# Local shielding requirements for the STAR detector Page: 3 of 15

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surrounds a 3.55 mm radially thick beam pipe.8 If the cylinder (magnet) has a length L in

the beam (Z) direction, then we define loss "on a magnet" as incident particles interacting

uniformly along the length L at a depth of 1 mm into the beam pipe at the midplane

azimuthal position. Uniformity in the Z direction is chosen simply because, in the absence

of a fault model, no other choice is reasonable. Loss is forced on the magnet midplane

because both many fault conditions (e.g. - a shorted coil in a dipole) will affect the bending

plane orbit more than the vertical and because this choice gives somewhat higher radiation

levels. The choice of 1mm depth comes from the following order-of-magnitude argument.

In a linear machine, the divergence, x', in the transverse coordinate x is of order a-x/p

where a and p are the usual lattice parameters. If one pretends that the beam could blow

up to a value of x equal to the vacuum pipe radius, then an x' is defined and a reasonable

depth of interaction would be It-x' where I in the nuclear interaction length. In the

insertion regions close to the experimental halls, the vacuum pipe radius, lattice functions,

and interaction lengths all vary (the last because both protons and heavy ions are

considered), but typical values for the depth of interaction obtained in this way range

between .05 mm and 2 mm. Although the value of 1 mm was assumed in all cases for the

results given below, a limited number number of calculations were performed forcing

interactions at 0.1 mm depth and no difference (<20%) was observed.

III. Description of the Calculations

The approximation used for the magnets in the immediate vicinity of the 6 o'clock

region is sketched in Fig. 1. Only one ring is included in the simulation whose axis is the

beam axis (Z coordinate) in the hall. The outer boundaries of the magnets shown in Fig.

1 are the approximate radii of the yokes and no distinction is made between the coils and

yokes both of which are taken to be steel. In all calculations magnetic fields (appropriate

for p = 6m) are assumed within the aperture shown. No fringe fields are included and the

"return fields" in the yokes are ignored.

Fig. 2 shows the two-dimensional approximation of the geometry in the hall region.

In this figure Z=0 marks the beginning of the hall and corresponds to Z ~ 26.5m in Fig.

1. The only materials considered to be present in the hall are the beam pipe, the return

yoke and end cap(s) of the STAR solenoid9, and the enclosure itself. The latter is assumed

to be heavy concrete0 whose front wall and side wall begin at R = 4.4m and Z = 2.75m

respectively. Both walls are 1.20m thick (-4 ft.) which preliminary calculations showed to

be approximately the required thickness. The dashed lines on the enclosure and magnet

indicate that most calculations were terminated at Z - 9m, which a subset of calculations

showed to be sufficient.

Two-dimensional calculations are required because of the prohibitive computer time

required to obtain good statistical accuracy in a full three-dimensional geometry. The

meaning of "two-dimensional" in the CASIM context is that the material and star binning

assume azimuthal symmetry. However, the tracking is performed in three dimensions which

allows approximate "corrections" to be made for effects which break this symmetry. In this

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A., Stevens. Local shielding requirements for the STAR detector, report, June 1, 1992; United States. (digital.library.unt.edu/ark:/67531/metadc863727/m1/3/: accessed January 19, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.