plasma_physics.py

import numpy as np
import scipy.constants as const

import numpy as np
import scipy.constants as const

class OhmicHeating:
    def __init__(self, grid_size, plasma_density, electrical_conductivity, time_step):
        self.grid_size = grid_size
        self.plasma_density = plasma_density
        self.electrical_conductivity = electrical_conductivity
        self.time_step = time_step
        self.initialize_ohmic_parameters()

    def initialize_ohmic_parameters(self):
        # Initialize Ohmic heating parameters

        # Resistivity is the reciprocal of electrical conductivity
        self.electrical_resistivity = 1.0 / self.electrical_conductivity

    def calculate_electrical_current_density(self, electric_field):
        # Calculate the electrical current density based on Ohm's law
        # The electric field (E) and electrical resistivity (rho) are related to the current density (J) as:
        # J = E / rho
        return electric_field / self.electrical_resistivity

    def calculate_joule_heating_rate(self, electrical_current_density, electric_field):
        # Calculate the Joule heating rate in the plasma due to Ohmic heating
        # The Joule heating rate is given by J.E, where J is the electrical current density and E is the electric field.
        return np.sum(electrical_current_density * electric_field)

    def update_electron_temperature(self, joule_heating_rate):
        # Update the electron temperature based on the Joule heating rate
        # The increase in electron temperature is proportional to the Joule heating rate
        delta_t = self.time_step
        self.electron_temperature += delta_t * joule_heating_rate / (3 * const.k * self.plasma_density)

    def simulate_ohmic_heating(self, electric_field, num_time_steps):
        # Simulate Ohmic heating over multiple time steps
        for t in range(num_time_steps):
            # Calculate the electrical current density based on Ohm's law
            electrical_current_density = self.calculate_electrical_current_density(electric_field)

            # Calculate the Joule heating rate in the plasma due to Ohmic heating
            joule_heating_rate = self.calculate_joule_heating_rate(electrical_current_density, electric_field)

            # Update the electron temperature based on the Joule heating rate
            self.update_electron_temperature(joule_heating_rate)

        # Return the updated electron temperature after Ohmic heating
        return self.electron_temperature

import numpy as np

class LaserHeating:
    def __init__(self, grid_size, laser_intensity, laser_wavelength, plasma_density, plasma_temperature, time_step):
        self.grid_size = grid_size
        self.laser_intensity = laser_intensity
        self.laser_wavelength = laser_wavelength
        self.plasma_density = plasma_density
        self.plasma_temperature = plasma_temperature
        self.time_step = time_step
        self.initialize_laser_parameters()

    def initialize_laser_parameters(self):
        # Initialize laser parameters

        # Calculate the laser wave number (k) from its wavelength (lambda)
        self.laser_wave_number = 2 * np.pi / self.laser_wavelength

    def calculate_laser_intensity_profile(self):
        # Calculate the spatial distribution of the laser intensity
        # You can model the laser beam profile based on the specific laser setup and optics.

        # Example: Gaussian laser beam profile
        laser_intensity_profile = self.laser_intensity * np.exp(-0.5 * ((self.grid_size / 2 - np.arange(self.grid_size)) / (self.grid_size / 6)) ** 2)

        return laser_intensity_profile

    def calculate_laser_plasma_interaction(self, laser_intensity_profile):
        # Calculate the laser-plasma interaction and energy absorption in the plasma
        # The laser's optical propagation and its interaction with the plasma are complex.
        # You can use numerical methods like the finite-difference time-domain (FDTD) or ray tracing to simulate the interaction.
        # The absorbed energy can lead to changes in plasma temperature and electron density.

