Holding Field Control

This is to discuss controling holding field of Polarized He3 Target with Helmholtz coils and correction coils.

Introduction

Target Coil System in the Hall

Holding field is created by three orthognal Helmholtz coils. As shown here, the small and large coils are creating uniform magnetic field in horizontal directions and the vertical coil is for a vertical holding field. Since the fields from these three coils are orthognal to each other, a Coil System is defined.

In the configuration of Transveristy experiment, the coil system is rotated 37 degrees from the Hall System. That is small coil pointing to the right downstream of the beam and large coil to the left downstream.

Characteristics of Hoilding Field Coils

Coil Name	Radius (m)	Turns	Power Supply	I(A) for 35 G	U(V) for 35 G
Small	0.667	256	KEPCO	10	35
Large	0.758	272	KEPCO	10	35
Vertical	0.946	203	HP6675A	18	49

Coil Current Control

Vertical Coil

Vertical Coil is controlled in constant current mode by Power supply 6675A. In addition, there is a DS345 (GPIB Address 14) providing a control voltage to 6675A. Vertical coil current is baseline current set in 6675A plus a shift proportion to the control voltage.

• 6675A Baseline current is set by GPIB command CURR Base Line Current
• DS345 control voltage is set by GPIB command OFFS Control Setting

A calibration is performed on Sept 23, 2008. With Base Line Current=15A and 16A. Error is on the 0.1% level.

File:Vertical Coil Curr vs Setting.png

Calibration Data: Data Points are marked by circles and linear fitting is solid line. Red marks data with Base Line Current=15A, while blue mark Base Line Current=16A

• Base Line Current=15A Result:

     model:
       ''Control Setting''= a + b*''Coil Current''
     Coefficients (with 95% confidence bounds):
       a =      -2.652  (-2.654, -2.651)
       b =      0.1767  (0.1766, 0.1769)

• Base Line Current=16A Result:

     model:
       ''Control Setting''= a + b*''Coil Current''
     Coefficients (with 95% confidence bounds):
       a =      -2.828  (-2.831, -2.826)
       b =      0.1767  (0.1765, 0.1769)

• Further, it's reasonable to a extrapolation by assuming coefficient b in unrelated to Base Line Current:

       ''Control Setting''= 0.1767*(''Coil Current''-''Base Line Current'')

• According to vertical compass work which was done on Sep 27, to get vertical field, the currents are

     I_v = 16 A
     I_s = -0.370 A
     I_l = 0.345 A

Gradient of holding field & Correction Coils

Based on our compass measurement, we exactly know the relationship between current and direction.

for longitudinal direction:
    0.982[(0.056-0.424+I_l)/(0.101+0.291+I_s)]= tan(37.0508)
for longitudinal direction:
    0.982[(0.056-0.424+I_l)/(0.101+0.291+I_s)]= tan(127.0508)
for vertical direction:
    General Equation is
      K[(I_v + E + BB)/sqrt{R*R(I_l+beta+delta)^2 +(I_s+ alpha+gamma)^2}]
    where
      K=0.546212 +/- 0.0022 and E= 0.176966 +/- 0.0354  for BigBite is off
      K= 0.552358 +/- 0.0022 and BB= 0.500829 +/- 0.034 for BigBite is on

On the other hand we need the amplitude of combined field to be about 25 Gauss, such as

    I_l^2 + I_s^2 = 49    for in-plane case
    I_v = 14 A            for vertical case

In each case, we have 2 equations and two variables. So we can determine the currents for each direction and take them into our field mapping data, choose the one of two settings which has less gradient. To choose the gradient made by correction coil, we use a code on matlab to minimize the eigenvalue of the gradient matrix. Then use

longitudinal field

The current we use:

    current in small coil: 5.1699340 A
    current in large coil: 4.7192990 A

The gradient without correction coil: (in mG/cm)

                              dBx/dx      dBy/dy     dBz/dz       dBy/dx      dBz/dx      dBz/dy
average in pumping chamber: -6.593216   -6.993122   13.586337   -10.687164   4.486893   -0.722354
average in target chamber:  -5.022424   -16.447674   21.470098   -0.880998   -6.230476  -1.056020

The current of correction coils should be:

    current in correction coils along small coil: 5.1699340 A
    current in correction coils along large coil: 4.7192990 A