Magnetometric Mapping of Superconducting RF Cavities

A scalable mapping system for superconducting RF cavities is presented. Currently, it combines local temperature measurement with 3D magnetic field mapping along the outer surface of the resonator. This allows for the observation of dynamic effects that have an impact on the superconducting properties of a cavity, such as the normal to superconducting phase transition or a quench. The system was developed for a single cell 1.3 GHz TESLA-type cavity, but can be easily adopted to arbitrary other cavity types. A data acquisition rate of 500 Hz for all channels simultaneously (i.e.2ms) acquisition time for a complete map) and a magnetic field resolution of currently up to 14 mA/m/mu0 = 17 nT has been implemented. While temperature mapping is a well known technique in SRF research, the integration of magnetic field mapping opens the possibility of detailed studies of trapped magnetic flux and its impact on the surface resistance. It is shown that magnetic field sensors based on the anisotropic magnetoresistance (AMR) effect can be used in the cryogenic environment with improved sensitivity compared to room temperature. Furthermore, examples of first successful combined temperature and magnetic-field maps are presented.


I. INTRODUCTION
Superconducting radio-frequency (SRF) cavities are enabling components of many modern particle accelerators from spallation lasers. As CW applications become more and more important, and repetition rates are increasing to obtain higher beam currents, the power dissipation in the cavity walls becomes a major limiting factor, not only from a maximum performance point of view, but also with respect to cost minimization. In the attempt to push superconducting materials to elevated performance, the degrading impact of trapped magnetic vortices must be investigated, understood, and ideally eliminated. Although much insight can be gained this way, an extended, systematic approach has to include effects originating from the global distribution of the magnetic field around a cavity. Most notably, with a single 1D sensor it is impossible to distinguish between a change in absolute value and a change in direction of a measured magnetic field vector.
Hence, a new affordable type of sensor had to be found which allows for high resolution magnetic field mapping at cryogenic temperatures in all three spatial directions and as a function of time. Here, we present a suitably arranged array of sensors which utilize the anisotropic magnetoresistance (AMR) effect that meets all of our requirements.
Furthermore, the magnetic field mapping was combined with temperature mapping 9-12 to monitor phase transitions, quench events, and local RF power dissipation during operation. Due to the flexible design of the system, additional diagnostics such as OST sensors 13,14 can be added to the basic setup in future tests. The focus of this paper, however, is on the magnetic-field mapping. The following section will give a more detailed explanation of the two types of measurement boards with the main focus on the magnetometry system. Also, the underlying physics of the AMR effect and its application in the magnetic field sensor will be explained. The design of the dedicated PCBs will be shown and the handling and calibration of the sensors at cryogenic temperatures will be discussed. Finally, initial results obtained with the system will be presented.

A. The AMR Effect
The AMR effect is a quantum mechanical effect whose macroscopic manifestation was already discovered around 1850 18 . It was found that the electrical resistance of a ferromagnetic material varies depending on the angle between the vector of an applied electric current and the direction of magnetization. In general, the origin for the effect lies in the combined action of magnetization and spin-orbit interaction while the magnitude of the effect is material dependent. [19][20][21] .
The AMR effect can be utilized to measure magnetic fields. Here, a ferrite with a defined preferential magnetization (easy axis) and an externally applied electric current is placed in the magnetic field that is to be measured. If the applied field is parallel to where V out is the output voltage of the bridge and V cc is the supply voltage.
Depending on the amplitude of the applied field, the output signal follows a cos 2 (Θ) function where Θ is the angle between magnetization and current with lium.

C. Magnetometry Boards
To achieve a three-dimensional mapping, where the super-scripted + denotes that the At liquid nitrogen temperature, the sensitivity of the sensor is increased given by the steeper slope which will be discussed later.  In addition, the magnetic field generated by the test-coil only depends on the supply current and the geometry of the coil and can be written as where C is the geometry factor of the coil which includes, for example, its length, the  The main change in the present system is the data acquisition which omits multiplexing as described in Section II. Each thermometer is read out with a maximum sampling rate of 500 Hz. A complete map of the cavity can therefore also be obtained every 2 ms without any crosstalk between thermometers due to multiplexing.

VI. SUMMARY AND OUTLOOK
We have shown that AMR sensor AFF755 can be used reliably at cryogenic tempera- In combination with temperature map-ping, the local dynamics of the superconducting phase front becomes accessible at a maximum data acquisition rate of 500 Hz which makes the presented system a powerful tool for SRF cavity diagnostics.
Future steps will first target the absolute measurement of the magnetic field at the sub- Furthermore, a possible degradation due to radiation must be investigated. AMR sensors have been tested for aerospace application and achieved a radiation hardness of over 10 kGy 25 . However, this value was obtained in experiments that also included the readout electronics exposed to the radiation -which is not the case for our setup. Since the AMR sensors themselves are passive devices a much higher radiation limit is to be expected. Dur-ing the tests presented we found no limitation so far. However, the radiation hardness will be included in further testing. In addition, the degradation of all materials during frequent testing will be studied and the mechanical components as well as the circuitry will be optimized.
Additionally, it is planned to integrate temperature and magnetic sensors on a single board in order to eliminate "blind spots" in the azimuthal direction. Finally, other types of magnetic field sensors are investigated for SRF application in the medium term. The use of GMR-utilizing the giant magnetoresistance effect or even TMR sensors utilizing the tunnel magnetoresistance effect will be evaluated because they feature different sizes as well as different sensitivities.