Particle Acceleration, Collective Methods of

The acceleration of charged particles in present-day accelerators occurs as a result of the interaction of a particle’s charge with an externally produced electromagnetic field (see). The acceleration efficiency—that is, the mean energy imparted to the particle by an electric field per unit length of the accelerating device—is determined by the electric and magnetic field strengths and is limited by the capabilities of the devices that generate the fields. For different types of accelerators the acceleration efficiency ranges from 1 to 50 million electron volts per meter (MeV/m) of the system’s length.

Figure 1. The motion of a ring bunch of electrons and positively charged ions in an externally produced field E_ext, in a collective accelerator. Under the action of the field E_ext, the ions move toward the edge of the ring in the direction opposite to that of E_ext. However, the self-field of the electrons confines the ions in the ring, and the ions are accelerated together with the electrons.

In the 1960’s a new field of research in accelerator physics was founded by V. I. Veksler, namely, coherent methods of acceleration. In principle, coherent methods make it possible to circumvent the difficulties of “classical” accelerators. The main task of coherent methods of acceleration is to obtain high acceleration efficiencies. A characteristic feature of such methods is that the electromagnetic field that accelerates the particles is not externally produced but arises as a result of the interaction of a group of accelerated particles with another group of charges, with a plasma, or with electromagnetic radiation which for that purpose must have coherent, or synchronous, action on the entire accelerated group of particles. Such synchronism usually occurs automatically. The magnitude of the accelerating field depends on the number of particles that take part in the interaction and may reach large values—100 or more megavolts per meter (MV/m). However, the implementation of these methods is impeded by the plasma and hydrodynamic instabilities that arise; at present, therefore, coherent acceleration does not have practical value for particle acceleration.

If the accelerated particles do not take part in the generation of the accelerating fields and if the fields are generated not by means of electrodes, as in “classical” accelerators, but by means of fluxes, bunches, or rings of charged particles, then we speak of collective methods of acceleration. As of 1976, about 20 different schemes for the collective acceleration of particles had been proposed. In contrast to the case of plasma accelerators, relativistic electrons take part in the generation of the accelerating field in all collective particle accelerators.

Some of the most typical collective methods of acceleration are examined below.

Ion acceleration by electron beams. When a high-density electron beam passes through a gas, ions of the gas are formed and accelerated to energies that substantially exceed the energy of the beam electrons. Although the mechanism of ion acceleration has not been definitively explained, the ion acceleration process can be described in a simplified way.

Upon entering a metal tube containing a gas, a high-density electron beam produces a field so strong that the beam is slowed down in the field and loses speed even over very short distances. The electron density is at a maximum in the region of entry because of the decrease in velocity. The beam then begins to break up as a result of space-charge forces. The energy of the electron beam is expended not only in the generation of the field but also in the ionization of the gas in the tube. In a characteristic ionization time, which depends on the densities of the beam and the gas, a number of positively charged ions that is sufficient to neutralize the space charge of the electron beam and to localize the field within the beam are formed along the entire beam trajectory up to a point where the beam is essentially stopped. The retarding effect of the field on electrons arriving after the characteristic ionization time is reduced, the energy losses cease, and the electron beam moves farther along the tube. The entire process is then repeated and continues in this way until the beam has traversed the entire tube. The point of the highest electron density thus moves along the tube at a rate proportional to the ionization time. Positively charged ions that entered the dense part of the electron beam at the initial moment are confined by the negatively charged electrons and move, together with the density discontinuity, along the tube with the same velocity. Because of their large mass, the ions have a much higher energy than the electrons. The acceleration efficiency in this method is as high as 100 MeV/m. To date, acceleration lengths of only a few centimeters have been achieved, and much work has to be done on testing the validity of the acceleration scheme discussed above.

