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[edit] Lab Frame

[edit] Origin and Other Definitions

• Beamline refers to the nominal beam transport path.
• The terms origin and target are used interchangeably, as the scattering target is (usually) located at this nominal position.
• Downstream refers to a vector whose component along the nominal beam direction is positive. For example, the beam dump is downstream of the target. Upstream has a negative beam-direction component.
• The laboratory frame coordinate system origin is at the mutual focus of the array and of the beam.

[edit] Cartesian Coordinates

The Lab Frame Cartesian coordinate system (x,y,z)_lab:

• The unit vector is in the (nominal) direction of the incoming beam momentum vector, i.e., points downstream.
• The unit vector
  • points vertically up if the incoming beam is horizontal
  • points vertically up in the beam-optics coordinate system at the last horizontal segment
• The coordinate system is right-handed
• On SEBT3A, these constraints fix the system as follows (approximately):
  • points north.
  • points up.
  • points east.

[edit] Polar Coordinates

In general, polar coordinates (r,θ,φ) are defined as such:

• r ≥ 0, 0 ≤ θ ≤ π, 0 ≤ φ ≤2π .
• For θ =0, coincides with .
• For φ =0, is perpendicular to and is perpendicular to .

In the lab frame with the array on SEBT3A, for the vector =(r,θ,φ)_SEBT3A:

• θ_SEBT3A = 0 is along the beamline downstream (east); θ_SEBT3A= π points upstream (west).
• θ = π/2 = 90 deg and φ_SEBT3A = 0 points horizontally north.
• θ_SEBT3A = π/2 = 90 deg φ_SEBT3A = π/2 = 90 deg points straight up.

[edit] Cylindrical coordinates

In general:

• r ≥ 0, 0 ≤ φ ≤ 2π.
• The cylindrical and Cartesian z are identical.
• The cylindrical and spherical $phi; are identical.

In the lab frame for the vector =(z,r,φ)_lab:

• z_lab > 0 is downstream; z_lab < 0 is upstream.
• r_lab= 0 is on the beam axis.
• On SEBT3A, φ_SEBT3A= 0, z_SEBT3A= 0, r_SEBT3A> 0 points north.

[edit] Other Systems

[edit] Clovers

The internal, "clover-frame" coordinate system of a clover detector is defined as follows:

• The origin is at the nominal centre of the outer front flat face of the cryostat ("can"). (Vacuum causes the surface to deform, so this datum is actually with respect to a flat surface defined by the edges of the front of the can.)
• The x and y axis are selected so that the "blue" crystal is in the first quadrant.
• The z axis decreases going into the detector (i.e., from the front face through the cryostat and cold finger into the reservoir).

[edit] Individual crystals

The internal, "crystal-frame" coordinate system of an individual crystal is defined as follows:

• The concentric core and cylindrical outer surfaces of the crystal are at (x,y)=(27.2 mm, 27.2 mm).
• The untapered flat surfaces are nearest to and parallel to the x=0 and y=0
• The z=0 plane is at the front of the crystal.
• The z==(-90) mm plane is at the back of the crystal.

See Canberra drawing 77009-C and 78562-A.

[edit] Suppressors

Installed suppressors are to be considered in the coordinate system of their clover.

[edit] Numbering conventions

Numbering is a function of physical location in the relevant coordinate system. For a lab experiment, this is the lab frame as defined above. Numbering of a detector or detector element should be defined as best as possible by the spatial centre of sensitivity of the element. Usually the centre of mass is an accurate approximation to this. Often, just a rough idea of the middle is good enough, as long as that best guess is applied consistently to otherwise identical elements. The selection of the centre of sensitivity, and the appropriate coordinate system (spherical or cylindrical), should be motivated by physics and physical relevance.

[edit] Numbering in spherical systems

In a system best defined by spherical symmetry (e.g. the positions of clovers array, or a downstream CD Si):

• The major index (e.g. outer loop, more significant digit) runs with increasing θ.
• The minor index (e.g. inner loop, less significant digit) runs with increasing φ on fixed θ.

[edit] Numbering in cylindrical systems

In a system best defined by cylindrical symmetry (e.g. barrel part of Si, or the outer contacts on a Ge crystal):

• • The major index (e.g. outer loop, more significant digit) runs with decreasing z.
  • The minor index (e.g. inner loop, less significant digit) runs with increasing φ on fixed z

[edit] Equivalence

Neglecting r, these two systems should and will normally give identical numbering.

[edit] The role of r

In general, an increasing r coordinate would normally be interpreted as most-major index (most-outer loop, or most significant digit), since this would normally be interpreted as a different type of detector (e.g. r < 11 cm for Si, r > 11 cm for Ge). Strict adherence to this concept could lead to misleading numbering. Consider for example a DSSD close to the beamline, with the centre normal to the beamline. The segments at the edges would have a larger r. However, the essential physical significance is the angular part of the coordinate (θ,φ, or both). In this case, strict numbering by r would obscure the essential physics (for example, the Rutherford scattering cross-section would be immediately apparent in a hit pattern of strips with increasing θ but would be lost in strictly increasing r) As such, there is no strict convention for numbering by r. Use of r in the numbering scheme should be guided by physics or physical layout of the apparatus.