# Analysing ITER parameters¶

Let’s try to look at ITER plasma conditions using the physics subpackage.

from astropy import units as u
from plasmapy import formulary
import matplotlib.pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D


The radius of electric field shielding clouds, also known as the Debye length, would be

electron_temperature = 8.8 * u.keV
electron_concentration = 10.1e19 / u.m**3
print(formulary.Debye_length(electron_temperature, electron_concentration))


Out:

/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:372: ImplicitUnitConversionWarning: The argument 'T_e' to function Debye_length() has a non-standard unit conversion...converting keV to K
f"{err_msg} has a non-standard unit conversion..."
6.939046810942984e-05 m


Note that we can also neglect the unit for the concentration, as 1/m^3 is the a standard unit for this kind of Quantity:

print(formulary.Debye_length(electron_temperature, 10.1e19))


Out:

/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:350: UnitsWarning: The argument 'n_e' to function Debye_length() has no specified units. Assuming units of 1 / m3. To silence this warning, explicitly pass in an astropy Quantity (e.g. 5. * astropy.units.cm) (see http://docs.astropy.org/en/stable/units/)
f"{err_msg} has no specified units. Assuming units of "
6.939046810942984e-05 m


Assuming the magnetic field as 5.3 Teslas (which is the value at the major radius):

B = 5.3 * u.T

print(formulary.gyrofrequency(B, particle='e'))



Out:

932174605709.2465 rad / s
/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:372: ImplicitUnitConversionWarning: The argument 'T_i' to function gyroradius() has a non-standard unit conversion...converting keV to K
f"{err_msg} has a non-standard unit conversion..."
/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/checks.py:1392: RelativityWarning: thermal_speed is yielding a velocity that is 18.559% of the speed of light. Relativistic effects may be important.
RelativityWarning,
/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:372: ImplicitUnitConversionWarning: The return value  to function gyroradius() has a non-standard unit conversion...converting m / rad to m
f"{err_msg} has a non-standard unit conversion..."
5.968562765183547e-05 m


The electron inertial length would be

print(formulary.inertial_length(electron_concentration, particle='e'))


Out:

/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:372: ImplicitUnitConversionWarning: The return value  to function inertial_length() has a non-standard unit conversion...converting m / rad to m
f"{err_msg} has a non-standard unit conversion..."
0.0005287720427518426 m


In these conditions, they should reach thermal velocities of about

print(formulary.thermal_speed(T=electron_temperature, particle='e'))


Out:

/home/docs/checkouts/readthedocs.org/user_builds/plasmapy/checkouts/latest/plasmapy/utils/decorators/validators.py:372: ImplicitUnitConversionWarning: The argument 'T' to function thermal_speed() has a non-standard unit conversion...converting keV to K
f"{err_msg} has a non-standard unit conversion..."
55637426.422858626 m / s


And the Langmuir wave plasma frequency should be on the order of

print(formulary.plasma_frequency(electron_concentration))


Out:

566959736448.652 rad / s


Let’s try to recreate some plots and get a feel for some of these quantities. We will also compare our data to real-world plasma situations.

n_e = np.logspace(4, 30, 100) / u.m**3
plt.plot(n_e, formulary.plasma_frequency(n_e))
plt.scatter(
electron_concentration,
formulary.plasma_frequency(electron_concentration),
label="Our Data")

# IRT1 Tokamak Data
# http://article.sapub.org/pdf/10.5923.j.jnpp.20110101.03.pdf
n_e = 1.2e19 / u.m**3
T_e = 136.8323 * u.eV
B = 0.82 * u.T
plt.scatter(n_e, formulary.plasma_frequency(n_e), label="IRT1 Tokamak")

# Wendelstein 7-X Stellerator Data
# https://nucleus.iaea.org/sites/fusionportal/Shared%20Documents/FEC%202016/fec2016-preprints/preprint0541.pdf
n_e = 3e19 / u.m**3
T_e = 6 * u.keV
B = 3 * u.T
plt.scatter(n_e, formulary.plasma_frequency(n_e), label="W7-X Stellerator")

# Solar Corona
# Estimated by Nick Murphy
n_e = 1e15 / u.m**3
T_e = 1e6 * u.K
B = 0.005 * u.T
T_e.to(u.eV, equivalencies=u.temperature_energy())
plt.scatter(n_e, formulary.plasma_frequency(n_e), label="Solar Corona")

# Interstellar (warm neutral) Medium
# Estimated by Nick Murphy
n_e = 1e6 / u.m**3
T_e = 5e3 * u.K
B = 0.005 * u.T
T_e.to(u.eV, equivalencies=u.temperature_energy())
plt.scatter(n_e, formulary.plasma_frequency(n_e), label="Interstellar Medium")

# Solar Wind at 1 AU
# Estimated by Nick Murphy
n_e = 7e6 / u.m**3
T_e = 1e5 * u.K
B = 5e-9 * u.T
T_e.to(u.eV, equivalencies=u.temperature_energy())
plt.scatter(n_e, formulary.plasma_frequency(n_e), label="Solar Wind (1AU)")

plt.xlabel("Electron Concentration (m^-3)") 