Abstract
We present new exact solutions of the Landau–Lifshitz (LL) and higher-order LL equations describing particle motion, with radiation reaction, in intense electromagnetic fields. Through these solutions and others we compare the phenomenological predictions of different equations in the context of the conjectured ‘radiation-free direction’ (RFD). We confirm analytically in several cases that particle orbits predicted by the LL equation indeed approach the RFD at extreme intensities, and give time-resolved signals of this behaviour in radiation spectra.
Highlights
Despite having been studied for more than a century [1,2,3], radiation reaction (RR) continues to attract theoretical [4,5,6,7,8,9], computational [10, 11], and experimental [12,13,14,15] interest
For recent reviews see Refs. [20, 21]. It is well-known that including RR effects allows for new phenomena, such as anomalous particle trapping [22], chaotic motion [23], symmetry breaking [24, 25], and significantly enhanced generation of certain plasma wave modes [26]. In such scenarios it is often expected that classical RR effects receive significant quantum corrections; the simpler setting of classical physics can, still provide important insight [27], and classical effects can persist in quantum theory [22]
As an application of these exact solutions, we provide analytic evidence confirming the tendency of radiation reaction in strong fields to align particle motion with the ‘radiation free direction’ (RFD) in which they locally experience zero acceleration transverse to their direction of motion, minimising radiation losses
Summary
Despite having been studied for more than a century [1,2,3], radiation reaction (RR) continues to attract theoretical [4,5,6,7,8,9], computational [10, 11], and experimental [12,13,14,15] interest. Eliminating the radiation fields, created by the charges, from the classical equations of motion, one arrives at the Lorentz-Abraham-Dirac (LAD) equation [1,2,3] which contains the third time derivative of position. This implies unwanted effects such as runaway solutions and pre-acceleration. For the longitudinal case we give the exact solution of the LL equation; and for transverse polarisation, i.e. plane waves, we solve.
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