Raster Correction

Procedure

To avoid burning the CH$_2$ target, beam will be rastered 5mm$\times$5mm on the target. A direct reconstruction with matrices obtained for point target gives much worse resolution, for example, the $\delta p$ resolution for HKS is $1.16\times10^{-4}$(rms) without raster, it becomes $6.64\times10^{-4}$ with 5mm$\times$5mm raster.

To do raster correction, the beam positions on target need to be determined by raster magnets X and Y current event by event. For rastered beam, The reconstructed target quantities can be expressed as functions of focal plane quantities and beam positions at target. It can be written as, for example:

$$\delta p = f(xfp, xpfp, yfp, ypfp)+g(xtar, ytar)$$

The raster correction function $g$ depends only on beam position. It can be fitted from nominal Raytrace data card. Even if the actual optics of the spectrometer system may deviate from the nominal data card, its effect on raster correction function $g$ is small so we can still use the nominal function (fig.1 and fig.2).

Figure 1: Comparison of Enge momentum(up) and angle(down) reconstruction resolution with rastered beam,with and without raster correction. Both resolutions are shown when the correction function $g$ fitted as a 3-order and 4-order polynomials. The rightmost point is the resolution after raster correction with wrong Enge optics.

Figure 2: Comparison of HKS momentum reconstruction resolution with rastered beam,with and without raster correction.

Code

Under directory jlabs1:/home/yuan/HKS/optics/:

• .matrixfit/matfit6_backward.f: Fortran program to fit target quantities as a function of focal plane quantities and beam position in the form of the above equation. It fits function $g$ as a 3-order polynomial of beam position. Need Raytrace simulation output as input data.

• .matrixfit/expon_rastercor.dat: input data file specifying the power of polynomial terms in functions $f$ and $g$.