SU1624713A1 - Method of obtaining pulsed electron beam - Google Patents

Abstract

The invention relates to a technique for the generation of ionizing radiation. The purpose of the invention is to simplify the method for producing pulsed beams of polarized electrons. The invention provides for the effect on electrons accumulated on the surface of a dielectric, which are oriented perpendicular to the surface by electric and magnetic fields. The inductance of the magnetic field is chosen such that the energy of the thermal motion of the spins of the accumulated electrons is less than the difference of the energies of the spins oriented along and against the scale field. Expressions are given to calculate the strength of the electric and magnetic fields. 2 hp f-ly, 2 ill. AND

Description

The invention relates to methods for producing beams of polarized particles and can be used to create sources of polarized electrons for accelerators.

The aim of the invention is to simplify the method for producing a pulsed beam of polarized electrons.

FIG. 1 schematically shows a device for implementing the method; in fig. 2 shows the dependence of the potential (mouth Z.

The method for producing a pulsed beam of polarized electrons is carried out as follows.

Electrons are placed on the flat surface 1 of the dielectric (Fig. 1) located in the XY plane, which can be done, for example, by electrifying by friction or using an auxiliary electron gun 2 from which a beam of low-energy electrons 3 is directed onto the surface of the dielectric. In the field of electron localization, a magnetic field is created (§ in Fig. 1) perpendicular to the surface of the dielectric. In the presence of a magnetic field, two states of electron polarization are possible: with a spin magnetic element directed along the magnetic field, and with an oppositely directed spin magnetic moment. The first state is energetically more favorable, and when choosing the magnitude of the magnetic field in which the difference between the energies of these states is greater than the energy of the thermal motion of the electron spins, almost all electrons enter this state in a time equal to the spin relaxation time in the magnetic field, t . the degree of polarization of oblique electrons will be close to 100%. After creating an electric field (E in FIG. 1), perpendicular to the surface of the dielectric, these electrons can be removed from

About hO 4

WITH

dielectric surfaces and form a beam of polarized electrons from them. Practically, this is easy to do, since the magnetic field, perpendicular to the surface of the dielectric, is directed along the path of this beam. The repetition frequency of the beam current pulses is determined by the spin relaxation time, which under the conditions under consideration does not exceed 1 G3s.

The magnitude of the electric field required to produce a beam of polarized electrons of a given intensity is determined as follows.

The energy levels of the electron on the surface of the dielectric are described by the following relationship:

 2Л2Ј0, Гехх272m

 (-Ј0 Z O

where n is the principal quantum number (n

1,2,3, ...);

ge is the classical electron radius, m: L: —Compton wavelength, m; EO is the rest energy of an electron, J;

J

Z l (F + 1 B Dielectric constant of the dielectric.

The potential of the image is

  -f (2)

In the presence of an electric field E, normal to the surface of the dielectric,

p, (3)

where EO is the intensity of the electric field, V / m.

The dependence of the potential on Z is shown in FIG. 2, in the absence (dashed line) and the presence (continuous curve) of an electric field. In the presence of an electric field, the transparency of the barrier D for an electron with an energy of EP is known to be

-Ј vЈT / Vep (z) -en

D

Z1

(four)

where) - constant plank, js;

c is the speed of light, m / s;

Zi and 7.d are shown in FIG. 2

Substituting the potential (3) into (4) and the wire integration, we get

50

D 47T2Z2cr, g, 3 (l) x

hehr / -JSj K -./1+-/ P-, "° v" g

. UGE (Y 2j- (t V; c-1

D exp {C V2Ј ° EoZ2 (Zi + Z2) x 55L to

xE () 2ZlK (} | (5)

where K, E are complete elliptic integrals of the first and second kind, respectively. Use ratio

ep (Zi) ey (Z2) en (6)

and formulas (1) and (3), we define Zi and 7.2. Substituting their values in (5), we get

k-1

The timeliness of a particle passing through the barrier over time is determined, as is well known, by the following ratio P-Dfr, (9)

where f is the oscillation frequency, s, of an electron to potential I (3), which, as it is easy to show, for a particle with energy Јn is equal to

fn

4rt2Z2C, Ge-.z

P3ge

(e N;

(with)

(ten)

Substituting (8) and (10) into (9), we get

D 4л: 2г2сг хге 4.3 Рп RISfc} N

35

and exp Jк (|

+

(eleven)

 one

or for an electron in the ground state

D 47T2Z2cr, g, 3 (l) x

If N electrons were accumulated on the dielectric surface, then the number of electrons in beam 4 (Fig. 1) is obviously equal to PiN, i.e. pulsed current of this beam

1 (13)

Therefore, to obtain a pulsed current of a beam of polarized electrons equal to I, the condition

47T2Z2cN Lechz

Consider an example of the practical implementation of the proposed method.

Let an electron beam 3 with a current of 0.2 mA and an electron energy, for example, 100 eV, be directed from an electron gun 2 to an Plexiglas surface with Ј 2.2 with an area of 10 m (1 in Fig. 1). In a time of 10 s, a charge of 2 C accumulates on the surface of the dielectric, i.e. N 1,2 1013 electrons. A magnetic field perpendicular to its surface is applied to the dielectric. In this case, the energy levels of the electrons are split. It is energetically more advantageous to have a state in which the electron spin magnetic moment is parallel to an external magnetic field. Therefore, all the electrons through time, equal to the relaxation time of the spins, pass into this state, provided that the energy of thermal motion is less than the difference of the energies of the indicated energy levels. The energy of thermal motion, which is per degree of freedom, is equal to

one

 kT, and the electron spin energy difference in

magnetic field - 2, m V. Therefore, the transition to the most favorable energy state will occur under the condition

2 / B 1 / 2kT (15)

or

B (16)

For example, at T 10 K, B 3.7 T.

