We employ the flux-flow instability (FFI) technique—a widely used method for determining the quasiparticle relaxation time (${\tau }_E$)—to investigate single-crystal superconducting titanium nitride (TiN) films characterized by weak vortex pinning and slow electron-phonon relaxation. By systematically varying the TiN strip width, we show that reliable extraction of the vortex velocity and ${\tau }_E$ is achievable only when the strip width exceeds the electron-phonon relaxation length. A comparative analysis of ${\tau }_E$ values obtained using various FFI models and other experimental methods reveals that quasiparticle relaxation within the vortex core is primarily governed by an increase in quasiparticle temperature. Our analysis provides a reliable way to determine ${\tau }_E$ from FFI measurements and may also be relevant to other superconducting systems in which fast electron-electron scattering is expected to lead to a thermal-like quasiparticle distribution function.

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• Critical current
• Flux pinning
• Vortices in superconductors
• Single crystal materials
• Thin films
• Resistivity measurements