        # Example: Simple energy absorption model
        energy_absorption_rate = 0.1 * laser_intensity_profile  # Replace with appropriate absorption model

        # Update plasma temperature based on the absorbed energy
        delta_t = self.time_step
        self.plasma_temperature += delta_t * energy_absorption_rate / (3 * const.k * self.plasma_density)

    def simulate_laser_heating(self, num_time_steps):
        # Simulate laser heating over multiple time steps
        for t in range(num_time_steps):
            # Calculate the laser intensity profile
            laser_intensity_profile = self.calculate_laser_intensity_profile()

            # Calculate the laser-plasma interaction and energy absorption
            self.calculate_laser_plasma_interaction(laser_intensity_profile)

        # Return the updated plasma temperature after laser heating
        return self.plasma_temperature

class MultiphysicsPlasmaSimulation:
    def __init__(self, grid_size, time_step, num_time_steps, plasma_density, plasma_temperature, laser_intensity, laser_wavelength):
        # Initialize the multiphysics plasma simulation with relevant parameters
        self.grid_size = grid_size
        self.time_step = time_step
        self.num_time_steps = num_time_steps
        self.plasma_density = plasma_density
        self.plasma_temperature = plasma_temperature
        self.laser_intensity = laser_intensity
        self.laser_wavelength = laser_wavelength

        # Initialize the FluidSolver, PlasmaModel, and LaserHeating instances
        self.fluid_solver = FluidSolver(grid_size, time_step, num_time_steps, turbulence_model, shock_model)
        self.plasma_model = PlasmaModel(grid_size, time_step, num_time_steps, plasma_density, plasma_temperature)
        self.laser_heating = LaserHeating(grid_size, laser_intensity, laser_wavelength, plasma_density, plasma_temperature, time_step)

    def run_multiphysics_simulation(self):
        # Run the multiphysics simulation over the specified number of time steps

        for t in range(self.num_time_steps):
            # Update the plasma properties using the PlasmaModel
            self.plasma_model.apply_plasma_model()

            # Calculate the fluid dynamics using the FluidSolver
            self.fluid_solver.compute_fluxes()

            # Simulate laser heating and update plasma temperature
            updated_temperature = self.laser_heating.simulate_laser_heating(num_time_steps=1)
            self.plasma_model.plasma_temperature = updated_temperature

            # Update boundary conditions as needed
            self.plasma_model.update_boundary_conditions()
            self.fluid_solver.update_boundary_conditions()

            # Save the simulation results
            self.plasma_model.save_results_to_file()
            self.fluid_solver.save_results_to_file()

        # Return the final plasma and fluid simulation results
        plasma_results = self.plasma_model.get_results()
        fluid_results = self.fluid_solver.get_results()

        return plasma_results, fluid_results

class TimeDependentHeating:
    def __init__(self, heating_function):
        # Initialize the TimeDependentHeating with the heating_function
        self.heating_function = heating_function

    def apply_time_dependent_heating(self, time):
        # Apply time-dependent heating to the plasma properties at the given time
        heating_rate = self.heating_function(time)
        # Update the plasma properties (density or temperature) based on the heating rate
        # For example, self.plasma_density += heating_rate * self.time_step

        return updated_plasma_properties

class MultiphysicsPlasmaSimulation:
    # ... (previous code)

    def __init__(self, grid_size, time_step, num_time_steps, plasma_density, plasma_temperature, laser_intensity, laser_wavelength, heating_function):
        # ... (previous initialization)

        # Initialize the TimeDependentHeating instance with the heating function
        self.time_dependent_heating = TimeDependentHeating(heating_function)

    def run_multiphysics_simulation(self):
        # ... (previous code)

        for t in range(self.num_time_steps):
            current_time = t * self.time_step

            # Update the plasma properties using the PlasmaModel and TimeDependentHeating
            updated_plasma_properties = self.time_dependent_heating.apply_time_dependent_heating(current_time)
            self.plasma_model.plasma_density, self.plasma_model.plasma_temperature = updated_plasma_properties

            # ... (continue with previous simulation steps)

        # ... (return final simulation results)

class PlasmaHeatingSource:
    def __init__(self, position, power_density_function):
        # Initialize the PlasmaHeatingSource with its position and power density function
        self.position = position
        self.power_density_function = power_density_function

    def calculate_power_density(self, position, time):
        # Calculate the power density of the heating source at the given position and time
        return self.power_density_function(position, time)

class MultiphysicsPlasmaSimulation:
    # ... (previous code)

    def __init__(self, grid_size, time_step, num_time_steps, plasma_density, plasma_temperature, plasma_heating_sources):
        # ... (previous initialization)

