Motion of a Single Particle in an Ideal Penning Trap

This chapter is concerned with the motion that is performed by a single confined test particle in a Penning trap. For now we disregard any realisation of a Penning trap and see it as the abstract combination of an ideally homogeneous static magnetic field \(B_0\) perfectly aligned with a quadrupolar electrostatic potential \(\bar{U}\) that creates a harmonic well across a ‘characteristic trap size’ d. We are concerned only with the motion of a single test particle of mass m and electric charge q in such an arrangement. Later we will discuss the effects that arise when each of these idealisations are dropped.