Higher order Motional Resonances Spectra of electrons with Non-linear Axial Oscillations in Quadrupole Penning trap

B M Dyavappa

doi:10.46481/jnsps.2022.371

Abstract

Experimentally the motional resonances spectra of an electron cloud confined in a quadrupole Penning trap, weakly excited with RF field, which is swept from 1 MHz to 1 GHz was examined. The higher order motional resonances of the electron cloud with non-linear axial oscillations show that they result from couplings in the motional degrees of freedom, which characterize the perturbations in the trap, and cause loss of electrons from the trap. The likely presence of perturbative terms of quadrupole potential is identified by studying the motional resonances spectra and hence the multipole terms are calculated. A periodically forced barrel spring with a steel ball at the free end can be regarded as a model of non-linear oscillator and a periodically forced steel ball hung through a flexible rod, which is deflected alternately toward the two magnets can be regarded as a mechanical model of Duffing oscillator are developed, in analogy to observed higher order motional resonances of the electron cloud excited with different RF field powers.

Highlights

The motional resonances spectra of electrons contain the fundamental eigen frequencies, viz. the modified cyclotron frequency, magnetron frequency, axial oscillation frequency and their linear combinations in Penning trap [1, 2]
In this paper investigations on motional resonances of an electron cloud probed from the radio frequency of 1 MHz to 1 GHz are presented, which helps in characterizing the instabilities of the electron plasma in the trap
The non-linear higher order motional resonances of the electron cloud show that they result from couplings in the motional degrees of freedom that characterize the perturbations in the trap [4, 5, 6]

Summary

Introduction

The motional resonances spectra of electrons contain the fundamental eigen frequencies, viz. the modified cyclotron frequency ( fc ), magnetron frequency ( fm), axial oscillation frequency ( fz) and their linear combinations in Penning trap [1, 2]. The modified cyclotron frequency ( fc ), magnetron frequency ( fm), axial oscillation frequency ( fz) and their linear combinations in Penning trap [1, 2] These frequencies can be measured by resonant excitation of the motion of electrons with RF-field applied to the trap electrode. The motional resonances spectra of trapped electrons contain the fundamental oscillation frequencies fc , fm, fz, in addition some of their linear combinations, satisfying the equation nc fc + nm fm + nz fz = C and multiples of these frequencies nc fc , nm fm, and nz fz. For non-linearities at the Figure 4: The strengths of 3rd harmonics in Motional resonances spectra for different magnetic fields, storage voltages and RF field powers of (i) 97G, 10V,-10dBm (ii) 97G, 10V,-100dBm (iii) 97G,2V,-10dBm, (iv) 258G,10V,-10dBm. higher powers of zn, the trapped cloud of electrons will generate the nth harmonic at frequency n f. The doublewell Duffing oscillator model considered here is a narrow ferromagnetic flexible rod whose one end is fixed to a rigid support attached to a driving system and the free end

Perturbative multipole terms in quadrupole potential

Conclusion