Anti-Solenoid Design

Design of CLEO-Solenoid-Compensating Anti-Solenoids

The CLEO detector solenoid field introduces coupling of the horizontal and vertical optics at the interaction region. This coupling effect has been compensated by skew quadrupoles near the IR since the beginning of CESR operation. In early spring of 2005, the reduced tune parameter observed in CESR-c operation led to consideration of a modified compensation design employing small solenoid magnets placed on either side of the IR just outside of the superconducting quads. A summary of investigations of the beam optics and dynamics which are motivating consideration of this new compensation strategy can be found here.

Calculations

Field and tracking calculations updated to match the design drawings of June, 2005. The principal change relative to earlier calculations is that the yoke diameter was increased to 7.75 inches. The total length is 114 cm and there are now conical cutouts in the endplates. The yoke barrel thickness is 2 inches. The coil carries 1.32M amp-turns. The field integral on axis is 16648 Gauss-m. The following plots show the (small) effects of reducing the endplate thickness from 2.0 to 1.75 inches on the field components and integrals and on the transfer functions (6 July 2005)

The effects of a 5-inch hole in the yoke for the helium transfer stack longitudinally offset by 3 inches on the field components and integrals and on the transfer functions (25 April 2005)

Field and tracking calculations for design which uses the coil parameters from the American Magnetics quote and the yoke iron geometry of the 1978 Janis design:

Effects of a 5-mm longitudinal offset of the yoke on the field components and integrals and on the transfer functions (21 April 2005)
Effects of a 5-mm transverse offset of the yoke on the field components and integrals and on the transfer functions (21 April 2005)

Some examples of 1.8 GeV electron trajectories (14 April 2005)
Exit angles and offsets as functions of entrance position (14 April 2005)

Some characteristics of the field for the preliminary design parameters of 25 March 2005 can be found here.

Talks

Alignment Errors and Offset Stack Model (25 April 2005)

Field Integrals and Transfer Functions (18 April 2005)
This talk mistakenly reported a 1.1% change in the field integral due to the stack hole. In fact, the stack hole does not change the field integral on axis.

The transfer matrix of a solenoid can be decomposed into two rotations on either side of a lens which focuses in both planes. The angle of rotation and the focal length may be calculated as follows. Note that the total angle of rotation is twice the value calculated here.

Transfer matrix parameters for a Solenoidal Field

The rotation angle is given by

$\Theta = K\;L = \frac{\strut B_z\;L}{\strut 2\;B\rho},$

where $B_z\;L$ is the field integral of the solenoid and $B\rho$ is the magnetic rigidity.

The focal length of the focusing in both planes is given by
$F_x = F_y = \frac{1}{\strut K \sin{K L}}$

Typical values for CESR-c are:
$B\rho = \frac{\strut P}{\strut 0.29979} = \frac{\strut 1.885}{\strut 0.29979} = 6.3 \; {\rm Tm}$

$L = 0.6 \; {\rm m}$

$B_z = 2.8 \; {\rm T}$

$B_z\;L = 1.7 \; {\rm Tm}$

$K=\frac{2.8}{12.6} = 0.23 \; {\rm m}^{-1}$

$\Theta = K\;L = 67 \; {\rm mrad} = 3.87 \; {\rm degrees}$

$F_x = F_y = \frac{1}{\strut K \sin{K L}} = 33 \; {\rm m}$

Jim Crittenden
E-mail: critten@lepp.cornell.edu
Wilson Synchrotron Laboratory
Room 212
Phone:(607) 255-4882
FAX:(607) 255-8062

Last modified 14 April 2005