Theory of collimators

The following figure illustrates a rectangular collimator inside of a rectangular pipe.

A collimator has two apertures, an inner and an outer, with a region of matter between them. Inside the inner aperture is a region of vacuum that will be referred to as region . The surrounding region of matter will be referred to as region and the region outside the outer aperture will be known as region . When a particle enters the collimator, it is in one of the three regions. If it is in region , it is lost to the beam; if it is in region , DREST, the distance along axis that the particle will travel before entering region , is calculated. A decay distance DPHI is also calculated. These two numbers are compared with TREST, the remaining distance along before the particle reaches the end of the beam element. One of three things can then happen.

1. If DREST < TREST, the particle enters region after travelling distance DREST in .
2. If DPHI TREST, the particle tracks a distance DPHI, undergoes decay and a new DREST will be calculated. This new DREST is then compared to the new TREST. If DREST < TREST, the particle travels the new distance DREST and then enters region . If DREST > TREST, the particle travels right through the beam element and exits.
3. If DPHI and DREST are both > TREST, the particle travels right through the beam element and exits.

Once the particle is in region , it is treated in the following way. An interaction distance DIS is calculated. The particle undergoes multiple scattering in small steps. The step-size is determined by the value of TMAX that is supplied by the user and by how likely the particle is going to re-enter region . If the probability is high, the next step will be small, thus giving better resolution to the exact spot of re-entry. The particles continue in little steps until

Another assumption in the theory of collimators is that the central momentum and energy of the beam is unaltered by the collimator. This means that rays that lose a substantial fraction of their energy traversing the collimator(s) will have their calculated as if they had their normal undegraded momentum. Thus the program will underestimate . The program does however take account of change in central momentum of the beam that has traversed absorbers with fractional area covered equal to 1.

REVMOC also allows the simulation of a tapered circular cylinder of material inside a larger circular, elliptical or rectangular beam pipe. Simply set the ``collimator'' aperture to the negative of the cylinder radius. There will of course be no material outside this radius up to the beam pipe aperture. Beyond the beam pipe aperture the region is opaque and any particles traversing this region will be immediately lost.

On February 19, 1985 an experimental feature was added to allow collimators to have superimposed on them a quadrupole field. This field is set by the 8 field on the first of each of the drift records. Thus for a circular beam pipe there would be four zeroes following the radius parameter and then the quadrupole field in kg/cm. This feature makes possible studies of scattering from collimators placed inside quadrupoles.

Quadrupoles

These are modelled using a first order transformation matrix but the exact momentum for each particle is used. Thus, in effect, the calculations are good to second order.

Bending magnets

The sign convention, as in TRANSPORT, is that a positive bend is to the right looking in the direction of particle travel. To bend in other directions use the Rotate element. Thus to bend upwards precede the bend with a Rotate element with angle of 90 degrees; to bend to left an angle of 180 degrees is used.

The second-order gradient is calculated as in TRANSPORT

where , the radius of curvature of the central trajectory, is measured in units of horizontal beam width (normally cm.) and = 1. is defined by