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A particle driven by active self-propulsion can be subject to inhomogeneouspotential fields, steering its orientation and leading to confinement andeventual trapping. Analytical treatment of capture and/or release dynamics forgeneral steering potentials presents a challenge due to its coupling betweenexternal potential fields and intrinsic active noise. By using the projectionoperator method we obtain the coarse-grained Dynkin equations with orientationintegrated out in the large fluctuations limit, and derive explicit analyticalsolutions for the mean first passage time in radially symmetric point sourcetrapping potentials. We analyze the ensuing trapping instabilities related to acritical value of the steering potential strength below which the particleeither cannot be lured into the trap, or above which it is unable to leave thetrap after being lured into it.

Trapping Instability of an Active Particle in Steering Potential Fields