MM's    Gen-Picture Gallery   Version II

Contents

The Acceptance

The Virtual Image

The Vertical Beam Offset

The Reconstruction

Including the Beam Offset
and the Target Magnetic Field

The Kinematics

The Acceptance

The accepted angles (dx/dz and dy/dz) are determined by the octogon-shaped entrance-window of HMS. The target field introduces a shift to smaller values of dx/dz and tilts the octagon of accepted angles slightly. The figure on the right shows this effect for the Q2=0.5 kinematic and a point target.  Similar plots for all the kinematics studied are shown on this viewgraph (.ps).

The figure on the left pictures where the electrons are lost inside HMS for the Q2=0.5 kinematic and an extended target(length: 3cm, width and heigth: 2cm). The color shows the momentum displacement (delta) of the particles lost.  The same plots are also available in higher resolution for the four kinematics measured, namely  Q2=0.5 (.ps),  Q2=1.0 (.ps),  Q2=1.5 (.ps) and  Q2=1.86 (.ps).

The Virtual Image

The figure on the right shows the deviation  (x0-x, y0-y) of the virtual points from their corresponding interaction points  (x0,y0) at  Q2=0.5.  for a couple of discrete points (x0,y0) distributed over the target face covered by the beam raster. As the simulation includes the whole phase space accepted by HMS we get a cloud of virtual points for a single interaction point.    Similar plots for all kinematics studied are shown on this viewgraph (.ps)

The influence of a vertical beam offset on the y difference is rather big, the y shift ranges from -1mm to 1mm for x₀=[-1cm,1cm] at Q²=0.5 and about half the value at higher Q²'s.
 

The Vertical Beam Offset

The effect of the vertiacl beam offset was studied without the target magnetic field. For HMS moving the electron beam up or down looks like a shift in delta, the relative momentum displacement.
 
 

The figure on the right shows the shift of the the focal plane coordinate xFP as a function of the vertical beam displacement  x0 for a couple of discrete delta values in the range -6% to 6% (and with dx0/dz and dy0/dz = 0). A beam offset of  x0 =1cm, if not corrected for,  would introduce an error of about 1% in the delta reconstruction.  As the dependence of xFP from x0 looks pretty linear, it should be possible to apply a correction - based on a few callibration measurements - to the focal plane xFP measured to compensate the effect of the vertical beam offset.

 

There is a similar effect on the focal plane dxFP/dz as shown in the figure on the left.  The influence on the focal plane yFP and dyFP/dz is only minor and can be neglected  The two plots are combined on a single viewgraph (.ps)

 

The Reconstruction

The methode of correcting the measured focal plane quantities according to the vertical beam offset has the main advanage that we can use the standard HMS reconstruction function with full symmetrie and all the knowledge therein to find the target coordinates.
 

The figure on the right visualizes the coefficients Aijkl for the delta reconstruction. The value of delta is calucalated from the (corrected) focal plane quantities as the  SUMijkl(Aijkl . xi . (dx/dz)j . yk . (dy/dz)l ).  In order to show the most imported coefficients the Aijkl are weighted with the maximum range of the focal plane quantities to the power of i, j, k and l, respectively.  To get the ijkl indices you have to combine the numbers in the axis labels addressing one Aijkl  square.

There are also full size viewgraphs for all the quantities being reconstructed, namely
delta (.ps), dx/dz (.ps), y (.ps) and dy/dz (.ps).

 
The Reconstruction Including the Vertical Beam Offset
The methode how to treat the vertical beam offset is outlined on the program page. To test the quality of this methode a simulation was made covering the whole phase space accepted by HMS and the whole target volume (length 3cm, width and heigth 2cm). Then the resolution was determined by comparing the  target coordinates reconstructed from this sample with the original ones.

The figure on the right shows that we can obtain a resolution of about 0.1% (FWHM) in the delta reconstruction. The tail to the left ist mostly due to events at the edge of the accepted phase space with a delta below -12% and low values of dx0/dz (cf. detailed viewgraph (.ps)).

 

The figure on the left shows that we can obtain a resolution of about 0.1o (FWHM) in the dx/dz reconstruction. Again the tail to the left ist mostly due to events at the edge of the accepted phase space with a delta below -12% and low values of dx0/dz (cf. detailed viewgraph (.ps)).

 

The figure on the right shows that we can obtain a resolution of about 2mm (FWHM) in the y reconstruction.

 

The figure on the left shows that we can obtain a resolution of about 0.02o (FWHM) in the dy/dz reconstruction.

 
The four plots shown above are combined on a single viewgraph (.ps). More details can be found on viewgraphs showing the resolution for delta (.ps), dx/dz (.ps), y (.ps), dy/dz (.ps) as a function of the different target coordinates.
 

The Reconstruction Including the Vertical Beam Offset and the Target Magnetic Field

The methode how to treat the target magnetic field is outlined on the program page. To test the quality of this methode a simulation was made covering the whole phase space accepted by HMS and the whole target volume (length 3cm, width and heigth 2cm) for the four relevant kinematics as shown in the table above. Then the resolution was determined by comparing the  target coordinates reconstructed from this sample with the original ones.

The figure on the right shows that we can obtain a resolution of about 0.1% (FWHM) in the delta reconstruction (Q2=0.5). The tail to the left ist mostly due to events at the edge of the accepted phase space with a delta below -12% and low values of dx0/dz (cf. detailed viewgraph (.ps)).

 

The figure on the left shows that we can obtain a resolution of about 0.2o (FWHM) in the dx/dz reconstruction (Q2=0.5). Again the tail to the left ist mostly due to events at the edge of the accepted phase space with a delta below -12% and low values of dx0/dz (cf. detailed viewgraph (.ps)).

 

The figure on the right shows that we can obtain a resolution of about 2mm (FWHM) in the y reconstruction (Q2=0.5).

 

The figure on the left shows that we can obtain a resolution of about 0.04o (FWHM) in the dy/dz reconstruction (Q2=0.5).

 

The figure on the right shows that we can obtain a resolution of about 0.1mm (FWHM) in the x reconstruction (Q2=0.5). This small value does not surprise because x0-x1 is the convergence criteria for the iteration process.

 

The figure on the left shows that we can obtain a resolution of about 5mm (FWHM) in the z reconstruction (Q2=0.5).

 
The six plots shown above and similar ones for the other values of Q² combined on single viewgraphs are also available and even more details can be found on viewgraphs showing the resolution for delta, dx/dz, y , dy/dz, x and z as a function of the different target coordinates:
 

	Q2=0.5	Q2=1.0	Q2=1.5	Q2=1.86
Summary	viewgraph (.ps)	viewgraph (.ps)	viewgraph (.ps)	viewgraph (.ps)
Details	delta (.ps)	delta (.ps	delta (.ps	delta (.ps
	dx/dz (.ps)	dx/dz (.ps)	dx/dz (.ps)	dx/dz (.ps)
	y (.ps)	y (.ps)	y (.ps)	y (.ps)
	dy/dz (.ps)	dy/dz (.ps)	dy/dz (.ps)	dy/dz (.ps)
	x (.ps)	x (.ps)	x (.ps)	x (.ps)
	z (.ps)	z (.ps)	z (.ps)	z (.ps)