Merge branch 'p-docs-fix-induced-transfer' into 'master'

module_output: "PixelCharge"

---

# InducedTransfer

**Maintainer**: Simon Spannagel (simon.spannagel@cern.ch)

**Status**: Functional

**Input**: PropagatedCharge

**Output**: PixelCharge

## Description

Combines individual sets of propagated charges together to a set of charges on the sensor pixels by calculating the total induced charge during their drift on neighboring pixels by calculating the difference in weighting potential.

This module requires a propagation of both electrons and holes in order to produce sensible results and only works in the presence of a weighting potential.

The induced charge on neighboring pixel implants is defined the Shockley-Ramo theorem \[[@shockley], [@ramo]\] as the difference in weighting potential between the end position $`x_{final}`$ retrieved from the `PropagatedCharge` and the initial position $`x_{initial}`$ of the charge carrier obtained from the `DepositedCharge` object in the history.

The total induced charge is calculated by multiplying the potential difference with the charge of the carrier, viz.

$` Q_n^{ind}  = \int_{t_{initial}}^{t_{final}} I_n^{ind} = q \left( \phi (x_{final}) - \phi(x_{initial}) \right)`$

```math

Q_n^{ind} = \int_{t_{initial}}^{t_{final}} I_n^{ind} = q \left( \phi (x_{final}) - \phi(x_{initial}) \right)

```

The resulting induced charge is summed for all propagated charge carriers and returned as a `PixelCharge` object. The number of neighboring pixels taken into account can be configured using the `induction_matrix` parameter.