# Propagation and extrapolation¶

The track propagation is an essential part of track reconstruction. This section describes the high-level classes and concepts used for this task in Acts.

## Overview: Steppers, Navigators and Actors¶

The propagation through a geometry is based on the interaction of two different components:

• The Stepper provides the implementation of the the solution of the equation of motion (either by analytical means or through numerical integration).

• The Navigator keeps track of the current position in the geometry and adjusts the step size so that the stepper does not step through a surface.

Following the general Acts design, these classes do not manage their internal state via member variables, but provide an internal State struct which contains all relevant data and is managed by the propagator.

The interaction of these two components is handled by the Acts::Propagator class template that takes the stepper and the navigator as template parameters:

Propagator<Navigator, Stepper>


Additional to these mandatory components, the propagator can be equipped with Actors and Aborters to allow for custom behaviour. These are function objects that are hooked in the propagation loop. Actors just perform some action on the propagator state (e.g. the Acts::KalmanFitter is an actor), aborts can abort propagation (e.g., the Acts::PathLimitReached).

The propagator exposes its state to the actors and aborters as arguments to operator(). Actors must define a default-constructable result_type, which can be modified in each call:

template<typename propagator_state_t, typename stepper_t>
auto operator(propagator_state_t &state, const stepper_t &stepper, result_type &result) const {
const auto &stepperState = state.stepping;
const auto &options = state.options;
}


The result of a propagation consists of the track parameters at the endpoint of the propagation as well as the results of all actors.

## Initialization and running¶

The Acts::Propagator is initialized with the helper class Acts::PropagatorOptions, which is templated on the list of actors and aborters. This is done with the classes Acts::ActionList and Acts::AbortList (which are in fact small wrappers around std::tuple):

using MyOptions = Acts::PropagatorOptions<
Acts::ActionList<MyActor1, MyActor2>,
Acts::AbortList<MyAborter1, MyAborter2>
>;


The actors and aborters are instantiated with the options and can be accessed with the get-method that expects the corresponding actor type as template parameter. Besides this, the Acts::PropagatorOptions also contains a lot of general options like the maxStepSize:

auto options = MyOptions();
options.actionList.get<MyActor1>().foo = bar;
options.maxStepSize = 100;


All available options can be found in the Acts::PropagatorPlainOptions, from which Acts::PropagatorOptions inherits.

Tip

The propagator also contains a loop-protection mechanism. It estimates a circle perimeter from the momentum and the magnetic field, and aborts the propagation when a certain fraction (default: 0.5) of the circle has been propagated. This behaviour can be changed in the Acts::PropagatorOptions via the boolean loopProtection and the float loopFraction.

To run the propagation, we must call the member function propagate(...) with the initial track parameters and the propagator options. There are several overloads to the propagate(...) function, which allow further customization:

• With/without a target surface: The overload with a target surface automatically adds an aborter for the passed Surface to the AbortList.

• With/without a prepared result object: Without a result object, a suitable result object is default-constructed internally.

The result is an instance of Acts::Result. It contains the actual result, or an error code in case something went wrong. In the actual result, the results of the different actors can again be accessed via a get method:

auto res = propagator.propagate(myParams, options);

if( res.ok() ) {
res.value().get<MyActor1::result_type>();
}


## Steppers¶

Acts also provides a variety of stepper implementations. Since these in general can work very differently internally, the state itself is not the main interface to the steppers. Instead all steppers provide a common API, to that we can pass instances of the stepper state. This allows a generic and template-based design even for very different steppers:

template<typename propagator_state_t, typename stepper_t>
auto operator(propagator_state_t &state, const stepper_t &stepper) const {
stepper.foo(state.stepping);
}


### AtlasStepper¶

The Acts::AtlasStepper is a pure transcript from the ATLAS RungeKuttaPropagator and RungeKuttaUtils.

### StraightLineStepper¶

The Acts::StraightLineStepper is a very stripped down stepper that just performs a linear propagation without magnetic field. It can be used for debugging, validation or other simple tasks.

### EigenStepper¶

The Acts::EigenStepper implements the same functionality as the ATLAS stepper, however, the stepping code is rewritten by using Eigen primitives. Thus, it also uses a 4th-order Runge-Kutta algorithm for the integration of the EOM. Additionally, the Acts::EigenStepper allows to customize the concrete integration step via extensions.

The extensions encapsulate the relevant equations for different environments. There exists a Acts::DefaultExtension that is suited for propagation in a vacuum, and the Acts::DenseEnvironmentExtension, that contains additional code to handle the propagation inside materials. Which extension is used is selected by a bidding-system.

The extension can be configured via the Acts::StepperExtensionList:

using Stepper = Acts::EigenStepper<
Acts::StepperExtensionList<
Acts::DefaultExtension,
Acts::DenseEnvironmentExtension
>
>;


By default, the Acts::EigenStepper only uses the Acts::DefaultExtension.

### MultiEigenStepperLoop¶

The Acts::MultiEigenStepper is an extension of the Acts::EigenStepper and is designed to internally handle a multi-component state, while interfacing as a single component to the navigator. It is mainly used for the Acts::GaussianSumFitter.