[Paper Review] Cyclotron motion in a gravitational-wave background

J.W. van Holten|ArXiv.org|Jun 29, 1999

Pulsars and Gravitational Waves Research4 references4 citations

TL;DR

This paper investigates the dynamics of a relativistic charged particle undergoing cyclotron motion in a constant magnetic field perturbed by gravitational waves propagating along the field direction. Using a generalized energy conservation law, it computes changes in kinetic energy and orbital parameters, showing that waves with constant curvature induce measurable modifications to the particle's trajectory and energy, offering a potential mechanism for detecting gravitational waves via particle motion in magnetic fields.

ABSTRACT

We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the variations of the kinetic energy of the particle during passage of the waves. We also explicitly compute the change in the orbit due to a wave with constant curvature.

Motivation & Objective

• To understand how gravitational waves affect the motion of relativistic charged particles in a magnetic field.
• To investigate the impact of gravitational waves on the kinetic energy and orbital parameters of a particle undergoing cyclotron motion.
• To apply a generalized energy conservation law to quantify energy variations during wave passage.
• To compute explicit changes in particle orbit due to gravitational waves with constant curvature.
• To explore the potential for detecting gravitational waves through their influence on charged particle trajectories in magnetic fields.

Proposed method

• The study employs a relativistic formulation of cyclotron motion in the presence of a constant magnetic field perturbed by gravitational waves.
• A generalized energy conservation law is derived and applied to compute variations in the particle's kinetic energy during the passage of gravitational waves.
• The analysis focuses on gravitational waves propagating parallel to the magnetic field direction.
• For waves with constant curvature, exact solutions are computed to determine changes in the particle's orbital radius and energy.
• The method uses perturbation theory in the weak-field limit, assuming small gravitational wave amplitudes.
• The core approach combines relativistic mechanics with linearized general relativity to model wave-particle interactions.

Experimental results

Research questions

• RQ1 How does a gravitational wave incident along the magnetic field direction alter the kinetic energy of a relativistic charged particle in cyclotron motion?
• RQ2 What is the quantitative change in the particle's orbital radius due to a gravitational wave with constant curvature?
• RQ3 Can a generalized energy conservation law be applied to systems with gravitational wave perturbations in the presence of electromagnetic fields?
• RQ4 How do the dynamics of cyclotron motion respond to the spacetime curvature induced by gravitational waves?
• RQ5 What observable signatures could gravitational waves imprint on charged particle trajectories in magnetic fields?

Key findings

• The kinetic energy of the charged particle experiences periodic variations during the passage of gravitational waves, as predicted by the generalized energy conservation law.
• For waves with constant curvature, the particle's orbital radius undergoes a net, non-oscillatory change, indicating a permanent modification to the orbit.
• The magnitude of the energy variation depends on the amplitude and frequency of the gravitational wave, as well as the particle's charge and mass.
• The analysis shows that gravitational waves can induce measurable changes in cyclotron motion, even in the weak-field regime.
• The results suggest that high-precision measurements of charged particle trajectories in magnetic fields could serve as a detection mechanism for gravitational waves.
• The study provides a theoretical framework for probing gravitational wave effects on relativistic particles in astrophysical or laboratory settings.