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

https://doi.org/10.46481/jnsps.2022.371

Authors

  • B. M. Dyavappa Department of Physics, Government College for Women, Kolar, Karnataka, India

Keywords:

Quadrupole Penning trap, Motional resonance spectrum, quadrupole potential, Duffing oscillator, non-linear oscillator

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.

Dimensions

P. Paasche, T. Valenzuela, D. Biswas, C. Angelescu, & G. Werth , “Individual and center of mass resonances in the motional spectrum of an electron cloud in a Penning trap” Eur. Phys. J. D 18 (2002) 295. DOI: https://doi.org/10.1140/epjd/e20020033

P. Paasche, C. Anglescu, S. Ananthamurthy, D. Biswas, T. Valenzuala, G. Werth, “Instabilities of an electron cloud in a Penning trap”, Eur. Phys. J. D 22 (2003) 183. DOI: https://doi.org/10.1140/epjd/e2002-00239-3

G. Tommaseo, P. Paasche, C. Angelescu, & G. Werth, “Subharmonic excitation of the eigenmodes of charged particles in a Penning trap”, Eur. Phys. J. D 28 (2004) 39. DOI: https://doi.org/10.1140/epjd/e2003-00296-0

A. Drakoudis, A. M. Sallner, & A. G. Werth, “Instabilities of ion motion in a linear Paul trap”, Int. J. Mass Spectrom. 252 (2006) 61. DOI: https://doi.org/10.1016/j.ijms.2006.02.006

X. Z. Chu, M. Holzki, R. Alheit, & G. Werth, “International Journal of mass spectrometry and Ion Processes” 173 (1998) 107. DOI: https://doi.org/10.1016/S0168-1176(97)00262-0

R. Alheit, S. Kleineidam, F. Vedel, M. Vedel, & G. Werth, “International Journal of mass spectrometry and Ion Processes” 154 (1996) 155. DOI: https://doi.org/10.1016/0168-1176(96)04380-7

F. G. Major, V. N. Gheorghe, & G. Werth, “Charged Particle Traps, Physics and techniques of charged particle confinement”, (Springer) (2005).

P. K.Ghosh, “Ion Traps”, (Clarendon Press, Oxford ) (1995) 72.

K. T. Satyajit, D. Datar & S. Ananthamurthy, “Electron Storage Instabilities and Resonances in a Quadrupole Penning Trap”, Asian Journal of Physics 19 (2010) 1.

M. Kretzschmar, “Single particle motion in a penning trap: description in the classical canonical formalism”. Physica Scripta 46 (1992) 544. DOI: https://doi.org/10.1088/0031-8949/46/6/011

B. M. Dyavappa, “Spectroscopy of non-neutral plasmas in ion traps”, Motional Resonances Spectra of electrons, (Ph.D. thesis, Bangalore University, (2017).

K. T. Sathyajith, “Spectroscopy of Electrons and ions in Electromagnetic Traps”, Ph.D. thesis, Bangalore University, (2010).

Y. Ueda, “Randomly transitional phenomena in the system governed by Duffing’s Equation”, Journal of Statistical Physics 20 (1979) 181. DOI: https://doi.org/10.1007/BF01011512

“Driven Nonlinear Oscillators”, Physics 15a Lab, (Spring) (2013).

B. . Roberts, “Notes on Linear and Nonlinear Oscillators, and Periodic Waves,” Department of Physics, Boston University, PY231 (2011).

“Maple worksheets on the Duffing equation”, http://www.peterstone.name/Maplepgs/duffing. html.

T. Kanamaru, “Duffing Oscillator”, Scholarpedia 3 (2008) 6327. DOI: https://doi.org/10.4249/scholarpedia.6327

A. Champion, R. Granowski, A. Lodhi, & S. Ravi. “Dynamics of a Periodically Forced Duffing Oscillator with Asymmetric Potential” (2012).

“Bistable Duffing Oscillator with Piezoelectric Coupling: The Piezo-magneto-elastic Energy Harvester, Piezoelectric energy harvesting, New and Renewable Energy Technologies for Sustainable Development”, (2004).

G. Donoso & C. L. Ladera, “Nonlinear dynamics of a magnetically driven Duffing-type spring-magnet oscillator in the static magnetic field of a coil”, European Journal of Physics A 33 (2012). DOI: https://doi.org/10.1088/0143-0807/33/6/1473

M. Rafikov, J. M. Balthazar, & A. M. Tusset, “An optimal linear control design for non-linear systems”, J. Braz. Soc. Mech. Sci. & Eng. 30 (2008) 1473.

H. J. Korsch, H. J. Jodl, & T. Hartmann, “Chaos, A Program Collection for the PC”, 3rd edition, (Springer) (2008).

M. Rafikov, J. M. Balthazar, A. M. Tusset, & J. Braz. “An optimal linear control design for nonlinear systems”, Soc. Mech. Sci. & Eng. 30 (2008). DOI: https://doi.org/10.1590/S1678-58782008000400002

Published

2022-02-27

How to Cite

Dyavappa, B. M. (2022). Higher order Motional Resonances Spectra of electrons with Non-linear Axial Oscillations in Quadrupole Penning trap. Journal of the Nigerian Society of Physical Sciences, 4(1), 75–82. https://doi.org/10.46481/jnsps.2022.371

Issue

Section

Original Research