Ion motion in a Penning trap

 

 

The ion motion in a Penning trap is composed of three independent harmonic oscillations which have characteristic frequencies.  Click here for a movie.

 

Axial motion: Oscillation between both end caps of the trap. The frequency depends on the mass of the ion and is independent of the magnetic field strength B.

Magnetron motion: Circular ExB drift about the trap axis. The magnetron frequency depends on the strength of both the magnetic and electric field. For a weak electric field it is practically mass independent.

Reduced Cyclotron Motion: Circular motion perpendicular to the magnetic field axis. Its frequency is the pure cyclotron frequency reduced by the magnetron frequency. 

More details on the ion motion are given below.

Equation of Motion

            r+: radius of (reduced) cyclotron motion

            r-: radius of magnetron motion

            rz: amplitude of axial motion

 

 

Eigen Frequencies

               U0: trapping voltage

               d: characteristic trap dimension

               q,m :charge and mass of ion

 

 

 

Pure Cyclotron Frequency

 

                         B: magnetic field strength

 

 

 

Important Relations for Mass Determination