        # Initialize the plasma heating sources
        self.plasma_heating_sources = plasma_heating_sources

    def calculate_total_power_density(self, position, time):
        # Calculate the total power density contributed by all plasma heating sources at a given position and time
        total_power_density = 0.0
        for heating_source in self.plasma_heating_sources:
            power_density = heating_source.calculate_power_density(position, time)
            total_power_density += power_density

        return total_power_density

    def apply_plasma_heating_interaction(self, time):
        # Apply the interaction between plasma heating sources and the plasma
        for i in range(self.grid_size):
            for j in range(self.grid_size):
                position = (i, j)
                power_density = self.calculate_total_power_density(position, time)

                # Update plasma properties based on the power density from heating sources
                # For example, self.plasma_density[i, j] += heating_rate * self.time_step

    def run_multiphysics_simulation(self):
        # ... (previous code)

        for t in range(self.num_time_steps):
            current_time = t * self.time_step

            # Apply plasma heating interaction for the current time step
            self.apply_plasma_heating_interaction(current_time)

            # ... (continue with previous simulation steps)

        # ... (return final simulation results)

class PlasmaHeatingSource:
    # ... (previous code)

    def apply_boundary_conditions(self, plasma_boundary):
        # Apply advanced boundary conditions for the heating source
        # This method can be used to enforce the interaction between the heating source and the plasma boundary
        # For example, you can ensure that the power density at the plasma boundary matches the desired value
        pass

class MultiphysicsPlasmaSimulation:
    # ... (previous code)

    def apply_boundary_conditions(self, plasma_boundary):
        # Apply advanced boundary conditions for the entire simulation
        # This method can be used to enforce the interaction between all heating sources and the plasma boundary
        for heating_source in self.plasma_heating_sources:
            heating_source.apply_boundary_conditions(plasma_boundary)

        # Additional boundary conditions for the plasma itself can also be applied here
        # For example, enforcing no-flux or insulated boundary conditions for the plasma density and temperature

    def run_multiphysics_simulation(self):
        # ... (previous code)

        # Get the plasma boundary from the plasma containment system
        plasma_boundary = self.plasma_containment.get_boundary()

        for t in range(self.num_time_steps):
            current_time = t * self.time_step

            # Apply plasma heating interaction for the current time step
            self.apply_plasma_heating_interaction(current_time)

            # Apply advanced boundary conditions for the heating sources and the plasma
            self.apply_boundary_conditions(plasma_boundary)

            # ... (continue with previous simulation steps)

        # ... (return final simulation results)




class RFHeating:
    def __init__(self, grid_size, plasma_density, electron_temperature, rf_power, rf_frequency, time_step):
        self.grid_size = grid_size
        self.plasma_density = plasma_density
        self.electron_temperature = electron_temperature
        self.rf_power = rf_power
        self.rf_frequency = rf_frequency
        self.time_step = time_step
        self.initialize_rf_parameters()

    def initialize_rf_parameters(self):
        # Initialize RF heating parameters such as wave frequency and wave vector
        self.wave_vector = np.array([1.0, 0.0])  # Wave propagation direction (along x-axis)
        self.wave_length = 2 * np.pi / np.linalg.norm(self.wave_vector)

    def calculate_rf_wave_amplitude(self):
        # Calculate the amplitude of the RF wave based on the provided RF power and wave frequency
        # For simplicity, we assume a constant amplitude, but more sophisticated models can be used
        return np.sqrt(2 * self.rf_power)

    def calculate_rf_wave_vector(self):
        # Calculate the wave vector of the RF wave based on the wave frequency and propagation direction
        omega = 2 * np.pi * self.rf_frequency
        return omega * self.wave_vector / np.linalg.norm(self.wave_vector)

    def calculate_electric_field_amplitude(self):
        # Calculate the electric field amplitude of the RF wave using wave equation and plasma parameters
        # Solving the wave equation numerically for the electric field amplitude (E) is complex and may require
        # advanced numerical techniques such as finite-difference time-domain (FDTD) or spectral methods.
        # For demonstration purposes, we use a simplified expression that assumes a uniform electric field:
        return self.calculate_rf_wave_amplitude()

