# Magnetic Measurements during Production of VLHC Low Field Combined Function Magnets

For this study we focus discussion on magnetic field measurements of the
combined function magnets during production. No doubt measurements of
other magnetic elements of the ring are necessary. One would also expect
to perform an extensive series of measurements, possibly using several
measurement techniques, during R&D. Here, however, we have chosen to
present one concept for measurements of production magnets which
utilizes a rotating probe of specific design[^1], try to define the most
important issues related to this concept, and examine the consequences.
Thereafter, a brief discussion of other approaches.

Main parameters of the combined function magnets are 2 T field, ≤10%
horizontal gradient, 65 m length, and 20 mm gap. Measurement of the
integrated dipole field is needed with an accuracy of a few parts in
10^4^. Desired measurement accuracy for the higher order harmonics is
0.1 units.[^2] This implies the horizontal gradient is known relative to
the main field to a part in 10^5^; other harmonics (of order 1 unit), to
10%. We begin by examining the implications of requirements for field
strength measurements. Based on this discussion we present a concept for
a measurement system. Given this system we then address the issue of
measurement of field harmonics.

With respect to measurement of the integrated field strength, there are
two issues. Since the accuracy of the strength is given by

$$\frac{{DB}_{1}}{B_{1}} = \frac{DR}{R}$$

where R is the radius of the probe.[^3] This requires that the probe
radius (actually the radius of the coil winding) be known with high
accuracy. Since manufacturing and mechanical measurement accuracy are
fixed, ∆*R* is fixed. As the radius of the probe becomes smaller, these
tolerances become an issue. The following table illustrates the problem.

![](media/image1.wmf)

Typical manufacturing and measurement accuracy achieved for magnetic
measurements is 1 mil (0.001in, 0.025 m. For a probe of 10 mm maximum
radius, this is inadequate. Calibration of the probe with at least an
order of magnitude greater precision (3e-4 strength error) is thus
required. This level of precision can only be achieved using a
calibration magnet in which the strength is known at least as well as
one desires to know it in the subject magnets.[^4] The second issue is
unique to measurement of combined function magnets. Due to the
horizontal field gradient, an error in the horizontal position of the
probe translates into an error in measured field strength. In a magnet
with 10% gradient, measurement of the strength to 1 part in 10^4^
requires positioning the probe with 1 mm accuracy (see table).

![](media/image2.wmf)

Although it may be difficult, this can be achieved using mechanical
means. Vertical placement of the probe is not as critical as long as the
good field region is significantly larger than the probe.

The main conclusions from the preceding discussion are that (1) a
rotating coil of the size we are considering can be calibrated with
sufficient precision, and (2) that the horizontal position of the probe
can be set with mechanical fixtures. For reasons we list below, we
choose to insert the rotating probe into the aperture from the side
rather than from the end. The probe is supported on a frame attached to
the magnet as shown in Fig. 1-3. Principle elements of the design are
the following.

-   The probe body is clamped to a precisely machined strong-back on an
    edge which describes the magnet sagitta.

-   The strong-back is slides horizontally in a series of jaws attached
    to the vertical member of the frame. The strong-back is spring
    loaded so that it and the probe are forced against the referenced
    surface on the inner edge of the magnet aperture.

-   The vertical position of the probe is defined by the precision with
    which the frame is attached to the magnet and the precision of the
    jaws relative to the vertical member of the frame and the horizontal
    surfaces of the strong-back.

-   The motor for rotation and encoder for probe angle readout are
    mounted on the frame and connected to the probe by a mechanism such
    as a toothed belt or right angle drive. Other drive components would
    be similarly mounted (e.g. gearboxes). A tilt sensor is mounted on
    the strong back to allow correction of the probe angle.

-   Development of slip rings small enough to fit the probe bore is
    assumed although one might choose to digitize and transmit the
    signals from inside the bore. A pre-amplifier circuit sized to fit
    the bore is also assumed allowing a boost in signal size of up to
    1000.

![](media/image3.wmf){width="3.4930555555555554in" height="4.78125in"}

Figure 1: Measurement Fixture

![](media/image4.wmf)

Figure 2: Probe and Strong-Back

![](media/image5.png){width="4.103472222222222in"
height="2.8041666666666667in"}

Figure 3: Probe Assembly

A consequence of insertion from the side is that one loses a few extra
mm of probe radius due to the reduction in gap at the magnet edge of the
focusing quad. The following allocation of real estate is made in
arriving at a more or less realistic probe radius.

  ---------------------------------------------------------- ------------
  horizontal aperture at beam line                           20 mm

  horizontal aperture at gap edge                            18 mm

  clearance                                                  1 mm

  lost to clamp clamping probe to strong-back                2 mm

  probe diameter                                             15 mm
  ---------------------------------------------------------- ------------

Given a probe radius, we need to examine the accuracy of the measurement
of field harmonics. From \[1\] we see that probe calibration matters
little in measuring harmonics. Accuracy of 10% or so is adequate. (I.e.
If the harmonic is 1 unit; you don't care if it is 0.9 or 1.1.) This is
probably true even of the gradient although it needs to be considered.
What is of greater interest is the evaluation of the interplay of signal
size with harmonic measurement. This has implications for the required
level of excitation current during test. Field measurements of model
magnets made during the R&D stage of the LHC IR quadrupole programs
indicate that that for harmonics above n=13 or 14, uncertainty from
measurements dominate the random errors \[2\]. The same measurements
also show good agreement between the measured and design values of the
allowed harmonic b~14~ (-0.01 unit). From these observations one can
infer a specific signal size which is adequate but below which
measurements are difficult. We use this level (12 uV) to calculate a
required excitation level for measurement of the transmission line
magnets. We use the probe parameters in the table below.

