[docs]
class ColdPlasma(StruphyModel):
"""Cold plasma model: electron-fluid current coupled with Maxwell's equations via a cold-plasma Ohm's law.
Parameters
----------
base_units: BaseUnits
Base units for normalization (default: BaseUnits())
charge_number: int
Charge number (in units of the positive elementary charge) of the electron species (default: -1)
mass_number: float
Mass number (in units of Proton mass) of the electron species (default: 1/1836)
alpha: float, optional
Dimensionless parameter: plasma frequency / cyclotron frequency. If None, computed from units and charge/mass numbers.
epsilon: float, optional
Normalized cyclotron period: 1 / (cyclotron frequency × time unit). If None, computed from units and charge/mass numbers.
"""
@classmethod
def model_type(cls) -> LiteralOptions.ModelTypes:
return "Fluid"
## species
class EMFields(FieldSpecies):
def __init__(self):
self.e_field = FEECVariable(space="Hcurl")
self.b_field = FEECVariable(space="Hdiv")
self.init_variables()
class Electrons(FluidSpecies):
def __init__(
self,
charge_number: int = 1,
mass_number: float = 1.0,
alpha: float = None,
epsilon: float = None,
):
self.current = FEECVariable(space="Hcurl")
self.init_variables(
charge_number=charge_number,
mass_number=mass_number,
alpha=alpha,
epsilon=epsilon,
)
## propagators
class Propagators:
def __init__(self):
self.maxwell = MaxwellWeakAmpere()
self.ohm = OhmCold()
self.jxb = JxBCold()
## abstract methods
def __init__(
self,
base_units: BaseUnits = BaseUnits(),
charge_number: int = -1,
mass_number: float = 1 / 1836,
alpha: float = None,
epsilon: float = None,
):
# 0. store input parameters
self.params = copy.deepcopy(locals())
# 1. instantiate all species
self.em_fields = self.EMFields()
self.electrons = self.Electrons(
charge_number=charge_number,
mass_number=mass_number,
alpha=alpha,
epsilon=epsilon,
)
# 2. derive units (must be done after instantiating species to access charge and mass numbers)
self.setup_equation_params(base_units=base_units)
# 3. instantiate all propagators
self.propagators = self.Propagators()
# 4. assign variables to propagators
self.propagators.maxwell.variables.e = self.em_fields.e_field
self.propagators.maxwell.variables.b = self.em_fields.b_field
self.propagators.ohm.variables.j = self.electrons.current
self.propagators.ohm.variables.e = self.em_fields.e_field
self.propagators.jxb.variables.j = self.electrons.current
# 5. define scalars to be tracked during simulation
electric_energy = BilinearEnergyFEEC(self.em_fields.e_field)
magnetic_energy = BilinearEnergyFEEC(self.em_fields.b_field)
kinetic_energy = BilinearEnergyFEEC(
self.electrons.current,
bilinear_form_name="M1ninv",
normalization=self.electrons.equation_params.alpha**2,
)
total_energy = electric_energy + magnetic_energy + kinetic_energy
self.scalars = Scalars(
electric_energy=electric_energy,
magnetic_energy=magnetic_energy,
kinetic_energy=kinetic_energy,
total_energy=total_energy,
)
@property
def bulk_species(self):
return self.electrons
@property
def velocity_scale(self):
return "light"
def allocate_helpers(self):
pass
[docs]
@classmethod
def doc_pde(cls):
r"""**PDEs solved by model:**
Cold-plasma current:
.. math::
\frac{1}{n_0} \frac{\partial \mathbf{j}}{\partial t} = \frac{1}{\varepsilon} \mathbf{E} + \frac{1}{\varepsilon n_0} \mathbf{j} \times \mathbf{B}_0
Faraday's law:
.. math::
\frac{\partial \mathbf{B}}{\partial t} + \nabla \times \mathbf{E} = 0
Ampère's law:
.. math::
-\frac{\partial \mathbf{E}}{\partial t} + \nabla \times \mathbf{B} = \frac{\alpha^2}{\varepsilon} \mathbf{j}
where :math:`(n_0, \mathbf{B}_0)` denotes an inhomogeneous background.
"""
[docs]
@classmethod
def doc_normalization(cls):
r"""Velocities are normalized with the speed of light and the fields satisfy
.. math::
\hat v = c,\qquad \hat E = c \hat B.
The dimensionless plasma parameters are the cold-species
:math:`\alpha = \hat\Omega_\mathrm{p}/\hat\Omega_\mathrm{c}` and
:math:`\varepsilon = 1/(\hat\Omega_\mathrm{c}\hat t)`."""
[docs]
@classmethod
def doc_scalar_quantities(cls):
r"""**The following scalars are tracked during simulation:**
- Electric field energy: ``electric_energy``
- Magnetic field energy: ``magnetic_energy``
- Cold-current energy: ``kinetic_energy``
- Total energy: ``total_energy``"""
[docs]
@classmethod
def doc_discretization(cls):
"""Time integration is performed by the following propagators (in sequence):
1. :class:`~struphy.propagators.maxwell_weak_ampere.MaxwellWeakAmpere`
2. :class:`~struphy.propagators.ohm_cold.OhmCold`
3. :class:`~struphy.propagators.jxb_cold.JxBCold`
"""
doc = rf"""**1. propagators.maxwell.Maxwell:**
{MaxwellWeakAmpere.__doc__}
**2. OhmCold:**
{OhmCold.__doc__}
**3. JxBCold:**
{JxBCold.__doc__}
"""
return doc
[docs]
@classmethod
def doc_long_description(cls):
r"""This is a fluid electromagnetic model for a cold plasma response. The
electron fluid is represented only through its current, so thermal
pressure and kinetic velocity-space effects are omitted. It is useful as
a reduced model between vacuum Maxwell and fully kinetic Vlasov-Maxwell
dynamics."""
[docs]
@classmethod
def doc_examples(cls):
r"""Create and initialize a cold-plasma model:
.. code-block:: python
from struphy.models import ColdPlasma
model = ColdPlasma()
model.em_fields.e_field
model.em_fields.b_field
model.electrons.current
"""
[docs]
@classmethod
def doc_use_cases(cls):
r"""This model is appropriate for:
- cold-plasma wave propagation studies
- electromagnetic benchmarks with a fluid current response
- regimes where thermal pressure can be neglected
- algorithm verification for Maxwell plus current coupling"""
[docs]
@classmethod
def doc_cannot_be_used_for(cls):
r"""This model is not suitable for:
- finite-temperature or pressure-driven plasma dynamics
- kinetic resonances or velocity-space instabilities
- multi-species hybrid or fully kinetic problems
- collisional closures beyond the built-in cold-plasma approximation"""
