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Algebra of Symmetries for the Secondary Resonance in the Penning Trap

Student: Ekaterina Zubkova

Supervisor: Mikhail Karasev

Faculty: Faculty of Applied Mathematics and Cybernetics

Educational Programme: Specialist

Year of Graduation: 2014

<p>In this work we consider the mathematical model of the Penning trap. We study the behavior of a single charged particle inside such a trap in the resonance case 2 : (-1) : 2.</p><p>In the case of the secondary resonance k:l=1:1 the averaged hamiltonian was calculated. It was proved that it doesn&rsquo;t depend on the creation and anihilation operators.</p><p>For the resonance k:l=0:1 the irreductible hermitian presentation of the secondary resonance algebra was derived and, moreover, it appeared that all the generators of this presentation are given by ordinary third- and secondary- order differential operators.</p>

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