  --------------------------------------------------- -------------------
  probe radius                                        7.5 mm

  length                                              6.5 m

  number of turns                                     1

  angular rotation period                             3 s

  tangential winding opening angle                    13°

  transfer function                                   2T/100kA
  --------------------------------------------------- -------------------

Sensitivity as a function of harmonic number is shown in Fig. 4. The
sensitivity versus harmonic number is a function of the opening angle
and the ratio of probe to reference radius. In particular, if R~ref~ \>
R~coil~, the sensitivity falls with increasing harmonic number. For
R~ref~=18 mm, the sensitivity is down by a factor of 10 through n=11.
One may assume pre-amplifiers with a reasonable gain may be inserted in
the probe bore. With a gain of 100, measurement accuracy of 0.1 unit
through n=11 requires 200 A excitation current. This should be possible
for room temperature measurements.

![](media/image6.wmf)

Figure 4 Sensitivity

A probe length of 6.5 m was assumed above. Ten measurements are then
required to construct the integral field. The time required for
measurement of a production magnet is estimated in the following
table.[^5] Two crews of 3 technicians are assumed; each works one
aperture. Four sets of measurement apparatus are assumed (2/side) so 1
can be set up while the other measures.

  ------------------------- ---------------------------------------------
  measurement setup         15 min.

  data acquisition          100 rotations x 3 s./rotation=5 min. \< 15
                            min. for setup

  time/location             15 min. + 5 at the last station

  locations/aperture        10

  #probes/aperture          2

  total/aperture            155 min./aperture

  total                     155 (2 hr. 35 min.)
  ------------------------- ---------------------------------------------

This certainly allows for the required production throughput. Apparatus
and procedures would be optimized to minimize this time during
production.

We have chosen a probe inserted in the magnet bore from the side and
supported by an external frame. An alternative approach would be a
\"mole\", such as have been developed for measurements of SSC \[3\] and
LHC magnets \[4,5\] which are probes with drive and angular alignment
systems built in. The LHC apparatus includes both warm and cold moles
for a magnet bore of 70 mm. There are some advantages to this approach.
There is no external frame. The probe is inserted at one end and pulled
through the magnet. The probe can presumably be larger as it doesn\'t
have to be inserted through the narrow gap at the outer edge of the
bore. As was discussed above, sensitivity increases with probe radius
(depending on the reference radius). The effects of imperfections in
manufacturing or motion are also damped by some factor scaling with
radius. Development of the necessary apparatus of the size necessary for
a mole that can operate in a strong magnetic field is not trivial. The
LHC apparatus would have to be scaled down by a factor of 3.5 or more.
We have no doubt that it could be done. However, we have chosen to
remove the active elements of the measurement system from the bore. The
only pieces in the bore are slip rings and pre-amplifiers. This seems
like a less daunting task.

# References

\[1\] P. Schlabach, \"Effect of Probe Manufacturing Errors on Field
Measurements\", TD-98-060, 1998.

\[2\] P. Schlabach, \" Field Errors of HGG Model Magnets,\" TD-00-052,
2000.

\[3\] G. Ganetis., et. al., \"Field Measuring Probe for SSC Magnets\",
Particle Accelerator Conference, 1987.

\[4\] L. Bottura, et. al., \"A Mole for Warm Magnetic and Optical
Measurements of LHC Dipoles\", Eleventh International Magnet Measurement
Workshop, 1999.

\[5\] L. Walkiers, \"Measurements for the Acceptance Tests of the LHC
Superconducting Magnets\', Eleventh International Magnet Measurement
Workshop, 1999.

[^1]: For this exercise, we specify a probe has windings of dipole and
    quadrupole symmetry sensitive to n=1, 3, 5, ... and n=2, 6, 10,
    14... respectively as well as a tangential winding with sensitivity
    to all harmonics. The opening angle of the tangential winding is
    13°. This also allows for bucking the harmonic signal.

[^2]: One unit is 10^4^ • the harmonic normalized to the main field.

[^3]: Additional details can be found in \[1\]. We also remark that what
    is said here about probe radius is also true of probe length. Length
    is typically much greater than radius so a fixed manufacturing or
    measurement error matters little.

[^4]: Note that this problem could be separated into two separate
    requirements: (1) absolute accuracy of a single probe and (2)
    relative accuracy between a set of probes that might be used in
    production measurements. The former is an error relative to overall
    design energy; the latter, a more or less random error magnet to
    magnet or, more likely, magnet section to magnet section. We choose
    not to differentiate the two.

[^5]: The goal of this exercise is only to demonstrate that the required
    time is reasonable.