    def calculate_energy_transfer_rate(self, electron_density, electric_field_amplitude):
        # Calculate the rate of energy transfer from the RF wave to electrons through wave-particle interactions
        # The energy transfer rate depends on the plasma density and electric field amplitude
        # For advanced simulations, a more realistic model, such as the Landau damping or Fokker-Planck equation,
        # can be used to calculate the energy transfer rate.
        return 0.5 * electron_density * const.e**2 * np.abs(electric_field_amplitude)**2 / (const.m_e * const.epsilon_0)

    def update_electron_temperature(self, energy_transfer_rate):
        # Update the electron temperature based on the energy transfer rate
        # The increase in electron temperature is proportional to the energy transfer rate
        delta_t = self.time_step
        self.electron_temperature += delta_t * energy_transfer_rate / (3 * const.k)

    def simulate_rf_heating(self, num_time_steps):
        # Simulate RF heating over multiple time steps
        for t in range(num_time_steps):
            # Calculate the amplitude and wave vector of the RF wave
            electric_field_amplitude = self.calculate_electric_field_amplitude()
            wave_vector = self.calculate_rf_wave_vector()

            # Calculate the energy transfer rate from the RF wave to electrons
            energy_transfer_rate = self.calculate_energy_transfer_rate(self.plasma_density, electric_field_amplitude)

            # Update the electron temperature based on the energy transfer rate
            self.update_electron_temperature(energy_transfer_rate)

        # Return the updated electron temperature after RF heating
        return self.electron_temperature

class NeutralBeamInjection:
    def __init__(self, grid_size, plasma_density, injection_rate, injected_particle_energy_mean, injected_particle_energy_std):
        self.grid_size = grid_size
        self.plasma_density = plasma_density
        self.injection_rate = injection_rate
        self.injected_particle_energy_mean = injected_particle_energy_mean
        self.injected_particle_energy_std = injected_particle_energy_std
        self.initialize_beam_parameters()

    def initialize_beam_parameters(self):
        # Initialize beam parameters such as injection direction and injection profile
        # For simplicity, we assume a uniform injection rate and direction here
        self.injection_direction = np.array([1.0, 0.0])  # Injection along the x-axis
        self.injection_profile = np.ones((self.grid_size, self.grid_size))

    def inject_neutral_particles(self, plasma_density, injection_rate, injection_profile):
        # Simulate the injection of neutral particles into the plasma
        # The injected particle density is proportional to the injection rate and the injection profile
        return injection_rate * injection_profile

    def sample_injected_particle_energy(self):
        # Sample the energy of injected neutral particles from a normal distribution
        return np.random.normal(self.injected_particle_energy_mean, self.injected_particle_energy_std)

    def ionize_neutral_particles(self, neutral_density, injected_particle_energy):
        # Simulate the ionization of neutral particles
        # For simplicity, assume all neutral particles are ionized with a sampled energy
        return neutral_density * injected_particle_energy

    def scatter_and_charge_exchange(self, ion_density, plasma_density):
        # Simulate scattering and charge exchange processes
        # For simplicity, assume that scattering and charge exchange do not change the ion energy
        return ion_density

    def calculate_energy_deposition(self, ion_density, injected_particle_energy):
        # Calculate the energy deposition profile of fast ions within the plasma
        # Energy deposition is proportional to the ion density and their energy
        return ion_density * injected_particle_energy

    def simulate_heating(self, num_time_steps):
        # Simulate neutral beam injection heating over multiple time steps
        ion_density = np.zeros_like(self.plasma_density)
        for t in range(num_time_steps):
            # Inject neutral particles into the plasma with a time-varying profile
            injection_profile = self.injection_profile * np.sin(2 * np.pi * t / num_time_steps)
            neutral_density = self.inject_neutral_particles(self.plasma_density, self.injection_rate, injection_profile)

            # Sample the energy of injected neutral particles
            injected_particle_energy = self.sample_injected_particle_energy()

            # Ionize the neutral particles
            ion_density += self.ionize_neutral_particles(neutral_density, injected_particle_energy)

            # Scatter and charge exchange the ions
            ion_density = self.scatter_and_charge_exchange(ion_density, self.plasma_density)

            # Calculate energy deposition and contribute to plasma heating
            energy_deposition = self.calculate_energy_deposition(ion_density, injected_particle_energy)
            self.plasma_density += energy_deposition

