gcmotion.plot.fixed_points_energy_contour

gcmotion.plot.fixed_points_energy_contour(profile: Profile, **kwargs)

Plots the Profile’s energy contour plot.

Parameters:

profile: Profile

The Profile entity.

Other Parameters:

thetalimlist, optional

The \(\theta\) span in radians. Defaults to [-π,π].

psilimlist, optional

The \(\psi\) span in units of psi_wall. Defaults to [0, 1.2].

levelsint, optional

The number of contour lines. Defaults to 25.

flux_unitsstr, optional

The units of the psi/Ptheta axis. Can be “Magnetic_flux”(same as “Tesla * meters^2”), “NUmagnetic_flux” (same as “NUTesla * NUmeters^2”), “psi_wall”, “NUpsi_wall”, or any other pint unit with the same dimensionality. Defaults to “Tesla * meters^2”.

E_unitsstr, optional

The Energy units. Can be “eV”, “keV”, “Joule”, “NUJoule” or any other pint unit with the same dimensionality. Defaults to “keV”.

potentialbool, optional

Whether or not to add the potential Φ term when calculating the Energy. Defaults to True.

wallbool, optional

Whether or not to shade the area above \(\psi_wall\). Defaults to True.

grid_density: int, optional

The contour’s grid density. Defaults to 200.

psilimlist, optional

Limits of the of the \(\theta\), \(\psi\) search area with respect to the \(\psi\) variable. Defaults to [0.01 , 1.8]. CAUTION-> The limits are given normalized to \(\psi_{wall}\).

thetalimlist, optional

Limits of the of the \(\theta\), \(\psi\) search area with respect to the \(\theta\) variable. Defaults to [-\(\pi\), \(\pi\)].

methodstr, optional

String that indicates which method will be used to find the system’s fixed points in single_fixed_point(). Can either be “fsolve” (deterministic) or “differential evolution” (stochastic). Defaults to “fsolve”.

dist_tolfloat

Tolerance below which two fixed points are not considered distinct. The differences between both \(\theta\) and \(\psi\) of the fixed points must be below this tolerance for the fixed points to be considered the same. Defaults to 1e-3.

fp_ic_scan_tolfloat

Tolerance below which the sum of the squares of the time derivatives of the \(\theta\) and \(\psi\) variables is considered zero. It is passed into fp_ic_scan(). Defaults to 5 * 1e-8.

ic_theta_grid_densityint, optional

Density of the \(\theta\), \(\psi\) 2D grid to be scanned for initial conditiond (fixed points candidates) with respect to the \(\theta\) variable. It is passed into fp_ic_scan(). Defaults to 400.

ic_psi_grid_densityint, optional

Density of the \(\theta\), \(\psi\) 2D grid to be scanned for initial conditiond (fixed points candidates) with respect to the \(\psi\) variable. It is passed into fp_ic_scan(). Defaults to 400.

psi_dot_scaling_factorfloat,optional

Scaling factor that is used in the sum of squares of the time derivatives of the \(\theta\) and \(\psi\) values like so –> \(\dot{\theta}^2\) + (psi_dot_scaling_factor:math:dot{psi})^2 because physiacally the time derivative of \(\psi\) is quite smaller than that of \(\theta\). Defaults to 70.

random_init_condbool, optional

Boolean determining weather random initial conditions are to be used instead of those provided by fp_ic_scan(). Defaults to False.

infobool, optional

Boolean determining weather fixed points’ information is to be is to be printed in the log. Defaults to False.

ic_infobool, optional

Boolean determing weather information on the initial condition is to be is to be printed in the log. Defaults to False.

plot_init_condbool, optional

Boolean that determines weather the initial conditions passed into fixed_points() will be plotted. Defaults to False.

only_confinedbool, optional

Boolean determining if the search for \(\psi_{fixed}\) will be conducted only for \(\psi\) < \(\psi_{wall}\) (confined particles). Defaults to False.