Abstract
We use a model of vortex dynamics and collective weak pinning theory to study the residual dissipation due to trapped magnetic flux in a dirty superconductor. Using simple estimates, approximate analytical calculations, and numerical simulations, we make predictions and comparisons with experiments performed in CERN and Cornell on resonant superconducting radio-frequency NbCu, doped-Nb and Nb$_3$Sn cavities. We invoke hysteretic losses originating in a rugged pinning potential landscape to explain the linear behavior of the sensitivity of the residual resistance to trapped magnetic flux as a function of the amplitude of the radio-frequency field. Our calculations also predict and describe the crossover from hysteretic-dominated to viscous-dominated regimes of dissipation. We propose simple formulas describing power losses and crossover behavior, which can be used to guide the tuning of material parameters to optimize cavity performance.
Highlights
Vortex matter is the “smoking gun” of type-II superconductors [1,2,3,4], typically appearing in the form of a lattice of quantized magnetic flux lines in equilibrium superconductor states at intermediate ranges of applied magnetic fields and low temperatures
We propose simple formulas describing power losses and crossover behavior, which can be used to guide the tuning of material parameters to optimize cavity performance
We use a model of vortex dynamics and collective weak-pinning theory [4] to study the dissipation of an isolated superconducting vortex line in a Gaussian random-disordered potential, subject to a time-dependent forcing near the surface
Summary
Vortex matter is the “smoking gun” of type-II superconductors [1,2,3,4], typically appearing in the form of a lattice of quantized magnetic flux lines in equilibrium superconductor states at intermediate ranges of applied magnetic fields and low temperatures. We use a model of vortex dynamics and collective weak-pinning theory [4] to study the dissipation of an isolated superconducting vortex line in a Gaussian random-disordered potential (due to weak pinning on defects), subject to a time-dependent forcing near the surface (due to the alternating magnetic fields Brf parallel to the inner surface of the SRF cavity). The vortex line depinning transition is thought to be continuous—the force per unit length resisting the motion of a slowly moving vortex will approach fp as the velocity goes to zero (unlike, say, the textbook behavior of static vs sliding friction) We simulate this depinning explicitly, and provide a mean-field model, incorporating the depinning threshold fp but ignoring the critical fluctuations, avalanches, and scaling characteristic of continuous dynamical phase transitions. III to make contact between our calculations and the experimental measurements
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