# Ultra High Precision Fluxmeters - Oldy but goody!

**From flip-coils used to measure the earth’s magnetic field in the mid 19 ^{th} century, to today's rotating-coil fluxmeters used to measure a magnet’s effect on the particle beam in the accelerator labs, fluxmeters never stopped improving, and remain a very popular method of measuring magnetic fields.**

Five years ago, the CERN launched an enormous measurement program to characterize the thousands of magnets for the Large Hadron Collider (LHC). The backbone of this program was a series of rotating-coil benches, backed by hundreds of precision digital integrators.

Such precision fluxmeters are anything but “point-and-shoot” instruments. They require thought, beautiful mechanics, and impeccable technique. At first sight, they appear to be an outdated and overly complicated measurement method. Why, then, have they remained so popular?

First, fluxmeters can be of great precision, on the order of 10^{-5}, surpassed only by NMR techniques. Next, they are extremely flexible, as the coil design can be adapted for an extremely wide range of problems: from µT to tens of T, from mm to km, homogeneous or highly non-uniform fields, stable or time-varying fields, point measurements, gradients, integrals along a path, in air or in iron. In short, given the right coil, fluxmeters can do it all.

**Basic principles**

Fluxmeters are based on Faraday’s Law of Induction, which states that the voltage induced by a coil equals the time rate of change of the included magnetic flux. Or, taking the integral: the flux change is equal to the time integral of the voltage. (Actually, by convention, it’s minus the integral.)

So, to measure the field strength in the gap of a large direct current (DC) magnet, we could move a coil from a zero-field region into the gap, all while measuring the time integral of the voltage induced by the coil. The starting flux is zero, and the voltage integral at the end gives the flux in the gap. To finish, we divide the flux by the coil area to give flux density. This is the principle of a moving-coil measurement.

**Mapping is built in**

Even better: if we record the partial voltage integrals at regular intervals, we automatically get a map of the field along the path of the coil. The entire field map can be generated in a single, continuous movement. And as we mentioned, special coil designs can directly measure the field integral – or gradient – along another axis. Depending on the problem, field mapping with a fluxmeter can be orders of magnitude faster than other techniques.

The basic elements required for a fluxmeter mapping system are:

- coil;
- positioning jig;
- integrator with the ability to record partial integrals;
- temperature control to minimize thermal expansion of the coil;
- coil area calibration, usually an NMR-controlled reference magnet.

**Key progress in the integrators**

Evidently, all these elements have evolved since the 19^{th} century, but the greatest improvements lie with the integrators. The first major step was the transition to analog electronics, particularly op-amp based integrators. However, these have limited bandwidth, are subject to many different noise sources, and still require a digitizer.

Another approach converts the input voltage to a frequency, which is then measured with a high-precision counter. Inherently digital and with outstanding precision, this design – also used in Metrolab’s PDI5025 – has been the champion amongst precision integrators for the last 20 years. Its main limitation is the frequency range of the voltage-to-frequency converter (VFC), requiring relatively long integration times – at least on the order of a millisecond.

A third, more brute force approach is to digitize the input voltage and to compute the integral numerically. This approach depends critically on the performance of the analog digital converter (ADC): range, resolution, speed, linearity, noise – every conceivable ADC parameter influences the integrator performance.

**Leveraging latest CERN developments**

CERN and the University of Sannio have recently developed a new high-speed, high-precision integrator, based on the ADC approach. Coupled with a new high-speed rotating coil system, its purpose is to study dynamic effects such as eddy currents and the decay/snapback phenomena observed when ramping superconducting magnets.

The principle is simple, the implementation everything but. In addition to amplifying and digitizing the input voltage with great precision, the instrument must measure time very accurately. A high-resolution clock synchronizes the ADC with the arrival of trigger pulses, and a digital signal processor (DSP) interpolates the ADC values to determine the exact voltage at the time of the trigger. With the following ADC values, the DSP then computes a trapezoidal approximation of the integral until the next trigger. These partial integrals are output continuously on a PCI bus, interfaced directly to a computer.

The design has been licensed by Metrolab and will be commercialized as the Fast Digital Integrator FDI5026. Compared to the PDI5025, the FDI5026 offers 100x faster trigger rate and 100x better resolution, making it the new world champion amongst precision integrators.