History: BigBite Optics

!Magnetic Midplane Model

BigBite optics are handled using a very simple model we call a "magneti midplane model". All interaction is treated at a single point on the midplane of the BigBite magnet. No change in the non-dispersive direction is assumed. With these assumptions, one can then trace a track back to a unique point on the midplane and along the beam. This fully describes the track as it was leaving the target.

!!Vertex Reconstruction

First order corrections are made to the vertex based upon calibration to carbon foil data. The carbon foils allow us to identify fixed points along the beamline. First order corrections are applied:

::v_z = c_0*v0 + c_x*B.tr.x + c_x'*B.tr.xp + c_y*B.tr.y + c_y'*B.tr.yp::

Where v0 is the naive point found by assuming no change of the track in the nondispersive direction. B.tr.x, B.tr.y are the x and y positions on the detector z = 0 plane (in detector coordinates in meters). B.tr.xp, B.tr.yp are the tanget values of the track in detector coordinates, x' and y'.

!!Momentum Reconstruction

Momentum reconstruction is determined by a simple dipole model with (effectively) first order corrections. Elastic events on a hydrogen target is used for calibration.

::p = (c0 + c_bendx*B.tr.bendx)/B.tr.defang + c_theta*atan(B.tr.fT.xp) + c_y*B.tr.y + c_y'*B.tr.yp::

Where B.tr.bendx is the vertical position on the magnetic midplane (in meters in detector coordinates), B.tr.fT.xp is the x tanget in the TARGET coordinate system. B.tr.y and B.tr.yp are the same y and y' variables in the vertex reconstruction.

Using hydrogen data, one is able to determine the scattered electron momentum from an elastic event soley from the scattering angle (given that the beam energy is known). This is given from the equation:

::p = (m_p * E_beam)/(m_p + E_beam*(1.0 - B.tr.pz/B.tr.p))::

where m_p is the mass of the proton (938MeV), E_beam is the beam energy, B.tr.pz is the z component of the scattered electron momentum in LAB coordinates and B.tr.p is the momentum of the electron. While B.tr.p and B.tr.pz are not well calibrated, the ratio is well defined and momentum independent (assuming the momentum B.tr.p is non-zero). This ratio is equivalent to cos(theta_e) where theta_e is the scattering angle.

!Extended optics

It has been seen that this model obviously fails at the extreme vertical positions of the magnet for both the vertex and momentum reconstruction. In an attempt to handle this a new class (called THaBBOptics) was written to provide position dependent corrections or coefficients for the reconstruction.

The positions that these are dependent on is the horizontal and vertical position at the magnetic midplane (B.tr.bendx and B.tr.bendy in the ROOT output). Independent calibrations for each solid angle "bin" are done as described below. To provide a smooth map, a bilinear interpolation method is used between the points on the grid.

The database description can be found here [http://hallaweb.jlab.org/experiment/E02-013/offline/BBoptics.txt|here].

!!Vertex

An additional correction to v_z is done:

::v_z += correction(bend_x, bend_y)::

!!Momentum

All 5 coefficients are interpolated based upon the magnetic midplane position. They in theory have the dependence c(bend_x, bend_y). In practice it is useful to remove some of this freedom to stabilize fitting. For example, the bend_x coefficient is not allowed to vary over bend_x.

!Calibration

Attached are calibration scripts. They require a few parameters to be adjusted and things such as a path to the ROOT files needs to be added, so they will not run on their own. They provide a framework that has been used to do calibrations in the past. There is a number of defined values that are required and can be found in a mwdc_defs.h header. (See ((BigBite Analysis Scripts|BigBite Analysis Scripts)) for a copy)

The vertex calibration is done by allowing just an offset to the applied.

The momentum calibration is done as described above, by allowing all coefficients to vary over the face of the magnet.

The low statistics calibration is done by just allowing the leading coefficient to vary over the face of the magnet. It requires that the rest of the coefficients already have reasonable values and that the fitting in the good central region is already done. It works by creating a histogram of the c0 value that would be necessary to give a momentum identical to pex(theta_e) for each magnet x,y bin and the appropriate c0 value is the value of the maximum bin of that histogram.