RU1823162C - Method for generating directional beams of electromagnetic radiation - Google Patents

Abstract

The invention relates to accelerator technology and can be used to generate directed electromagnetic radiation fluxes. The purpose of the invention is to narrow the angular distribution and the angular integral radiation frequency spectrum. For this, a high-energy electron beam moving in an external spatially periodic magnetic field of undulators or electromagnetic waves provides fast electron vibrations with a period w w and amplitude aj. act additionally excited by a magnetic field with a spatial period I w 2 l Yauu. This leads to the appearance of additional slower circulating oscillations of electrons with a period Uy and an amplitude Ar 2 L1. In addition, analytical expressions are given that govern the choice of the period and amplitude of the additional field and the number of periods of fast and slow oscillations. 2 s. F-crystals, 1 ill. (L

Description

The invention relates to an accelerator technique and can be used to generate directed beams of electromagnetic radiation using high-energy electron beams produced by an accelerator.

An object of the invention is to narrow the angular distribution and the angular integral radiation frequency spectrum.

The drawing shows a diagram of a dual two-period undulator, allowing the proposed method for generating radiation. Here I w is the spatial period of the alternating linearly. a polarized magnetic field perpendicular to the Z axis; Av-spatial period of a circular (spiral) magnetic field perpendicular to the Z axis.

The method is carried out as follows.

The electron beam is directed along the Z axis of the dual undulator. The field amplitudes of each undulator are limited so that the dipole condition for high-frequency transverse electron vibrations is satisfied

00

Yu

Cj

oh go

ah I "/ 2lu

0)

Where

aj. - the amplitude of the transverse vibrations; y is the relativistic factor of the electron Her / te2.

The amplitude of the field of the long-period undulator and its period are selected from the condition of providing slow oscillations with a spatial period

Aw gk I "

(2)

where / s 2 is a numerical parameter proportional to the fold of decreasing the angular size of the radiation beam and the amplitude Ar

1

2 y

(3)

The number of periods of electron oscillations in the undulators on the path of exposure to spatially periodic magnetic fields is selected in accordance with the restrictions

Nw (

YES 7G

-1

N

Ј- nw 1

/ ate

From this it is seen that, as a result, the spectral and angular distribution of the total field of the electron radiation will depend on the shape of its trajectory.

5 In the case of dipole undulator radiation, the total radiation field is simulated by the field of a moving dipole emitter or, accordingly, by the field of a linear chain of phased dipole emitters.

Yu Ono turns out to be directed and concentrated within the angle 1 / y. Under a given angle of radiation, a certain wavelength A s ($) with a width of

fifteen

d AS / AS I / NW

(b)

twenty

where Nw is the number of periods in the ondul torus prototype.

For flat ondul torus

where NW is the number of periods A w;

nw is the number of periods .D;

YES / As is the minimum relative half-width of the radiation spectrum for which the radiation source is calculated.

To calculate the spectral-angular distribution of the radiation intensity, one usually uses the formula for the Fourier component of the electric field of radiation in the wave zone

E (wh

 ik // 4fn (n-4) / 9ll

 () 2

J (Ut - k g)

where a) is the radiation frequency;

k (about p / s is the wave vector;

p is a unit vector defining the direction of radiation;

/ 8 is the electron velocity in units of the speed of light;

p is the distance from the undulator to the observation point;

NWT is the total time the electron travels through the undulator.

According to (5), the radiation field generated by the electron as a result of passing through the undulator can be represented as the sum of the radiation fields of elementary emitters located along the electron path. The summation should be carried out taking into account the delay effect, i.e. taking into account the relative phase shift of the emitters, depending on the speed of the electron and the coordinates of the emitter.

L.L. (1 + 7G + XZ0) / 2 U2

(7)

„Where AW is the period of the ondul torus;

K is a constant undulator determined by the value of the deflecting field. In the dipole approximation, K 1.

In the proposed method, in compliance with conditions (1) - (4), the spectrum of elementary radiators remains dipole, corresponding to high-frequency oscillations in a short-period undulator.

Low-frequency oscillations at the same

Under these conditions, an adiabatic change in the transverse coordinates of dipole emitters is made within certain limited limits. The region occupied by the emitters becomes two-dimensional, and in the general case

4Q three-dimensional. The presence of finite transverse dimensions at the radiation source leads to the appearance of interference maxima and an increase in radiation directivity.

c A strong effect is achieved when the emitters describe in the plane transverse to the Z axis not a curve, but a certain area, for example, a circle. Obviously, the angular dimensions of the radiation beam in this

CQ case is determined by the size of the diffraction maximum

0t 1.2As / D.

(8)

where D is the diameter of the cross section of the radiation beam.

