source]¶
Creates a figure showing the electron ionisation, radiative recombination and, dielectronic recombination cross sections of the provided element.
- Parameters
element (ebisim.elements.Element or str or int) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
fwhm (float) – <eV> Energy spread to apply for the resonance smearing, expressed in terms of full width at half maximum.
**kwargs – Remaining keyword arguments are handed down to ebisim.plotting.decorate_axes, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- ebisim.plot_drxs(element, fwhm, **kwargs)[source]¶
Creates a figure showing the dielectronic recombination cross sections of the provided element.
- Parameters
element (ebisim.elements.Element or str or int) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
fwhm (float) – <eV> Energy spread to apply for the resonance smearing, expressed in terms of full width at half maximum.
**kwargs – ‘fig’ is intercepted and can be used to plot on top of an existing figure. ‘ls’ is intercepted and can be used to set the linestyle for plotting. Remaining keyword arguments are handed down to ebisim.plotting.decorate_axes, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- ebisim.plot_eixs(element, **kwargs)[source]¶
Creates a figure showing the electron ionisation cross sections of the provided element.
- Parameters
element (ebisim.elements.Element or str or int) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
**kwargs – ‘fig’ is intercepted and can be used to plot on top of an existing figure. ‘ls’ is intercepted and can be used to set the linestyle for plotting. Remaining keyword arguments are handed down to ebisim.plotting.decorate_axes, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- ebisim.plot_rrxs(element, **kwargs)[source]¶
Creates a figure showing the radiative recombination cross sections of the provided element.
- Parameters
element (ebisim.elements.Element or str or int) – An instance of the Element class, or an identifier for the element, i.e. either its name, symbol or proton number.
**kwargs – ‘fig’ is intercepted and can be used to plot on top of an existing figure. ‘ls’ is intercepted and can be used to set the linestyle for plotting. Remaining keyword arguments are handed down to ebisim.plotting.decorate_axes, cf. documentation thereof. If no arguments are provided, reasonable default values are injected.
- Returns
matplotlib.Figure – Figure handle of the generated plot.
- @numba.jitebisim.rrxs_energyscan(element, e_kin=None, n=1000)[source]¶
Creates an array of RR cross sections for varying electron energies.
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (None or numpy.ndarray, optional) – <eV> If e_kin is None, the range of sampling energies is chosen based on the binding enrgies of the element and energies are sampled on a logscale. If e_kin is an array with 2 elements, they are interpreted as the minimum and maximum sampling energy. If e_kin is an array with more than two values, the energies are taken as the sampling energies directly, by default None.
n (int, optional) – The number of energy sampling points, if the sampling locations are not supplied by the user, by default 1000.
- Returns
e_samp (numpy.ndarray) – <eV> Array holding the sampling energies
xs_scan (numpy.ndarray) – <m^2> Array holding the cross sections, where the row index corresponds to the charge state and the columns correspond to the different sampling energies
- @numba.jitebisim.rrxs_mat(element, e_kin)[source]¶
Radiative recombination cross section.
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
- Returns
numpy.array – <m^2> The cross sections for each individual charge state, arranged in a matrix suitable for implementation of a rate equation like dN/dt = j * xs_matrix dot N. out[q, q] = - cross section of q+ ion out[q, q+1] = + cross section of (q+1)+ ion
See also
ebisim.xs.rrxs_vec
Similar method with different output format.
- @numba.jitebisim.rrxs_vec(element, e_kin)[source]¶
Radiative recombination cross section according to [Kim1983].
- Parameters
element (ebisim.Element) – An ebisim.Element object that holds the required physical information for cross section calculations.
e_kin (float) – <eV> Kinetic energy of the impacting electron.
- Returns
numpy.ndarray – <m^2> The cross sections for each individual charge state, where the array-index corresponds to the charge state, i.e. out[q] ~ cross section of q+ ion.
References
- Kim1983
“Direct radiative recombination of electrons with atomic ions: Cross sections and rate coefficients”, Young Soon Kim and R. H. Pratt, Phys. Rev. A 27, 2913 (1983), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.27.2913
See also
ebisim.xs.rrxs_mat
Similar method with different output format.
