MD1 and MD2

Using the EPICS control system, NMR readings for MD1 and MD2 were taken at evenly space intervals of current over the range 250A to 450A. The range of DAC values for which the NMR would lock onto the field was also determined. This data is presented in Tables 1 and 2. (The NMR DAC value given is the average of its range.)

Data was taken both in the direction of increasing current and in the direction of decreasing current to determine the extent of hysteresis in the dipoles. Though small, hysteresis was noticeable, with $\Delta$B as high as 12G for MD1 and 15G for MD2 (see Figures 1 and 2).

Quadratic fits were calculated for sets of data taken in both the direction of increasing current, and the direction of decreasing current. The fit for the data taken in the direction of increasing current was favoured because it was found to deviate less from the data. The average absolute error for this set of data was 0.005% for MD1 and 0.006% for MD2, as compared to 0.03% and 0.02% for the data taken in the direction of decreasing current (see Figures 3 and 4).

The data was fit in two separate ways - first, the magnetic field was fit as a function of the setpoint current, and then, the current was fit as a function of the field. These fits are given below:

$$B_{MD1} = 13.5 + 12.1 I - 0.000433 I^2$$ (1)

$$I_{MD1} = -1.01 + 0.0825 B - 2.64\times10^{-7} B^2$$ (2)

$$B_{MD2} = -0.983 + 16.8 I - 0.000521 I^2$$ (3)

$$I_{MD2} = 0.140 + 0.0595 B + 1.18\times10^{-7} B^2$$ (4)

The percentage error given in Figures 3 and 4 was calculated according to Eq. 5. Absolute error was calculated by taking the absolute value of the difference between the measured and fitted values.

$$\% \mbox{ Error} = \frac{(\mbox{Measured Value - Fitted Value})}{\mbox{Measured Value}}$$ (5)

Table 1: MD1 magnetic field as a function of setpoint current.

Current I (A)	Field B (Gauss)	NMR DAC	% Error in Fit
250	3012.7	3.161	-0.001
275	3309.9	3.452	0.007
300	3606.1	3.720	0.001
325	3901.5	3.974	-0.011
350	4197.0	4.258	-0.006
375	4492.1	4.575	0.002
400	4786.6	4.894	0.007
425	5080.3	5.394	0.007
450	5372.7	6.116	-0.007
425	5087.3	5.407	-0.029
400	4794.2	4.916	0.038
375	4504.1	4.584	-0.013
350	4208.9	4.268	0.005
325	3912.3	3.997	-0.021
300	3614.6	3.717	-0.036
275	3316.4	3.458	-0.018
250	3017.7	3.171	0.042

Table 2: MD2 magnetic field as a function of setpoint current.

Current I (A)	Field B (Gauss)	NMR DAC	% Error in Fit
250	4164.4	1.713	0.015
275	4576.1	2.262	-0.013
300	4988.6	2.713	-0.006
325	5400.3	3.065	-0.004
350	5811.6	3.336	0.003
375	6222.1	3.555	0.006
400	6631.5	3.752	0.002
425	7040.6	3.993	0.004
450	7448.3	4.100	-0.005
425	7048.4	3.929	0.017
400	6644.0	3.759	0.025
375	6236.5	3.568	0.015
350	5826.6	3.342	-0.006
325	5415.3	3.078	-0.022
300	5002.8	2.742	-0.026
275	4589.4	2.284	-0.011
250	4175.2	1.726	0.034

Figure 1: Extent of hysteresis in MD1.

Figure 2: Extent of hysteresis in MD2.

Figure 3: Percentage error in fit for data from MD1 taken in the direction of increasing current.

Figure 4: Percentage error in fit for data from MD2 taken in the direction of increasing current.