Using an Asymmetric Heating Profile Under the Single-fluid Approximation

In this example, we force the electron and ion populations to have the same temperature to illustrate the single fluid case.

import astropy.units as u
import matplotlib.pyplot as plt
import numpy as np

from astropy.visualization import quantity_support

import ebtelplusplus

from ebtelplusplus.models import DemModel, HeatingEvent, HeatingModel, PhysicsModel

quantity_support()

<astropy.visualization.units.quantity_support.<locals>.MplQuantityConverter object at 0x71408bbee480>

Set up a trapezoidal heating profile that rises for 250 s, stays constant for 750 s at a heating rate of 0.05 erg per cubic centimeter per second, and then decays linearly to the background rate over the course of 1000 s.

event = HeatingEvent(0*u.s,
                     2000*u.s,
                     250*u.s,
                     1000*u.s,
                     0.005*u.Unit('erg cm-3 s-1'))

In this heating model, we equally partition the injected energy between the electrons and the ions.

heating = HeatingModel(background=3.5e-5*u.Unit('erg cm-3 s-1'),
                       partition=0.5,
                       events=[event])

Note that we also need to enforce the single-fluid requirement in our physics model.

physics = PhysicsModel(force_single_fluid=True)

Now run the simulation for a 40 Mm loop lasting a total of 3 h. We’ll also specify that we want to compute the DEM

result = ebtelplusplus.run(5e3*u.s,
                           40*u.Mm,
                           heating=heating,
                           physics=physics,
                           dem=DemModel(calculate_dem=True))

Let’s visualize the heating profile, temperature, and density as a function of time.

fig, axes = plt.subplots(3, 1, sharex=True)
axes[0].plot(result.time, result.heat)
axes[1].plot(result.time, result.electron_temperature, label='electron')
axes[1].plot(result.time, result.ion_temperature, label='ion')
axes[2].plot(result.time, result.density)
axes[1].legend()

<matplotlib.legend.Legend object at 0x71408a443530>

Finally, let’s visualize the DEM distribution. We’ll first time-average each component over the duration of the simulation.

delta_t = np.gradient(result.time)
dem_avg_total = np.average(result.dem_tr+result.dem_corona,
                           axis=0,
                           weights=delta_t)
dem_avg_tr = np.average(result.dem_tr,
                        axis=0,
                        weights=delta_t)
dem_avg_corona = np.average(result.dem_corona,
                            axis=0,
                            weights=delta_t)

And now we can plot each component

fig = plt.figure()
ax = fig.add_subplot()
ax.plot(result.dem_temperature, dem_avg_total, label='Total')
ax.plot(result.dem_temperature, dem_avg_tr, label='TR')
ax.plot(result.dem_temperature, dem_avg_corona, label='Corona')
ax.set_xlim([10**(4.5), 10**(7.5)]*u.K)
ax.set_ylim([10**(20.0), 10**(23.5)]*u.Unit('cm-5 K-1'))
ax.set_xscale('log')
ax.set_yscale('log')
ax.legend()

plt.show()