Chaotic motion of a single charged particle in a nonlinear Penning trap
Penning traps have long been an important tool for high precision measurements in physics, such as the measurements of the g-factor of the electron and the proton/electron mass ratio. The ideal Penning trap features a spatially uniform magnetic field and an electrostatic quadrupole potential. A charged particle moving in such an ideal trap is a linear system and thus generates harmonic oscillations. It is the accuracy of measuring those harmonic frequencies that determines the accuracy of a measurement. A great deal has been done to minimize the nonlinearity which arises in the actual construction of a Penning trap. In this dissertation, the author investigates the possibility of observing chaos in a system of a driven single charged particle moving in a nonlinear Penning trap, in which the nonlinearity is large and not just a perturbation of the linear Penning trap. The analysis shows that Penning traps may be used as a tool to study the behavior of a nonlinear system. A design is suggested of a nonlinear Penning trap in which the electrostatic potential would greatly differ from the quadrupole potential. In particular, their design is to generate a strong nonlinear axial potential-the potential along the magnetic field axis. The author then discusses the motion of a single charged particle in the nonlinear axial potential. The resultant equation of motion is Duffing's equation which physically describes a damped nonlinear oscillator driven by a periodic force. The dynamical behavior of this Duffing's equation is studied numerically by varying the damping and the driving frequency parameters as well as the amplitude parameter. The author finally discusses the possibility of observing chaos in such a nonlinear system. Some chaotic regions in the parameter space are identified.
- Research Organization:
- Auburn Univ., AL (United States)
- OSTI ID:
- 6972148
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
74 ATOMIC AND MOLECULAR PHYSICS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EQUATIONS OF MOTION
EQUIPMENT
HARMONIC OSCILLATORS
ION SOURCES
MULTIPOLES
NONLINEAR PROBLEMS
OSCILLATORS
PARTIAL DIFFERENTIAL EQUATIONS
PENNING ION SOURCES
QUADRUPOLES
RANDOMNESS
TRAPS