Andreas Krämer, GSI Darmstadt 1

Problems of Measuring Magnetic Permeabilityof Vacuum Chambers

Requirements:

For all FAIR magnet vacuum chambers a relative magnetic permeability of

µµµµr≤1.005 (µµµµr≤1.01)

at room temperature under a magnetic field of H=80kA/m (equivalent to B=1T) is required.

Measuring Equipment:

Non-destructive testing with fluxgate-magnetometer (Foerster probe)

Andreas Krämer, GSI Darmstadt 2

Commercial Devices for Measurement of relative magnetic permeability

used at GSI in magnet testing

price ~18000 DM (1998)

lowest measuring range is 1 - µr= 0.03 full scale

Foerster MAGNETOSCOP ® 1.069

Measurement of material permeability in the range of µ = 1.001 to 2.00.

Measurement precision: 5%-10%

µr=1.000-1.001, resolution: 0.00001

µr=1.000-1.010, resolution: 0.00001 used at CERN and Forschungszentrum Jülich

price: 8500 €

Foerster MAGNETOSCOP ® 1.068

Andreas Krämer, GSI Darmstadt 3

Commercial Devices for Measurement of relative magnetic permeability

price ~2000€

measuring range: µr = 1.001 to 1.999Resolution: 0.001

Accuracy of calibration @20°C: (1-µ)x5%, ref. to NPL calibration standards

Permeability Meter FERROMASTER (Stefan Mayer Instruments, Germany)

Andreas Krämer, GSI Darmstadt 4

Criteria of Good Measuring Equipment

• There is no ‘good measuring instrument’– it can only be good enough!

• This is determined in comparison to the

tolerance T := Tmax – Tmin to be controlled

Andreas Krämer, GSI Darmstadt 5

Criteria of Capable Measuring Instruments

• Quality of measuring equipment is determined in

comparison to the tolerance T to be controlled

• Resolution must be ≤ T/20

• Accuracy := closeness of agreement between measured value and true value. Accuracy, however, can never be better than

trueness.

• Trueness := closeness of agreement between the

average of an infinite number of replicate

measurements and a reference value.

Trueness, however, can never be better than precision.

• Precision := closeness between indications obtained by replicate measurements of the same

objects. Precision must be small compared to T.

Andreas Krämer, GSI Darmstadt 6

1. Collect enough sample objects for covering the measuring range you are interested in

(≥ 30 different measuring points (MP) are required!).

2. Mark each MP so it can be identified unambiguously (e.g. by a serial #).

3. Measure each MP once. Record the MP-specific readings.

4. Measure each MP once again in another sequence, without looking at the 1st

readings. Record the MP-specific readings.

5. Plot the points and evaluate

a. Use the same scaling for both x (1st reading) and y (2nd reading).

b. Plot the points – one for each pair of measurements (belonging to one MP).

c. Draw the central line.

d. Find the second furthest point from the central line. Put the first limit line through

this point

e. and parallel to the average line.

f. Draw the second limit line equidistant from the central line.

g. Measure the distance between both limit lines.

How to Measure the Precision of the Instrument?

Andreas Krämer, GSI Darmstadt 7

The band contains 28.5/30 = 95% of all points measured.On the other hand, the 95% confidence interval for the center line of 30 points is ±���;�.�� ∙ �� ≈ ±2.045��

⇒ �� ≈�

�Δ�

If the width of the 99% confidence interval around the center line fits five to six

times in the given tolerance band the world is fine.2

⇒ � ≥ 5.5 ∙ 2 ∙ ���;�.�� ∙ �� ≈ 30�� ≈ 7.5Δ or

� ≥ ±15��

1 tn;p is the cumulated distribution function of Student’s t .

2 e.g. E. Dietrich und A. Schulze: Eignungsnachweis von Prüfprozessen; Carl Hanser, München und Wien, 20073

Is the Instrument Capable to Control a Tolerance Band Specified?

Andreas Krämer, GSI Darmstadt 8

A ‚Real Life‘ Case: Foerster Magnetoscop 1.068

1.005 1.010 1.015 1.020 1.025 1.030

smallest measurable tolerance TMin must be ±2.5 for measurement of µµµµr≤1.005

Andreas Krämer, GSI Darmstadt 9

A ‚Real Life‘ Case: Foerster Magnetoscop 1.069

1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1

smallest measurable tolerance TMin must be ±25 for measurement of µµµµr≤1.005

Andreas Krämer, GSI Darmstadt 10

A ‚Real Life‘ Case: Foerster Magnetoscop 1.069

1.005 1.010 1.015 1.020 1.025

smallest measurable tolerance TMin must be ±25 for measurement of µµµµr≤1.005

Andreas Krämer, GSI Darmstadt 11

• FERROMASTER features insufficient resolution for our application (and

more).

• Foerster MAGNETOSCOP® 1.068 shows excess zero variation. Even if zero

could be stabilized, its precision is insufficient for our application.

• Precision and stability of Foerster MAGNETOSCOP® 1.069 allow for

controlling a tolerance band of 1.000 ≤ µrel ≤ 1.010 .

• No mobile scientific instrument is known so far allowing for controlling

1.000 ≤ µrel ≤ 1.005 .

• Calibration was not required for these tests – it will not affect the results either.

• The method demonstrated allows for quick and easy qualification of arbitrarymeasuring equipment on site. Pencil, ruler, and quadrille paper will do.

Summary

Andreas Krämer, GSI Darmstadt 12

• How is the Foerster Probe used in other labs?

• All measurements shown were done under ‘ideal‘ conditions (use of a tripod to align probe on sample). How to deal with this in lab/workshop (probe very

sensitive to orientation in earth magnetic field & to other stray fields)

• Materials to be measured with permeability probes should be thicker than

approximately 8 mm when-ever possible. Accurate measurements of

materials that are thinner than 8 mm may be possible by stacking two pieces but the air gap between the two pieces must be as small as possible.

The flat area on which the permeability probe is placed must not be less than

approximately 20 mm in diameter. When testing on curved surfaces the radius of curvature must not be less

than approximately 40 mm. If any of the required dimensions are less than

those specified, the instrument will indicate permeability less than the actual

value. Most vacuum chambers have smaller wall thickness! How to compensate that?

Open Questions