Formula (8) qualitatively illustrates the effect of narrowing the angular distribution of radiation by the proposed method by increasing the transverse dimensions of the radiation source.

In this method, the conditions leading to relations (6) and (7) are not violated, therefore, all restrictions (6), (7) and (8) are satisfied simultaneously. This means that the narrowing of the angular distribution of type (8) should, by virtue of (7), lead to a narrowing of the emission spectrum, i.e. increase in monochromaticity.

The specific form of the emission spectrum is calculated by the formula (5) taking into account the parameters of the undulators, the shape of their fields, sizes, and the like. In particular, a two-period magnetic undulator, the field diagram of which is shown in the drawing, provides the electron trajectory

x R-sln D-Z + aSln2

7W

(9)

at R

/ Vuu

where R is the amplitude of circular oscillations with a spatial period Л I

a - the amplitude of linear oscillations with a period Aw AW / CL

Using (9) and (5), it can be shown that the spectral-angular distribution of the radiation intensity at R 0 acquires an additional dependence expressed in terms of the zero-rank Bessel function

1 (AS; R) l (0JAsO) IJ0 (0R) I2

(10)

where (, in As, 0) is the spectral-angular distribution function of the radiation in the linear undulator without additional circular oscillations (R 0).

With a sufficiently large number of undulator periods, this function reflects the dependence of the radiation wavelength on the radiation angle (7) with accuracy (6).

By changing the amplitudes of the field of the long-period undulator, it is possible to provide an adiabatic change in the amplitude of low-frequency oscillations A within O AG R.

In this case, for a sufficiently long undulator (nw 1), the spectral-angular distribution takes the form

Ji () 1 (O.L..CH) 1 (0.L. O) 1 I2

(11) where Ji is the Bessel function of the first rank.

From (10) and (11) it can be seen that for a sufficiently large amplitude of circular oscillations

0R As (12)

the effect of suppressing radiation appears Under condition (3), this effect will be manifested in the region of radiation angles of 1 / y. which means a narrowing of the angular and spectral distributions of radiation simultaneously. In this case, the electron emits along its direction of motion (Z axis) within the angle (8) with the relative width of the spectrum

YU

AAe / As-CAey / R) 2 (13)

An example of a specific implementation of the method. When choosing prototype options

15 Aw 5cm. Nw 100, the radiation is concentrated within the angle b - with a continuous spectrum from A s 375 A.

 In the proposed method, when choosing

J (A

of the parameters of the spiral undulator «™ ™ 100 cm, nw 5. To 1, the radiation of each electron is concentrated in the range of - 1 6 10 rad, and the spectrum of radiation is narrowed and

Is a line with a relative width (AAs / As) of 0.025. The effect of narrowing from 100% to 2.5%.

Thus, the proposed method allows to increase monochromaticity and

n directivity of radiation of an individual electron, which in turn allows you to:

remove restrictions on angular spread

"D electrons and use electron beams with a finite angular spread (1 / y) to generate quasi-monochromatic undulator radiation;

Claims (3)

. "Increase the receiving angle of the radiation up to 1 / y values in accordance with the actual dimensions of the receiver without affecting the spectrum of the perceived radiation; to reduce the energy spread of the ond. (l radiation of the electron beam to the limits determined only by the energy spread of the electrons in the beam. Claims 1. A method for generating directional beams of electromagnetic radiation, which consists in providing transverse vibrations of high-energy electrons with amplitude a JG spatial period A w by exposing them to a millet of spatially periodic magnetic polarizers or electromagnetic waves, characterized in that. in order to narrow the angular p distribution and integral over the angle of the frequency spectrum of radiation, in the area of electron oscillations, an additional magnetic field of undulators or electromagnetic waves with a spatial period A is excited, providing additional circular electron oscillations, the period A w and the amplitude Ar of which satisfy the expressions Aw 2l aw and l-hell, 1 2. The method according to claim 1, characterized in that, in order to increase the monochromaticity in the angle-integrated radiation frequency spectrum, the amplitudes of the magnetic fields providing transverse vibrations of the electrons are selected from the condition that the corresponding oscillations are different: a l Aw / 2 lu, Ar A w / 2 pu, where y is the relativistic factor of the electron, and the amplitude of the additional magnetic field along the electron path changes n y (and / and t y ( adiabatically without violating the dipole condition 2 Ah RT Z Armakc A "/ 2 y 3. The method according to PP. 1 and 2, on the basis of which. that the number of periods of the main field NW, the number of periods of the additional field nw and the amplitudes of these fields are limited from below by the following conditions Nw (L U / iU) 1 nw 1 (Arm8kc / 2 ai) (AVAe) -1/2 where DL / LV is the minimum relative width of the spectrum allowed by the energy spread of the electrons for which the radiation source is designed. / V. w