How to Measure Magnetic Energy in Particle Accelerator Magnets: A Comprehensive Guide

Measuring the magnetic energy in particle accelerator magnets is a crucial task for ensuring the optimal performance of these complex systems. This comprehensive guide will delve into the various techniques and methods used to quantify the magnetic field quality, providing a detailed understanding of the underlying principles and practical applications.

Harmonic Coil Measurement: Characterizing Small-Aperture Magnets

One of the most widely used methods for measuring magnetic energy in particle accelerator magnets is the harmonic coil measurement. This technique is specifically designed for small-aperture magnets, such as those employed in the Linac4 accelerator at CERN. The harmonic coil measurement involves the following steps:

1. In-situ Calibration: The system is calibrated in-situ, ensuring accurate measurements of the magnetic field.
2. Magnet Flipping: The magnet is flipped around its axis, allowing for the measurement of fluxes by stationary coils at different angular positions.
3. Flux Measurement: Fluxes are measured by the stationary coils for current cycles shorter than 1 second, capturing the dynamic behavior of the magnetic field.

The harmonic coil measurement system enables a complete characterization of a quadrupole magnet for particle accelerators. It provides insights into the multipole field components, magnetic axis position, and field direction, all of which are crucial for the performance of the accelerator.

Rotating Coil System: Measuring Magnet Multipoles in Static Conditions

Another approach to measuring magnetic energy in particle accelerator magnets is the rotating coil system. This method is considered the best solution for measuring magnet multipoles in static conditions. However, for small-aperture magnets, the small dimension of the external radius of the rotating shaft can limit the accuracy of the measurements.

To address this challenge, researchers have explored the use of printed circuit coils. By machining the coils as printed circuits, the errors on small coils can be reduced. However, this approach leads to a lower winding density, which in turn reduces the sensitivity of the measurement system.

Quantifying Magnetic Field and Energy

The magnetic field in particle accelerator magnets can be expressed in terms of magnetic flux density (B), measured in Gauss or Tesla. The variation of the magnetic field along the spatial coordinates (x, y, z) can be represented by an equation. For instance, in the case of a quadrupole magnet, the magnetic field can be expressed as a function of x and y, where Bx and By are the components of the magnetic field along the x and y axes, respectively.

The magnetic energy (U) stored in a magnet can be calculated using the following formula:

U = ∫B²/2μ dV

Where:
– μ is the magnetic permeability of the medium
– dV is the differential volume element
– The integral is taken over the entire volume of the magnet

By using this formula, the magnetic energy stored in a particle accelerator magnet can be quantified, providing valuable information for the design and operation of the accelerator.

Advanced Measurement Techniques

In addition to the harmonic coil measurement and rotating coil system, researchers have explored other advanced techniques for measuring magnetic energy in particle accelerator magnets. These include:

1. Vibrating Wire Technique: This method involves the use of a thin wire that is suspended in the magnetic field and set into vibration. The frequency of the vibration is directly related to the magnetic field strength, allowing for the measurement of the magnetic energy.

2. Hall Probe Measurements: Hall probes can be used to measure the magnetic field at specific points within the magnet. By mapping the magnetic field distribution, the magnetic energy can be calculated.

3. Pulsed Wire Technique: In this method, a current-carrying wire is placed in the magnetic field, and the resulting deflection is measured. This technique can be used to characterize the magnetic field and energy in pulsed magnets.

4. Magnetic Resonance Imaging (MRI): MRI techniques have been adapted for the characterization of particle accelerator magnets, providing high-resolution maps of the magnetic field and energy distribution.

These advanced techniques offer additional tools for researchers and engineers to accurately measure and analyze the magnetic energy in particle accelerator magnets, contributing to the optimization of accelerator performance.

Practical Considerations and Challenges

When measuring magnetic energy in particle accelerator magnets, several practical considerations and challenges must be addressed:

1. Magnet Geometry and Aperture: The size and shape of the magnet aperture can significantly impact the measurement techniques and accuracy. Small-aperture magnets, for instance, require specialized methods like the harmonic coil measurement.

2. Magnetic Field Homogeneity: Ensuring a homogeneous magnetic field is crucial for accurate measurements. Factors such as magnet design, materials, and manufacturing tolerances can affect the field homogeneity.

3. Temperature Dependence: The magnetic properties of materials used in accelerator magnets can be temperature-dependent. Maintaining a stable temperature during measurements is essential for reliable results.

4. Electromagnetic Interference: Particle accelerators operate in environments with high levels of electromagnetic interference, which can impact the accuracy of magnetic field measurements. Shielding and signal processing techniques are often employed to mitigate these effects.

5. Measurement Repeatability and Uncertainty: Ensuring the repeatability and quantifying the uncertainty of magnetic energy measurements is crucial for the reliable operation and optimization of particle accelerators.

Addressing these practical considerations and challenges requires a deep understanding of the underlying physics, advanced measurement techniques, and careful experimental design.

Conclusion

Measuring the magnetic energy in particle accelerator magnets is a critical task that enables the optimization of accelerator performance. This comprehensive guide has explored the various techniques and methods used in this field, including harmonic coil measurements, rotating coil systems, and advanced approaches like vibrating wire, Hall probe, and MRI-based techniques.

By understanding the principles, practical considerations, and challenges associated with magnetic energy measurements, researchers and engineers can develop more accurate and reliable measurement systems, contributing to the advancement of particle accelerator technology.

References

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2. DeflByMagnets.pdf – US Pas. (n.d.). Retrieved from https://uspas.fnal.gov/materials/02Yale/DeflByMagnets.pdf
3. Caspi, S. (2001). Magnetic Field Measurements. Lawrence Berkeley National Laboratory. Retrieved from https://cern.ch/acc-physics/Magnetic_Measurements/Caspi_Magnetic_Field_Measurements.pdf
4. Russenschuck, S. (1999). Field Computation for Accelerator Magnets: Analytical and Numerical Methods for Electromagnetic Design and Optimization. Wiley-VCH.
5. Todesco, E., & Bottura, L. (2016). Electromagnets for Superconducting Accelerators. Annual Review of Nuclear and Particle Science, 66, 253-280.