Angular Distributions of Radiation Polarization Components for A Charge Moving Along A Spiral
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ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY ANGULAR DISTRIBUTIONS OF RADIATION POLARIZATION COMPONENTS FOR A CHARGE MOVING ALONG A SPIRAL V. G. Bagrov,1,2 A. N. Kasatkina,1 and A. D. Saprykin1
UDC 530.145, 537.531
The angular distribution of polarization components of synchrotron radiation emitted by a charge moving along a spiral is investigated. The study is carried out within the framework of classical electrodynamics. Keywords: synchrotron radiation, radiation polarization, angular distributions of radiation.
INTRODUCTION The theory of synchrotron radiation is one of the deeply developed branches of theoretical physics. An initial object of the theory is a charge that uniformly moves in a circle and emits electromagnetic waves. The simplest model of this system is a charge in an external homogeneous magnetic field. However, in this case the problem of radiation emitted by a charge moving along a constant pitch spiral with a constant velocity modulus is solved by the simple Lorentz transformation. Indeed, the corresponding expressions for angular distributions of the total power emitted by a charge moving along a spiral were derived in [1–3]. However, these expressions were analyzed from the viewpoint of the effect of self-polarization of the electron spin, and the angular distribution of synchrotron radiation of the charge moving along a spiral was not analyzed in detail. In the present work, we analyze the angular distribution of polarization components of synchrotron radiation emitted by a charged particle moving along a spiral.
ANALYTICAL EXPRESSIONS FOR POLARIZATION COMPONENTS OF SYNCHROTRON RADIATION EMITTED BY THE CHARGE MOVING ALONG A SPIRAL Let us choose a system of coordinates. The charge e with mass m0 moves along a spiral in a constant and homogeneous magnetic field of strength H directed along the z axis. In our case, solutions of equations of motion in the Cartesian coordinates have the form ( c is the velocity of light)
z = c3t z0 , x = cos x0 , y = sin y0 ,
x =
0 eH sin , y = 0 cos , z = 3 , = , c c | eH |
1
National Research Tomsk State University, Tomsk, Russia, e-mail: [email protected]; [email protected]; [email protected]; 2Institute of High Current Electronics of the Siberian Branch of the Russian Academy of Sciences, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 123–129, June, 2020. Original article submitted January 27, 2020. 1064-8887/20/6306-1037 2020 Springer Science+Business Media, LLC
1037
= 0t 0 , 0 = cyc 1 2 ,
0 | eH | = 2 32 , cyc = . c m0c
(1)
2 2 2 In Eqs. (1), we have used the following designations: v = c is the squared constant velocity, c3 is the constant
drift velocity along the z axis, cyc is the cyclotron frequency, is the orbit radius, 0 is the particle rotation frequency, and 0 , x0 , y0 , z0 are the initial phase and the initial coordinates of the particle. Let us consider the emitted power averaged over time. In this case, w
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