        # Return the updated plasma density after heating
        return self.plasma_density

class PlasmaModel:
    def __init__(self, grid_size, time_step, num_time_steps, plasma_density, plasma_temperature):
        # Initialize the PlasmaModel with grid size, time step, number of time steps,
        # plasma density, and plasma temperature
        self.grid_size = grid_size
        self.time_step = time_step
        self.num_time_steps = num_time_steps
        self.plasma_density = plasma_density
        self.plasma_temperature = plasma_temperature
        self.initialize_plasma_properties()

    def initialize_plasma_properties(self):
        # Set initial conditions for plasma properties (e.g., electron density, electron temperature)
        # You can also initialize other plasma properties as needed for your simulation
        self.electron_density = np.ones((self.grid_size, self.grid_size)) * self.plasma_density
        self.electron_temperature = np.ones((self.grid_size, self.grid_size)) * self.plasma_temperature
        self.ion_density = np.zeros((self.grid_size, self.grid_size))
        self.ion_temperature = np.zeros((self.grid_size, self.grid_size))
        self.electron_velocity = np.zeros((self.grid_size, self.grid_size, 2))
        self.ion_velocity = np.zeros((self.grid_size, self.grid_size, 2))
        self.electric_field = np.zeros((self.grid_size, self.grid_size, 2))
        self.magnetic_field = np.zeros((self.grid_size, self.grid_size, 2))

    def apply_plasma_model(self):
        # Implement advanced plasma physics model to update plasma properties

        # Time-stepping parameters
        delta_t = self.time_step

        # Update plasma density and temperature (assuming no sources or sinks)
        self.electron_density += delta_t * (self.compute_density_diffusion() + self.compute_density_production())
        self.ion_density += delta_t * (self.compute_ion_density_diffusion() + self.compute_ion_density_production())

        self.electron_temperature += delta_t * (self.compute_temperature_diffusion() + self.compute_temperature_production())
        self.ion_temperature += delta_t * (self.compute_ion_temperature_diffusion() + self.compute_ion_temperature_production())

        # Update plasma velocity and electric field
        self.electron_velocity += delta_t * self.compute_electron_velocity()
        self.ion_velocity += delta_t * self.compute_ion_velocity()
        self.electric_field += delta_t * self.compute_electric_field()

        # Update magnetic field
        self.magnetic_field += delta_t * self.compute_magnetic_field()

        # You can include additional plasma physics model equations here based on your simulation needs.
        # For example, you can add momentum equations, energy equations, or other relevant equations.

    def compute_magnetic_field(self):
        # Calculate magnetic field based on solenoid coil system
        mu_0 = 4 * np.pi * 1e-7  # Permeability of free space (T m/A)
        I = 1.0  # Current in the coil (A)

        # Solenoid parameters (example values)
        coil_radius = 0.1  # Radius of the solenoid coil (m)
        coil_length = 0.5  # Length of the solenoid coil (m)
        num_coil_turns = 100  # Number of turns of wire in the solenoid coil

        # Create a grid of points where we want to calculate the magnetic field
        x = np.linspace(-coil_length/2, coil_length/2, self.grid_size)
        y = np.linspace(-coil_radius, coil_radius, self.grid_size)
        xx, yy = np.meshgrid(x, y)

        # Initialize magnetic field components
        Bx = np.zeros_like(xx)
        By = np.zeros_like(yy)
        Bz = np.zeros_like(xx)  # We assume the magnetic field has no component along the z-axis

        # Calculate magnetic field contributions from each turn of the coil
        for i in range(num_coil_turns):
            # Location of the current element of the coil (assuming it lies on the y-axis)
            coil_y = i * coil_radius * 2 / num_coil_turns

            # Vector pointing from the coil element to the point where the field is being calculated
            rx = xx
            ry = yy - coil_y

            # Distance from the coil element to the point where the field is being calculated
            r = np.sqrt(rx**2 + ry**2)

            # Cross product between the current element of the coil and the vector r
            cross_product = np.cross([0, I * coil_radius, 0], [rx, ry, 0])

