# Mapping

• A Lakeshore Hall probe was used for the mapping measurements. The probe has a linearity error as a function of magnetic field which was measured by the company ( Table of data). This linearity error is different for positive and negative field directions. In the data table, the Error = abs(Measured Field)-abs(True Field). So for positive fields True Field = Measured Field - Error. For negative fields True Field = Measured filed + Error.
• Document and plots about mapping of B versus I at center of HB bore and the fringe fields in the beam region.
• Measurements of B at bore center versus I when ramping magnet from 0 to +3900 and back to 0. Then switch polarity and ramp from 0 to -3900 and back to zero.
• plot of absolute difference between B when ramping magnet up and down versus I when going to +3900 and -3900.
• plot of relative difference between B when ramping magnet up and down versus I when going to +3900 and -3900.
• Plot of difference in B between ramping up to +3900 and ramping up to -3900 versus current.
• When ramping to negative currents there was a trip at I= -3139A. Plot of difference between first ramp to -3139A and the second.
• Document and plots about mapping Of B versus z for five different x,y locations (center,top,bottomleft and right) for I = 2000, 3000, 3500 and 3900A.
• Presentation on the harmonic analysis of the HB using field measurements at radius of 5.9cm at center of magnet at currents of -1200,-2000,-3000,-3500,-3900 and +3900.

# Sensitivity of scattering angle to HB central field setting

• The distance, d1, from the targe center to the magnetic entrance of the HB is 138.4cm.
• The effective length, d2, of the HB is nominally 75cm. This is presently used in COSY . Need to update using mapping data.
• The distance, d3, from the magnetic exit of the HB to he sieve is 40cm.
• The horizontal angle and position relative to the central ray are y and yp. Delta = 100*(p-pcentral)/pcentral .
• At HB magentic entrance, yp_ent=yp_tar and y_ent(cm) =y_tar(cm) + d1*yp_tar(radians)
• For the HB, the transport of yp and y only depends on delta and delta^2 terms.
• yp_exit (mr) = -0.52*delta + 0.0052*delta^2 + yp_ent(mr)
• y_exit (cm) = -0.019*delta + 0.00019*delta^2 + (d1+d2)*yp_tar(radians) + y_tar(cm)
• y_sieve (cm) = y_exit + d3*yp_exit(radians)
• To make it through y_sieve = 0 with y_tar = 0
• y_exit = -d3*(-0.52*delta + 0.0052*delta^2 + yp_tar(mr))
• (d1+d2+d3)*yp_tar(mr) = (0.019+0.52*d3)*delta - (0.00019+0.0052*d3)*delta^2
• yp_tar (mr) = 0.153*delta - 0.00153*delta^2 .
• So delta = 6.5% gives yp_tar = 1 mr.