1. Design of a High-Field Block-Coil Superconducting Dipole Magnet Evangelos I. Sfakianakis School of Electrical and Computer Engineering, National Technical University of Athens AT-MEL-EM Group CERN 2006 Summer Student Programme

2. Current Status & Future Goals The LHC Main Dipoles are the most state-of-the art superconducting dipole magnets worldwide. Their field producing capability exceeds 8 teslas. They are built in a twin aperture configuration with a common iron yoke. The windings follow the cos(θ) configuration and the material used for the cables is Nb-Ti. However, if the LHC has to be upgraded to reach even bigger energies, a field of 15 teslas will be needed, which current Nb-Ti magnets are unable to provide. Therefore research is carried out in both material science and design concepts (e.g. NED). So today the superconductor that is believed to be most suitable for such high- field magnets is Nb 3 Sn. The design of the next “big” magnet is still under debate.

3. Superconductivity It is known that superconductors can carry a large amount of electrical current without significant losses due to Ohm’s law. This makes them the only choice for building high-field magnets (in the multi-tesla region). However a lot of issues have to be taken into consideration when superconducting materials are used, such as  Temperature The cryogenics have to be able to keep the temperature at the desired level, which for the superconductors used in magnets is of the order of only a few Kelvin. Heike Kamerlingh Onnes  Quench Protection A local transition from the superconducting to the normal conducting state could drive the hole magnet to get normal conducting and eventually melt.  The Critical Temperature is a function of both the field and the Current of a superconductor, hence forming a Critical Surface, which determines the upper limit of a superconductor’s performance.

4. Magnet Anatomy (LHC Dipole)

5. Design Goals & Parameters  Field Strength For the same dipole length and the same angle of curvature, the field needed is proportional to the particles momentum. Hence if one wishes to go to higher energies (and higher momenta) the dipole field strength has to be increased proportionally.  Field Quality Since only a perfectly homogenous magnetic field can bend all particles in the same desired way, the field produced by the magnet inside the beam pipe should be as homogenous as possible, i.e. as closer to the ideal dipole as possible.  Stress Management Because of the extremely high current and field, the Lorentz force on the conductors has to be taken into account, so as not to damage the superconducting strands. This point, although important will be just briefly mentioned.  Other Parameters (e.g. cost) Several other parameters, such as the cost and time required for building the magnet, the robustness of the design as far as the fabrication imperfections are concerned, the power supply and cryogenics have to be taken into account, but will not be discussed further in this talk. The Simulation and Optimization were done using the ROXIE software package.

6. Multipole Field Errors (1) It is known that “any” periodic waveform can be expressed as a weighted (infinite) sum of real or complex trigonometric functions (Fourier Series). In exactly the same way any magnetic field configuration in an aperture can be analyzed as a weighted sum of the field produced by ideal multipoles. The main goal when designing a magnet is to be as close to the desired field as possible. A perfect dipole field can be obtained by a Current distribution that follows the law J=J o cos(θ).

7. Multipole Field Errors (2) The current distributions that are theoretically required for producing the field of an ideal multipole cannot be obtained in reality. That means that the resulting magnetic field is a sum of both the desired multipole field -in our case a dipole- and of higher order multipoles. Working on a small aperture magnet (30mm diameter) we were able to obtain a maximum field of about 16 T and keep the relative mutipole errors below 0.2. In order to design a larger aperture magnet (88mm) the resulting cross-section could be scaled up quite easily and when optimized the relative multipole errors were at about 0.3 or less and the maximum field exceeded 16T.

8. Effects due to the Iron Yoke The effects of the iron yoke differ from those of ordinary magnets. Its main purpose is to increase the field in the aperture while decreasing the field outside the magnet (fringe field). The iron leaves the linear region and saturates quite early because of the high field. This nonlinearity causes the multipole errors to vary with excitation current and has to be suppressed as much as possible. The coil was further optimized, taking the yoke’s contribution to the main field into account. The relative errors were kept below 0.2 and the maximum field exceeded 16T.

9. Persistent Currents Another source of errors is the so-called superconductor magnetization stemming from currents which are produced in order to screen the internal volume of the superconducting cable from the magnetic field. Because of the zero resistance of the cable they do not decay with time. In hard superconductors, such as the ones used for the coils, the persistent currents show a hystereses. In the region outside the cable the persistent currents produce a magnetic moment, that alters the field in the aperture.

10. Closing Remarks Special Thanks to: Nikolai Schwerg Bernhard Auchmann Stephan Russenschuck The Block-Coil Design is worth being studied in parallel to the cos(θ) configuration. It is easy to scale while keeping the main characteristics (field strength and multipole errors) in the desired region. The philosophy of the design follows the so-called Intersecting Ellipses scheme. Especially for large apertures, the cos(θ) Dipole suffers from stress due to the Lorentz force around the midplane. In a Block-Coil magnet stress is easier to handle by placing a non magnetic supporting structure around each conductor block. However the yoke and especially the persistent current compensation has to be further simulated and optimized. However a lot remains to be done and tested before a decision about the dipoles of the next high energy ring accelerator is reached.

11. Thank you!!! Superconducting Magnet Design is a challenging task where many contradicting parameters have to be taken into account and stands at the forefront of modern technology. Accelerator Technology is of great importance for High Energy Physics endeavors. Even for future linear colliders (ILC, CLIC), magnets will play an important role (e.g. focusing quadrupoles, damping ring dipoles).