# find_floating_potential¶

plasmapy.analysis.swept_langmuir.floating_potential.find_floating_potential(voltage: numpy.ndarray, current: numpy.ndarray, threshold: int = 1, min_points: Optional[Union[int, float]] = None, fit_type: str = 'exponential')

Determines the floating potential ($$V_f$$) for a given current-voltage (IV) curve obtained from a swept Langmuir probe. The floating potential is the probe bias where the collected current equals zero $$I = 0$$. (For additional details see the Notes section below.)

Aliases: find_vf_

Parameters
• voltage (numpy.ndarray) – 1-D numpy array of monotonically ascending/descending probe biases (should be in volts)

• current (numpy.ndarray) – 1-D numpy array of probe current (should be in amperes) corresponding to the voltage array

• threshold (positive, non-zero int) – Max allowed index distance between crossing-points before a new crossing-island is formed. That is, if threshold=5 then consecutive crossing-points are considered to be in the same crossing-island if they are within 5 index steps of each other. (Default: 1)

• min_points (positive int or float) –

Minimum number of data points required for the fitting to be applied to. See Notes section below for additional details. The following list specifies the optional values:

• min_points = None (Default) The largest of 5 and factor * array_size is taken, where array_size is the size of voltage and factor = 0.1 for fit_type = "linear" and 0.2 for "exponential".

• min_points = numpy.inf The entire passed array is fitted.

• min_points >= 1 Exact minimum number of points.

• 0 < min_points < 0 The minimum number of points is taken as min_points * array_size.

• fit_type (str) –

The type of curve to be fitted to the Langmuir trace, "linear" or "exponential" (Default). This selects which FitFunction class should be applied to the trace.

 linear Linear exponential ExponentialPlusOffset

Returns

• vf (float or numpy.nan) – The calculated floating potential (same units as the voltage array). Returns numpy.nan if the floating potential can not be determined. How $$V_f$$ is calculated depends on the fit function. This is described in the root_solve() method of the relevant fit function (e.g. the root_solve() method of ExponentialPlusOffset).

• vf_err (float or numpy.nan) – The uncertainty associated with the floating potential calculation (units same as vf). Returns numpy.nan if the floating potential can not be determined. Like $$V_f$$:, the calculation depends on the applied fit function. The root_solve() method also describes how this is calculated.

• rsq (float) – The coefficient of determination (r-squared) value of the fit. See the documentation of the rsq property on the associated fit function (e.g. the rsq property of ExponentialPlusOffset).

• func (sub-class of AbstractFitFunction) – The callable function $$f(x)$$ representing the fit and its results.

• islands (List[slice]) – List of slice objects representing the indices of the identified crossing-islands.

• indices (slice) – A slice object representing the indices of voltage and current arrays used for the fit.

Notes

The internal functionality works like:

1. The current array current is scanned for all points equal to zero and point pairs that straddle $$I = 0$$. This forms an array of “crossing-points.”

2. The crossing-points are then grouped into “crossing-islands” in based on the threshold keyword.

• A new island is formed when a successive crossing-point is more (index) steps away from the previous crossing-point than allowed by threshold.

• If multiple crossing-islands are identified, then the span from the first point in the first island to the last point in the last island is compared to min_points. If the span is less than or equal to min_points, then that span is taken as one larger crossing-island for the fit; otherwise, the function is incapable of identifying $$V_f$$ and will return numpy.nan values.

3. To calculate the floating potential…

• If the crossing-island contains fewer points than min_points, then each side of the crossing-island is equally padded with the nearest neighbor points until min_points is satisfied.

• A fit is then performed using scipy.stats.linregress for fit_type="linear" and scipy.optimize.curve_fit for fit_type="exponential".