 
Summary: SIAM J. APPL. MATH. c 2011 Society for Industrial and Applied Mathematics
Vol. 71, No. 3, pp. 829853
RESONANT CYCLOTRON ACCELERATION OF PARTICLES BY A
TIME PERIODIC SINGULAR FLUX TUBE
J. ASCH, T. KALVODA, AND P. STOV´ICEK§
Abstract. We study the dynamics of a classical nonrelativistic charged particle moving on a
punctured plane under the influence of a homogeneous magnetic field and driven by a periodically
timedependent singular flux tube through the hole. We observe an effect of resonance of the flux
and cyclotron frequencies. The particle is accelerated to arbitrarily high energies even by a flux of
small field strength which is not necessarily encircled by the cyclotron orbit; the cyclotron orbits
blow up and the particle oscillates between the hole and infinity. We support this observation by an
analytic study of an approximation for small amplitudes of the flux which is obtained with the aid of
averaging methods. This way we derive asymptotic formulas that are afterwards shown to represent
a good description of the accelerated motion even for fluxes which are not necessarily small. More
precisely, we argue that the leading asymptotic terms may be regarded as approximate solutions of
the original system in the asymptotic domain as the time tends to infinity.
Key words. electroncyclotron resonance, singular flux tube, averaging method, leading asymp
totic term
AMS subject classifications. 70K28, 70K65, 34E10, 34C11, 34D05
DOI. 10.1137/100809337
