Generation of Counterpropagating Electrons During Inductive Acceleration
Abstract Generated abstract
This paper proposes using induction acceleration to generate counterpropagating electron beams for electron-electron scattering studies, emphasizing that colliding beams can provide high reaction energies with much lower laboratory particle energies than fixed-target arrangements. It outlines two betatron-based installation schemes for accelerating electrons to about 25 MeV and directing them to a collision region, comparing their magnetic layouts, accessibility, beam-density conditions, and expected engineering difficulties. The discussion gives indicative magnet parameters and suggests that higher-energy induction accelerators, possibly iron-free betatron designs, could extend such experiments toward investigations of electron structure.
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Production of Beams of Counter-Propagating Electrons During Their Inductive Acceleration
A. A. VOROB'EV
In studying the scattering of high-energy particles by particles of low velocities, a considerable part of the energy is spent on phenomena associated with the motion of both particles relative to the center of mass after the collision. The part of the kinetic energy \(W_k\) expended on the reaction \(W_p\) depends on the energy and momentum of the colliding particles.
An increase in the velocity of a particle in the laboratory coordinate system in many practically important cases is accompanied by only a small increase in the reaction energy. In the case of a collision of electrons whose kinetic energy is large, the reaction energy is
\[ W_p^2 = W_k. \]
Thus, when electrons with energy \(W_k = 2500\ \text{MeV}\) are scattered, the reaction energy will be \(W_p = 50\ \text{MeV}\).
This result can be obtained in the interaction of electrons moving in the laboratory coordinate system toward one another with a velocity of \(25\ \text{MeV}\). In this case, when the electrons collide, their velocity relative to the center of the colliding masses is zero. The reaction energy will be \(50\ \text{MeV}\), and consequently the equivalent kinetic energy of the process under consideration will be \(2500\ \text{MeV}\).
To accelerate electrons to an energy of \(25\ \text{MeV}\), the induction method can be used effectively.
The induction method is one of the simplest for obtaining electrons with energies on the order of up to several hundred million electron-volts.
At present, effective methods have been developed for controlling a beam of electrons accelerated in a betatron chamber and for extracting them.
For the study of electron scattering by electrons using induction acceleration, the following devices may be proposed. Figures 1 and 2 show diagrams of an installation for the separate acceleration of electrons by the induction method in two chambers. After the electrons have reached the specified energy, they are directed to the collision point indicated in Figs. 1 and 2. The direction of the magnetic fluxes in the installation, as well as the corresponding design diagrams of the magnetic circuits, are shown in Figs. 1 and 2.
The electromagnet of an electron accelerator with an energy of \(25\ \text{MeV}\) will have a weight of \(4500\ \text{kg}\), an equilibrium-orbit radius of \(23\ \text{cm}\), the maximum magnetic-field intensity on the equilibrium orbit will be \(3600\ \text{oersted}\), and the maximum induction in the yoke will be \(8000\ \text{gauss}\) and in the gaps \(1200\ \text{gauss}\).
The advantages of such a design are:
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The possibility of observing acts of electron scattering by electrons outside the magnetic field.
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The presence of free access to chamber 3, in which the beams will meet.
The disadvantages are:
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The presence of losses of accelerated electrons on their path to chamber 3.
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The difficulty of creating devices that focus and deflect an electron beam with an energy of 25 MeV.
For the design shown in Fig. 2, at an electron energy of 25 MeV, the weight of the electromagnet will be
Fig. 1.
Below: diagram of the meeting of electron beams.
1 and 5 — devices for extracting the electron beam from the vacuum chamber.
2 and 4 — devices for focusing and deflecting the electron beam in two perpendicular directions.
3 — experimental chamber, shielded from electric and magnetic fields.
Above: diagram of a betatron for using electrons in colliding beams.
The dashed contour shows the direction of the magnetic flux in the electromagnet ($a$), $b$ — coils feeding the electromagnet, $v$ — vacuum chamber for accelerating electrons in it.
Fig. 2.
Below: diagram of the meeting of electron beams accelerated by the induction method.
1 — common vacuum chamber for accelerating electrons around two separate axes.
Above: diagram of the betatron device for using accelerated electrons in colliding beams. The dashed contours (2) show the direction of the magnetic flux in the electromagnet — 3, 4 — coils feeding the electromagnet.
5500 kg, the radius of the equilibrium orbit — 23 cm, the maximum magnetic-field strength on the equilibrium orbit — 3600 oersted.
The advantages of the design are:
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The meeting of the electron beams occurs as their equilibrium orbits expand.
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High beam density at the moment of their meeting.
The disadvantages are:
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The presence of a large azimuthal static inhomogeneity in the magnetic field of the betatron because of the close proximity of two poles.
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The point where the beams meet is located in the magnetic field.
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Access to the point where the beams meet is difficult.
If a magnetic-core material with a higher induction is used, then it is correspondingly possible to reduce the radius of the equilibrium orbit and the size—
of the installation. An installation for accelerating electrons by the induction method to an energy of \(300\ \mathrm{MeV}\) will make it possible to obtain a reaction energy, in collisions of opposing electron beams, on the order of \(360\ \mathrm{BeV}\). This will make it possible to conduct research on the structure of electrons. For the indicated purposes, the use of iron-free betatron designs is promising.