After the accumulation of electrons on the surface of the dielectric after a time equal to the relaxation time of their spins,

turn on the electric field on the day of their separation from the surface. Using formulas (14) and (8), we find the value of the electric field required for this. Under the conditions discussed above (e 2.2, N 1.2-1013), the calculation shows that to obtain a pulsed current of a beam of polarization electrons, for example, 0.5 A, an electric field E 9.2 106 V / is required. m Receive

10, the electric field of such intensity is easy.

In the case of accumulation of electrons on the surface of a ferrodielectric with a cubic crystal lattice, the magnitude of the induction of the magnetic field perpendicular to the surface of the ferrodielectric is chosen equal to the induction of its saturation. For real ferrodielectrics, these values are usually 0.15-0.45 T. Let on

20, the surface of a ferrodielectric, as in the previous example, is accumulated using an electron gun (1 in Fig. 1) N 1.2 1013 electrons per sec. After a time equal to the relaxation time of the spins of the accumulated electrons, each of them will be oriented in the direction of magnetization of the closest crystalline polycrystal to it. This process will occur at room temperature and relatively

30 small fields x (0.15-0.45 Tl, as indicated above), since the interaction in the case of a ferrodielectric has a collective character due to the exchange interaction. The calculation by the formulas (14) and (8) shows

35 that in this case, for real parameters of ferrite, the electric field required to obtain a pulsed beam current of 0.5 A has a value in the order of hundreds of kilovolts per centimeter.

40

Let us determine the degree of polarization of the beam of polarized electrons in the considered example. According to the main properties of the spinors for an electron with a spin spin at an angle in the direction of the magnetic field, the probability to detect a spin in the direction of the field is equal to

2 0 cos -n, and in the opposite direction

 - sin2 -. Consequently, the degree of polarization of this electron in the direction of polarization

Cos cos

at

sin

2 in cos in

(17)

Assuming that the crystallites in a polycrystal are arranged chaotically, we determine the degree of polarization of the electrons, the expression (17) is averaged

where dQ is a solid angle element;

W is the maximum angle between the direction of the electron spin and the direction of the magnetic field, i.e. maximum angle between the axis of easy magnetization of the polycrystal crystallite and the direction of the external magnetic field.

Since there are three easy magnetization axes in a second crystal, each of the crystallites will be magnetized along the one of them that is at the smallest angle away from the magnetic field direction. Therefore, it is easy to see that tg tu VJ2T

, 54040, cos2 0.79.

Thus, in the considered example, by accumulating electrons on the surface of a polycrystalline ferroelectric with a cubic lattice, an electron beam with an impulse current of 0.5 A and a degree of polarization of about 80% can be obtained.

A higher degree of polarization can be obtained by the accumulation of electrons on the surface of a single-crystal ferrodielectric. In this case, we directed the magnetic and electric half along the axis of easy magnetization of the single crystal, we obtain an electron beam with a degree of polarization of 100% (and with the same intensity 0.5 A), since all electrons on the surface of the dielectric after the spin relaxation time will be polarized in the direction of the axis of easy magnetization.

Based on this method, an electron beam with a degree of polarization of 100%, a pulsed beam current of 0.5 A, a pulse frequency of 100 Hz can be obtained.

Claims (3)

1. A method of producing a pulsed beam of polarized electrons, consisting in the accumulation of electrons on the surface of a dielectric and the action of an electric field perpendicular to the dielectric surface, characterized in that 0 five simplifying the method, the magnetic field is also oriented perpendicular to the surface of the dielectric, and its induction is chosen such that the energy of the thermal motion of the spins of the accumulated electrons is less than the difference of the energy of the spins oriented along the magnetic field and in the opposite direction, while the electric field is excited through time, greater than the relaxation time of electron spins in a magnetic field, and the magnitude of the intensity E0, V / m. choose from condition 4l: 222St / he p3 . / s-1 k-1 where e- 1 , Ј - dielectric po4 (Ј + 1) is a standing dielectric; C - the speed of light, m / s; ge is the classical electron radius, M; Ac - Compton wavelength, m; N is the number of electrons; r eoZ3 /WITH - eg) 4.- energy of peace Ge Eo electron, j; K, E are complete elliptic integrals of the first and second kind, respectively; I is the required pulse current of polarized electrons, A; e - electron charge, Cl. 2, the method according to claim 1, characterized in that the induction of the magnetic field B, T is chosen from the condition kT AT four/ where k is the Boltzmann constant, j / c; T is the temperature of the dielectric, K; / and - Bohr magneton, J / T, 3. The method according to claim 1, wherein that the accumulation of electrons is carried out on the surface of the ferrodielectric, and the magnitude of the magnetic field is chosen from the condition of magnetizing the ferrous dielectric to saturation. In k if  / / tVw.  //////////////////////////////////////////// 1 L Јm