Formulae for the calculation of energy deposition densities in the graphite dumps of the LHC

For dumping the 8 TeV/c proton beams of the LHC (Large Hadron Collider), each of the two beams will be extracted and then blown up along a several-hundred-meter-long transport channel to dilute the proton density to a level acceptable for the dump material. One way of diluting the beam is to let the beam pass strong quadrupoles; another much more efficient way, which can reduce the length of the transport channel considerably, is to sweep the beam by fast pulsed dipoles either linearly or in the form of circles or spirals. Formulas are derived which make it possible to calculate easily the energy deposition densities in the dump material to be expected for the different methods of beam dilution. As a basis, FLUKA results for the energy deposition in graphite of an infinitely thin beam were used. A formula is derived that fits these results and can be analytically integrated to obtain formulas for the energy deposition of Gaussian beams as well as for the different ways of diluting the beam, e.g. by deflecting it over straight lines or circles