.. _example_moving_pellet:

=============================================
Moving Fuel Pellet
=============================================

Problem Description
===================

A three-dimensional time-dependent problem in which a cylindrical fuel
pellet traverses a box of air-like material along a piecewise-linear
trajectory.  Both the cylindrical surface and the bounding planes of the
pellet move, demonstrating MC/DC's **moving-surface** capability for
transient geometry.

Geometry and Materials
======================

The computational domain is a rectangular box:
:math:`x \in [-5,5]`, :math:`y \in [-5,5]`, :math:`z \in [-10,10]` cm,
with vacuum boundary conditions on all faces.

A z-aligned cylindrical fuel pellet (radius 1 cm) is initially located
at :math:`z \in [6,9]` cm.  The pellet moves in three consecutive phases:

.. list-table::
   :widths: 15 40 40 15

   * - **Phase**
     - **Cylinder velocity**
     - **End-cap velocity**
     - **Duration (s)**
   * - 1
     - :math:`(-0.5,\; 0,\; 0)`
     - :math:`(0,\; 0,\; -2)`
     - 2 / 5
   * - 2
     - :math:`(1,\; 0,\; 0)`
     - :math:`(0,\; 0,\; 4)`
     - 5 / 2
   * - 3
     - :math:`(-2,\; 0,\; 0)`
     - :math:`(0,\; 0,\; -10)`
     - 1 / 1

Two materials are used:

.. list-table:: Cross-section data (mono-energetic, cm\ :sup:`-1`)
   :widths: 20 15 15 15 15

   * - **Region**
     - :math:`\Sigma_c`
     - :math:`\Sigma_s`
     - :math:`\Sigma_f`
     - :math:`\nu`
   * - Fuel pellet
     - 0.50
     - —
     - 0.25
     - 1.5
   * - Air
     - 0.002
     - 0.008
     - —
     - —

Neutron speed: :math:`v = 2 \times 10^{5}` cm/s (both regions).

Physical Assumptions
====================

* Mono-energetic (one-speed) neutron transport.
* Isotropic scattering.
* Time-dependent transport with moving geometry surfaces.
* Fission in the pellet region only.

Numerical Setup
===============

.. list-table::
   :widths: 35 65

   * - **Spatial mesh (tally)**
     - :math:`201 \times 201` in the :math:`(x,z)`-plane
   * - **Time mesh (tally)**
     - 46 equally spaced bins over :math:`t \in [0,9]` s
   * - **Tally score**
     - Fission rate
   * - **Source particles**
     - :math:`10^{5}`
   * - **Batches**
     - 2

Quantities of Interest
======================

* Time-resolved 2-D fission rate distribution in the :math:`(x,z)`-plane.
* Animation of the fission rate tracking the moving pellet geometry.

Reference Solution
==================

No analytical reference.  The solution is validated by verifying that
the fission rate follows the pellet trajectory and that particle
conservation is maintained.

Step-by-Step Walkthrough
========================

**1. Materials (lines 1–22)**

.. literalinclude:: ../../../examples/moving_pellet/input.py
   :language: python
   :lines: 1-22
   :linenos:
   :lineno-match:

A fissile fuel pellet (:math:`\Sigma_f = 0.25`, :math:`\nu = 1.5`) and
an air-like background.  Both include ``speed`` for time-dependent
transport.

**2. Surfaces and Moving Geometry (lines 24–30)**

.. literalinclude:: ../../../examples/moving_pellet/input.py
   :language: python
   :lines: 24-30
   :linenos:
   :lineno-match:

A z-cylinder and two z-planes define the pellet.  The key feature:
``surface.move(velocities, durations)`` makes these surfaces **time-dependent**.
The cylinder moves laterally while the endcaps move axially, simulating
a pellet traversing the domain.

**3. Container and Cells (lines 32–50)**

.. literalinclude:: ../../../examples/moving_pellet/input.py
   :language: python
   :lines: 32-50
   :linenos:
   :lineno-match:

The fuel pellet region is defined by the intersection of the cylinder
and the two planes.  The air fills the complement inside the bounding box.

**4. Source (lines 56–63)**

.. literalinclude:: ../../../examples/moving_pellet/input.py
   :language: python
   :lines: 56-63
   :linenos:
   :lineno-match:

A small box source near the pellet’s initial position, active over the
full simulation time :math:`t \in [0, 9]` s.

**5. Tallies, Settings, and Run (lines 69–83)**

.. literalinclude:: ../../../examples/moving_pellet/input.py
   :language: python
   :lines: 69-83
   :linenos:
   :lineno-match:

A structured mesh tally in the :math:`(x,z)`-plane with 46 time bins
captures the fission rate as the pellet moves.

**What to try:**

- Change the pellet velocities to create different trajectories.
- Set ``visualize = True`` to watch the geometry evolve with
  ``mcdc.visualize(..., time=...)``.
- Compare with ``moving_source`` to see source motion vs. geometry motion.

Full Input
==========

Click here to view the input file: `examples/moving_pellet/input.py <https://github.com/CEMeNT-PSAAP/MCDC/blob/dev/examples/moving_pellet/input.py>`_.

The complete input used for this example is embedded below:

.. literalinclude:: ../../../examples/moving_pellet/input.py
  :language: python
  :linenos:

How to Run
==========

From the repository root run::

  python examples/moving_pellet/input.py

Expected Output
===============

An HDF5 tally file with time-resolved fission rates and an optional
animation created by the example's post-processing script.