The plasma method of acceleration. A plasma is a medium in which fields of up to 1,000–10,000 MV/m exist between individual groups of charges. The generation of regular waves, that is, waves having a specific phase, in a plasma and the use of such waves to accelerate charged particles constitute the plasma method of acceleration, which was proposed by the Soviet physicist Ia. B. Fainberg. High-power electron beams are used to solve this problem. When such a beam passes through a plasma, conditions are created under which 20–30 percent of the beam energy is expended in the generation of a plasma wave. To maintain the regularity of the wave, a small preliminary modulation of the electron beam by an externally produced electromagnetic field is used. The generated wave can be controlled and made suitable for particle acceleration by varying the modulation frequency and phase and the plasma density.

Ion acceleration by electron rings. In this method of acceleration, a stable electron bunch is created, and positively charged ions are injected into it. The electric field of the electron bunch securely confines the ions. When the bunch is accelerated by an externally produced field, the ions are accelerated together with the bunch. The terminal energy of the ions is greater than the energy of the electrons in the bunch by the same factor as the mass of an ion is greater than the mass of an electron; if protons are accelerated, the ratio is equal to 1,836. This method is of the greatest practical value. Let us consider a specific scheme for creating a stable electron bunch.

PHYSICAL PRINCIPLES OF CREATING A STABLE BUNCH. To make an electron bunch stable, the Coulomb repulsive forces of the electrons in the bunch must be compensated for. This can be done by adding the required number of positively charged ions to the bunch. However, since acceleration depends on the charge-to-mass ratio, the number of ions must be small, so that the mass of the bunch is not substantially changed. These contradictory requirements are satisfied only for moving electrons. In fact, Coulomb repulsive forces act on the electrons in the bunch, leading to dispersion of the bunch. However, if the bunch is moving, magnetic forces appear in addition to the Coulomb forces; these magnetic forces are associated with the motion of the charges and directed opposite to the repulsive forces. The higher the velocity of the electrons, the stronger the magnetic forces. For electrons with a kinetic energy of, for example, 10 MeV, the resultant repulsive force is reduced by a factor of 400 in comparison with the force for electrons at rest. In this case, the Coulomb repulsion can be completely compensated for by injecting a small number of ions (1/400 of the number of electrons) into the electron bunch. For the subsequent acceleration of the electrons and ions in the externally produced field, the bunch is shaped as a ring of moving electrons. Ions that are practically at rest are situated within the cross section of the ring, in this case, a torus. The ring is used to accelerate the ions. The force acting on each ion in the ring as the ion moves in the externally produced field is directly proportional to the number of electrons in the ring and inversely proportional to the cross section of the ring. These parameters determine the acceleration efficiency in this method.

THE ELECTRON RING ACCELERATOR. The electron bunch is shaped in the following manner. An electron beam from a linear accelerator is injected into a magnetic field, such as that in an accelerator with weak focusing, and forms a large-diameter ring. The initial size of the ring is selected so that the necessary number of electrons is confined in the field. The magnetic field is then increased, and all the dimensions of the ring are reduced as the field becomes stronger. This process is continued until a ring bunch with the required parameters is obtained. In the final state of constriction, a gas valve is used to inject the necessary amount of gas into the ring region. The electrons ionize the gas, and the ions formed are trapped by the electron bunch. The number of trapped ions is controlled by varying the pressure of the injected amount of neutral gas. The configuration of the magnetic field that confines the electrons is then changed, and the ring, together with the ions, begins to accelerate along its own axis in the direction in which the magnetic field decreases. The accelerated motion of the ring is due to the transformation of the rotational energy of the electrons into the energy of translational motion of the ring. The ring is further accelerated by the externally produced electric field (see Figure 1); here, an accelerating system with a considerable energy reserve, such as a system of high-frequency cavity resonators, is needed.

Experiments carried out on models of such accelerators at the Joint Institute for Nuclear Research in the city of Dubna, USSR, have made it possible to obtain an acceleration efficiency of tens of millions of electron volts per meter. Research is being carried out in many countries to study the feasibility of obtaining efficiencies of hundreds of millions of electron volts per meter.