High-Temperature Superconductor Coatings for Beam Impedance Reduction in Particle Colliders: Nonlinear Effects

Abstract

Coating of surfaces facing particle beams with High-Temperature Superconductors (HTS) for reducing the beam coupling impedance is being considered for the next generation of hadron colliders, such as the FCC-hh at CERN, where HTS would be exposed to the high-frequency wakefields generated by the particle bunches and to the strong field of the steering magnets. In this frame, we present a simple model for the calculation of the microwave response of HTS exposed to a strong external magnetic field, which takes into account the nonlinearity of the pinning potential of the vortex lattice. The equation of motion of the vortex lattice is solved in first-order approximation, and we calculate the amplitude of the thirdharmonic components in the electric field produced by vortex oscillation. We deduce the time-dependent surface impedance which could serve as a boundary condition in the simulation codes for the calculation of beam-stability phenomena in particle accelerators. Finally, time-integration of the surface impedance allows exploring the dependence of the surface impedance on surface currents, useful for analyzing the experimental results obtained using simple resonators in terms of our model.

Potential impedance reduction by REBCO-coated conductors as beam screen coating for the Future Circular Hadron Collider

“…( 1) and (2). A notable gain of several orders of magnitude is readily visible at low frequencies for both longitudinal and transverse resistive wall impedance, at which the highest instabilities for a copper beam screen are predicted [14]. As discussed in the previous section, the difference in the surface impedance frequency dependencies between Cu and REBCO-CCs is noticeable in both complex resistive wall impedance planes leading to unique impedance behaviours.…”

“…In addition, the circulating proton bunches induced RF current interacts with the vortex lattice. The RF currents' Lorentz forces cause the vortex lattice to move in a lossy periodic manner, some forms of lattice motion involve net displacement of vortices, while others do not [7,14,15].…”

“…One such option is using high-temperature superconductors (HTSs), which have transition temperatures above 90 K [5], and whose surface resistances are reported to be significantly lower than those of Cu in the temperature range of interest. Several recent studies [6][7][8][9][10][11][12][13][14][15] have theoretically and experimentally proven that REBa 2 Cu 3 O 7−x coated conductors (REBCO-CCs, RE = Y, Gd, Eu) provide a lower surface impedance than copper. The data provided in the aforementioned studies has shown that REBCO-CCs can outperform Cu at the FCC-hh requirements by measuring the surface impedance of several commercially available REBCO-CCs close or at FCC-hh conditions and by extrapolating the data to FCC-hh conditions if necessary.…”

Evaluation of the nonlinear surface resistance of REBCO coated conductors for their use in the FCC-hh beam screen

“…A similar situation occurs in the REBCO-CCs in the FCC-hh BS where the vortices will be subject to a DC magnetic field perpendicular to the RF image currents induced by the beam. This scenario can give rise to a vortex oscillating motion [18] which may include net displacement. Hence, it is essential for the FCC-hh to determine whether the induced RF azimuthal magnetic field strength will be sufficient to fluctuate and/or displace the trapped vortices away from their static position.…”

“…One such possibility is the use of high-temperature superconductors (HTS) which have transition temperatures above 90 K and surface resistances well below that of copper in the temperature range of interest [8], i.e. between 40 and 60 K. In recent years, several studies have shown the potential of REBa 2 Cu 3 O 7−x coated conductors (REBCO-CCs, RE = Y, Gd, Eu) as coating materials for the BS in order to minimize the beam impedance [9][10][11][12][13][14][15][16][17][18]. Even though these previous works on coated conductors have shown that their small-signal surface resistance is significantly below that of Cu, there are other aspects related to their surface impedance that may compromise their use in the FCC-hh BS, specifically [19][20][21][22][23][24][25]: its dependence on radio-frequency (RF) strength under large applied DC magnetic fields, and the appearance of temperature effects, including self-heating, resulting from the application of large RF fields.…”