Subpackages¶
- ebisim.simulation package
AdvancedModel
AdvancedModel.count()
AdvancedModel.get()
AdvancedModel.index()
AdvancedModel.a
AdvancedModel.bg_gases
AdvancedModel.cxxs_bggas
AdvancedModel.cxxs_trgts
AdvancedModel.device
AdvancedModel.drxs
AdvancedModel.eixs
AdvancedModel.lb
AdvancedModel.nq
AdvancedModel.options
AdvancedModel.q
AdvancedModel.rrxs
AdvancedModel.targets
AdvancedModel.ub
AdvancedResult
AdvancedResult.abundance_at_time()
AdvancedResult.plot()
AdvancedResult.plot_charge_states()
AdvancedResult.plot_energy_density()
AdvancedResult.plot_radial_distribution_at_time()
AdvancedResult.plot_rate()
AdvancedResult.plot_temperature()
AdvancedResult.radial_distribution_at_time()
AdvancedResult.temperature_at_time()
AdvancedResult.times_of_highest_abundance()
BackgroundGas
BasicResult
Device
Device.count()
Device.get()
Device.index()
Device.b_ax
Device.current
Device.e_kin
Device.fwhm
Device.j
Device.length
Device.r_dt
Device.r_dt_bar
Device.r_e
Device.rad_fd_d
Device.rad_fd_l
Device.rad_fd_u
Device.rad_grid
Device.rad_phi_ax_barr
Device.rad_phi_uncomp
Device.rad_re_idx
Device.v_ax
Device.v_ax_sc
Device.v_ra
EnergyScanResult
ModelOptions
ModelOptions.count()
ModelOptions.index()
ModelOptions.COLLISIONAL_THERMALISATION
ModelOptions.CX
ModelOptions.DR
ModelOptions.EI
ModelOptions.ESCAPE_AXIAL
ModelOptions.ESCAPE_RADIAL
ModelOptions.IONISATION_HEATING
ModelOptions.OVERRIDE_FWHM
ModelOptions.RADIAL_DYNAMICS
ModelOptions.RADIAL_SOLVER_MAX_STEPS
ModelOptions.RADIAL_SOLVER_REL_DIFF
ModelOptions.RECOMPUTE_CROSS_SECTIONS
ModelOptions.RR
ModelOptions.SPITZER_HEATING
Rate
Rate.AX_CO
Rate.CHARGE_EXCHANGE
Rate.COLLISIONAL_THERMALISATION
Rate.COLLISION_RATE_SELF
Rate.COLLISION_RATE_TOTAL
Rate.CX
Rate.DIELECTRONIC_RECOMBINATION
Rate.DR
Rate.EI
Rate.ELECTRON_IONISATION
Rate.E_KIN_FWHM
Rate.E_KIN_MEAN
Rate.F_EI
Rate.IONISATION_HEAT
Rate.LOSSES_AXIAL_COLLISIONAL
Rate.LOSSES_RADIAL_COLLISIONAL
Rate.OVERLAP_FACTORS_EBEAM
Rate.RADIATIVE_RECOMBINATION
Rate.RA_CO
Rate.RR
Rate.SPITZER_HEATING
Rate.TRAPPING_PARAMETER_AXIAL
Rate.TRAPPING_PARAMETER_RADIAL
Rate.TRAP_DEPTH_AXIAL
Rate.TRAP_DEPTH_RADIAL
Rate.T_AX_CO
Rate.T_COLLISIONAL_THERMALISATION
Rate.T_CT
Rate.T_LOSSES_AXIAL_COLLISIONAL
Rate.T_LOSSES_RADIAL_COLLISIONAL
Rate.T_RA_CO
Rate.T_SH
Rate.T_SPITZER_HEATING
Rate.V_AX
Rate.V_RA
Rate.W_AX
Rate.W_RA
advanced_simulation()
basic_simulation()
boltzmann_radial_potential_linear_density
boltzmann_radial_potential_linear_density_ebeam
boltzmann_radial_potential_onaxis_density
energy_scan()
fd_system_nonuniform_grid
fd_system_uniform_grid
heat_capacity
radial_potential_nonuniform_grid
radial_potential_uniform_grid
tridiagonal_matrix_algorithm
Submodules¶
- ebisim.beams module
- ebisim.elements module
Element
Element.as_element()
Element.count()
Element.get()
Element.get_gas()
Element.get_ions()
Element.index()
Element.latex_isotope()
Element.a
Element.cx
Element.dr_cs
Element.dr_e_res
Element.dr_strength
Element.e_bind
Element.e_cfg
Element.ei_lotz_a
Element.ei_lotz_b
Element.ei_lotz_c
Element.ip
Element.kT
Element.n
Element.name
Element.rr_n_0_eff
Element.rr_z_eff
Element.symbol
Element.z
element_identify()
element_name()
element_symbol()
element_z()
get_element()
- ebisim.physconst module
- ebisim.plasma module
- ebisim.plotting module
- ebisim.utils module
- ebisim.xs module