Determining causality in Hall effect thrusters using extended convergent cross mapping, part I**

Convergent cross mapping (CCM) is an analytical technique with various applications in ecology, biology, and any other fields where causal links must be distinguished in dynamical systems. An extended version (herein referred to as eCCM) is used to determine the causal links between probe and grid signals in Hall effect thruster simulation results obtained from HPHall, though this technique can also be applied to experimental data. To curtail some of the limitations of eCCM due to signal noise and data capture rate, a new methodology is developed by introducing data splitting (into training and testing sets) and normalization by the self-reconstruction skill. This version of eCCM is validated with probe to probe cross mapping tests to ensure its accuracy and calibrate input parameters that balance resolution and computational cost. Probe to probe cross mapping results agreed to within 10% for most cases (once filtering was applied to remove noise), and probe to anode cross mapping results for several quiescent and an oscillatory operating modes agree very well with the expected flow of information carried by the ions. For instance, eCCM is shown to be able to distinguish the first two harmonic frequencies to less than to within 0.5% when the signal to noise ratio is sufficient. These results strongly affirm the usefulness of eCCM in Hall-effect thruster analysis.