            # Calculate the magnetic field contribution for this coil element
            dB = mu_0 * I * cross_product / (4 * np.pi * r**3)

            # Add the magnetic field contribution to the total magnetic field
            Bx += dB[0]
            By += dB[1]

        # Combine the components of the magnetic field
        B = np.sqrt(Bx**2 + By**2 + Bz**2)

        # Store the calculated magnetic field in the class instance
        self.magnetic_field = B

    def plasma_heating(self):
        # Simulate plasma heating mechanisms (e.g., neutral beam injection, RF heating)
        # Implement heating equations based on containment geometry and heating sources
        # Example: Simulate neutral beam injection heating
        pass

    def plasma_fueling(self):
        # Simulate plasma fueling mechanisms (e.g., pellet injection, gas puffing)
        # Implement fueling equations based on containment geometry and fueling sources
        # Example: Simulate pellet injection for plasma fueling
        pass

    def plasma_equilibrium(self):
        # Achieve plasma equilibrium by solving equilibrium equations
        # Incorporate external forces, magnetic fields, and pressure balance
        # Example: Solve pressure balance equations for plasma equilibrium
        pass

    def particle_transport(self):
        # Simulate particle transport (e.g., diffusion, convection) within the plasma
        # Implement equations for particle transport based on containment geometry
        # Example: Implement particle diffusion equations in magnetic confinement
        pass

    def energy_transport(self):
        # Simulate energy transport (e.g., heat conduction) within the plasma
        # Implement equations for energy transport based on containment geometry
        # Example: Implement heat conduction equations in magnetic confinement
        pass

    def stability_analysis(self):
        # Perform stability analysis to investigate plasma stability criteria
        # Identify and handle plasma instabilities and disruptions
        # Example: Perform MHD stability analysis to check for instabilities
        pass

    def diagnostic_outputs(self):
        # Enhance the save_results_to_file method to include diagnostic outputs
        # Save magnetic field profiles, temperature profiles, density profiles, etc.
        # Example: Save magnetic field and temperature profiles to file
        pass

    def run_simulation(self):
        # Run the plasma containment simulation for the specified number of time steps
        for t in range(self.num_time_steps):
            # Save the simulation data at each time step
            self.save_results_to_file()

            # Update boundary conditions for the current time step
            self.update_boundary_conditions()

            # Compute magnetic field based on the containment geometry and magnetic coils
            self.compute_magnetic_field()

            # Simulate plasma heating mechanisms
            self.plasma_heating()

            # Simulate plasma fueling mechanisms
            self.plasma_fueling()

            # Achieve plasma equilibrium
            self.plasma_equilibrium()

            # Simulate particle transport within the plasma
            self.particle_transport()

            # Simulate energy transport within the plasma
            self.energy_transport()

            # Perform stability analysis
            self.stability_analysis()

            # Apply the plasma model to update plasma properties for the current time step
            self.apply_plasma_model()

        # Save the final simulation results
        self.save_results_to_file()

    def get_results(self):
        # Retrieve simulation results (e.g., electron density, electron temperature)
        results = {
            'electron_density': self.electron_density,
            'electron_temperature': self.electron_temperature,
            # Include additional plasma properties if needed
            # 'plasma_property1': plasma_property1,
            # 'plasma_property2': plasma_property2,
            # ...
        }
        return results

    
    def compute_density_diffusion(self):
        # Compute density diffusion term (e.g., using the diffusion coefficient)
        # You can implement the specific diffusion equation based on your simulation requirements
        diffusion_coefficient = 1.0  # Replace with the appropriate value for your plasma
        return diffusion_coefficient * np.gradient(self.electron_density, axis=(0, 1))

    def compute_ion_density_diffusion(self):
        # Compute ion density diffusion term (e.g., using the diffusion coefficient)
        # You can implement the specific diffusion equation based on your simulation requirements
        diffusion_coefficient = 0.8  # Replace with the appropriate value for your plasma
        return diffusion_coefficient * np.gradient(self.ion_density, axis=(0, 1))

    def compute_density_production(self):
        # Compute density production term (e.g., due to ionization, recombination, etc.)
        # You can implement the specific production equation based on your simulation requirements
        production_rate = 0.1  # Replace with the appropriate value for your plasma
        return production_rate * np.ones((self.grid_size, self.grid_size))

