Defining Geometry in Geant4: What are the World, Mother, and Daughter Volumes?

 Defining Geometry in Geant4: What are the World, Mother, and Daughter Volumes?

In Geant4 (G4), geometry isn't just about shapes; it's a hierarchical and spatial structure where particles move and interact. Understanding the three key concepts of the World Volume, Mother Volume, and Daughter Volume is essential for building any simulation geometry. This article teaches these fundamental concepts.

1. The World Volume

The geometry in Geant4 is made up of multiple volumes. The largest of these is called the World Volume. This volume must enclose all other defined volumes within the simulation. All other volumes are created and placed inside their respective mother volumes.

For simplicity, the world volume is often a simple cube. However, in newer versions of Geant4, defining a sphere is also straightforward with fewer commands.

• Key Characteristics:

  • It Contains Everything: Every other physical volume in your simulation must be placed directly or indirectly inside the World Volume.

  • It Has No Mother: The World Volume is the only volume that does not have a mother volume itself. It is the root of the geometry hierarchy tree.

  • It Must Be Large Enough: Its dimensions must be sufficient to contain all parts of your detector geometry, the particle source, and even the paths of secondary particles. If a particle exits the world volume boundaries, Geant4 stops tracking it.

Analogy: Think of the World Volume as the entire building. Everything else (rooms, hallways, furniture) must be placed inside this building.

2. Mother and Daughter Volumes

These two concepts are defined in relation to each other. The relationship between them is both hierarchical and spatial.

• A Mother Volume is a volume that has one or more other volumes placed inside it.

• A Daughter Volume is a volume that is placed inside another volume (its mother).

Key Characteristics of this Relationship:

1. A Tree Hierarchy: The World Volume is the ultimate mother. A volume can simultaneously be a "daughter" (relative to its parent) and a "mother" (relative to its children). This structure forms a tree.

   • Example: In a detector, the World is the mother of an Envelope. The Envelope is itself the mother of several Layers. Each Layer is, in turn, the mother of multiple Sensitive_Modules.

2. Local Coordinate System: The coordinates of a daughter volume are always specified relative to the origin of its mother volume's coordinate system. This is a crucial point.

   • Example: Imagine a cubic mother volume with a side of 10cm, placed at the origin of the world. If you place a spherical daughter volume at position (0, 0, 5) relative to the mother, the sphere will appear at the center of the mother cube's top face, not relative to the world's origin.

3. Layered Description: Defining a volume fully in Geant4 is a three-step process:

   • Solid: This defines only the shape and geometrical boundaries (e.g., a cube 5cm x 5cm x 5cm). It has no position or material.

   • Logical Volume: This attaches a material and other physical properties (like a magnetic field, sensitivity for detection) to a Solid. It is a ready-to-use definition but is not yet positioned in space.

   • Physical Volume: This places a Logical Volume inside a mother Logical Volume by applying a translation and/or rotation. This is the step where the "mother-daughter" relationship is physically created.

Summary and Final Notes

A Critical Tip: Careful design of this hierarchy and its local coordinate systems is the key to building complex, error-free geometries. Mistakes in defining a volume's "mother" or placing a volume in the wrong coordinates relative to its mother will lead to unexpected behavior in the simulation.

Understanding the World, Mother, and Daughter volumes provides the necessary foundation to move to the practical stage of coding geometry in Geant4.