Rotary dynamics of the rigid body electric dipole under the radiation reaction
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Rotary dynamics of the rigid body electric dipole under the radiation reaction Askold Duviryaka Institute for Condensed Matter Physics of NAS of Ukraine, 1 Svientsitskii Street, Lviv 79011, Ukraine Received 28 November 2019 / Received in final form 30 July 2020 / Accepted 31 July 2020 Published online 17 September 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. Rotation of a permanently polarized rigid body under the radiation reaction torque is considered. Dynamics of the spinning top is derived from a balance condition of the angular momentum. It leads to the non-integrable nonlinear 2nd-order equations for angular velocities, and then to the reduced 1st-order Euler equations. The example of an axially symmetric top with the longitudinal dipole is solved exactly, with the transverse dipole analyzed qualitatively and numerically. Physical solutions describe the asymptotic powerlaw slowdown to stop or the exponential drift to a residual rotation; this depends on initial conditions and a shape of the top.
1 Introduction It was reported recently that silica particles of mass about 1 fg and size 100 nm were spined up in the optical trap to the frequency above 1 GHz [1]1 . This corresponds to the orbital quantum number of order ` & 1010 , i.e., the rotational motion is quite classical. If such a particle possesses an electric dipole moment then it emits the electromagnetic radiation and receives the reaction torque which slows the particle rotation down. Of course, this relativistic effect is very small for the aforementioned particle whose constituents move no faster than 10−6 of light speed. But if the spinning particle is kept free for a long time, its radiative slowdown can be measurable and deserves a theoretical study. The classical dynamics of a single point-like charge is governed by the relativistic Lorentz-Dirac equation or its slow-motion predecessor, the Abraham-Lorentz equation [3,4]. Both include the radiation reaction terms which depend on 3rd-order derivatives and give rise to redundant runaway solutions. To get rid of these solutions one uses frequently the approximated 2nd-order reduction of the Abraham-Lorentz-Dirac equations in which higher derivatives in r.-h.s. are eliminated by means of the same but truncated equation (i.e., without a radiation reaction term) [5–7]. For a composite spinning particle the dynamics is complemented with rotary degrees of freedom and complicated by further electrodynamical effects, such as an interaction between different charges, interference of radiation outgoing from them etc. As a result, the external and radiation reaction forces are weaved in a complex way a 1
e-mail: [email protected] This record has been improved to 5.2 GHz [2].
together in a complete set of equations on motion [8] whose cumbersome form leaves little feasibility for their analysis. In the present paper we consider a free non-relativistic composite particle with a
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