    def compute_ion_density_production(self):
        # Compute ion density production term (e.g., due to ionization, recombination, etc.)
        # You can implement the specific production equation based on your simulation requirements
        production_rate = 0.08  # Replace with the appropriate value for your plasma
        return production_rate * np.ones((self.grid_size, self.grid_size))

    def compute_temperature_diffusion(self):
        # Compute temperature diffusion term (e.g., using the thermal diffusivity)
        # You can implement the specific diffusion equation based on your simulation requirements
        thermal_diffusivity = 0.05  # Replace with the appropriate value for your plasma
        return thermal_diffusivity * np.gradient(self.electron_temperature, axis=(0, 1))

    def compute_ion_temperature_diffusion(self):
        # Compute ion temperature diffusion term (e.g., using the thermal diffusivity)
        # You can implement the specific diffusion equation based on your simulation requirements
        thermal_diffusivity = 0.04  # Replace with the appropriate value for your plasma
        return thermal_diffusivity * np.gradient(self.ion_temperature, axis=(0, 1))

    def compute_temperature_production(self):
        # Compute temperature production term (e.g., due to heating, cooling, etc.)
        # You can implement the specific production equation based on your simulation requirements
        production_rate = 0.01  # Replace with the appropriate value for your plasma
        return production_rate * np.ones((self.grid_size, self.grid_size))

    def compute_ion_temperature_production(self):
        # Compute ion temperature production term (e.g., due to heating, cooling, etc.)
        # You can implement the specific production equation based on your simulation requirements
        production_rate = 0.008  # Replace with the appropriate value for your plasma
        return production_rate * np.ones((self.grid_size, self.grid_size))

    def compute_electron_velocity(self):
        # Compute electron velocity based on the electric field and magnetic field
        # You can implement the specific electron velocity equation based on your simulation requirements
        return np.zeros((self.grid_size, self.grid_size, 2))

    def compute_ion_velocity(self):
        # Compute ion velocity based on the electric field and magnetic field
        # You can implement the specific ion velocity equation based on your simulation requirements
        return np.zeros((self.grid_size, self.grid_size, 2))

    def compute_electric_field(self):
        # Compute electric field based on the electron and ion densities and temperatures
        # You can implement the specific electric field equation based on your simulation requirements
        return np.zeros((self.grid_size, self.grid_size, 2))

    def compute_magnetic_field(self):
        # Compute magnetic field based on the electron and ion densities and temperatures
        # You can implement the specific magnetic field equation based on your simulation requirements
        return np.zeros((self.grid_size, self.grid_size, 2))

    def update_boundary_conditions(self):
        # Update boundary conditions for each time step in the simulation
        # You can implement specific boundary conditions based on your simulation requirements
        pass

    def save_results_to_file(self):
        # Save plasma model results to files for post-processing and visualization
        # You can save electron density, electron temperature, ion density, ion temperature,
        # electric field, magnetic field, or any other relevant plasma properties
        # at each time step to analyze the simulation results later.
        pass

    def run_simulation(self):
        # Run the plasma simulation for the specified number of time steps
        for t in range(self.num_time_steps):
            # Save the simulation data at each time step
            self.save_results_to_file()

            # Update boundary conditions for the current time step
            self.update_boundary_conditions()

            # Apply the plasma model to update plasma properties for the current time step
            self.apply_plasma_model()

        # Save the final simulation results (e.g., plasma profiles, particle distributions, etc.)
        self.save_results_to_file()

    def get_results(self):
        # Retrieve simulation results (e.g., electron density, electron temperature, ion density, ion temperature)
        results = {
            'electron_density': self.electron_density,
            'electron_temperature': self.electron_temperature,
            'ion_density': self.ion_density,
            'ion_temperature': self.ion_temperature,
            'electron_velocity': self.electron_velocity,
            'ion_velocity': self.ion_velocity,
            'electric_field': self.electric_field,
            'magnetic_field': self.magnetic_field,
            # Include additional plasma properties if needed
            # 'plasma_property1': plasma_property1,
            # 'plasma_property2': plasma_property2,
            # ...
        }
        return results