Electrostatic nuclear accelerator

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An electrostatic nuclear accelerator is one of the two main types of particle accelerators, where charged particles can be accelerated by subjection to a static high voltage potential. The static high voltage method is contrasted with the dynamic fields used in oscillating field particle accelerators. Owing to their simpler design, historically these accelerators were developed earlier. These machines are operated at lower energy than some larger oscillating field accelerators, and to the extent that the energy regime scales with the cost of these machines, in broad terms these machines are less expensive than higher energy machines, and as such they are much more common. Many universities world wide have electrostatic accelerators for research purposes.


Although these machines accelerate atomic nuclei, the scope of application is not limited to the nuclear sciences of nuclear physics, nuclear astrophysics and nuclear chemistry. Indeed, those applications are outweighed by other uses of nuclear beams. Of the approximately 26,000 accelerators worldwide, ~44% are for radiotherapy, ~41% for ion implantation, ~9% for industrial processing and research, ~4% for biomedical and other low-energy research (less than 1% are higher energy machines).[1]

These accelerators are being used for nuclear medicine in medical physics, sample analysis using techniques such as PIXE in the material sciences, depth profiling in solid state physics, and to a lesser extent secondary ion mass spectrometry in geologic and cosmochemical works, and even neutron beams can be made from the charged particles emerging from these accelerators to perform neutron crystallography in condensed matter physics. The principles used in electrostatic nuclear accelerators could be used to accelerate any charged particles, but particle physics operates at much higher energy regimes than these machines can achieve, and there are various better methods suited for making electron beams, so these accelerators are used for accelerating nuclei.

Single-ended machines[edit]

Using a high voltage terminal kept at a static potential on the order of millions of volts, charged particles can be accelerated. In simple language, an electrostatic generator is basically a giant capacitor (although lacking plates). The high voltage is achieved either using the methods of Cockcroft & Walton or Van de Graaff, with the accelerators often being named after these inventors. Van de Graaff's original design places electrons on an insulating sheet, or belt, with a metal comb, and then the sheet physically transports the immobilized electrons to the terminal. Although at high voltage, the terminal is a conductor, and there is a corresponding comb inside the conductor which can pick up the electrons off the sheet; owing to Gauss's law, there is no electric field inside a conductor, so the electrons are not repulsed by the platform once they are inside. The belt is similar in style to a conventional conveyor belt, with one major exception: it is seamless. Thus, if the belt is broken, the accelerator must be disassembled to some degree in order to replace the belt, which, owing to its constant rotation and being made typically of a rubber, is not a particularly uncommon occurrence. The practical difficulty with belts led to a different medium for physically transporting the charges: a chain of pellets. Unlike a normal chain, this one is non-conducting from one end to the other, as both insulators and conductors are used in its construction. These type of accelerators are usually called Pelletrons.

Once the platform can be electrically charged by one of the above means, some source of positive ions is placed on the platform at the end of the beam line, which is why it's called the terminal. However, as the ion source is kept at a high potential, one cannot access the ion source for control or maintenance directly. Thus, methods such as plastic rods connected to various levers inside the terminal can branch out and be toggled remotely. Omitting practical problems, if the platform is positively charged, it will repel the ions of the same electric polarity, accelerating them. As E=qV, where E is the emerging energy, q is the ionic charge, and V is the terminal voltage, the maximum energy of particles accelerated in this manner is practically limited by the discharge limit of the high voltage platform, about 12 MV under ambient atmospheric conditions. This limit can be increased, for example, by keeping the HV platform in a tank of an insulating gas with a higher dielectric constant than air, such as SF6 which has dielectric constant roughly 2.5 times that of air. However, even in a tank of SF6 the maximum attainable voltage is around 30 MV. There could be other gases with even better insulating powers, but SF6 is also chemically inert and non-toxic. To increase the maximum acceleration energy further, the tandem concept was invented to use the same high voltage twice.

Tandem accelerators[edit]

Conventionally, positively charged ions are accelerated because this is the polarity of the atomic nucleus. However, if one wants to use the same static electric potential twice to accelerate ions, then the polarity of the ions' charge must change from cations to anions or vice-versa while they are inside the conductor where they will feel no electric force. It turns out to be simple to remove, or strip, electrons from an energetic ion. One of the properties of ion interaction with matter is the exchange of electrons, which is a way the ion can lose energy by depositing it within the matter, something we should intuitively expect of a projectile shot at a solid. However, as the target becomes thinner or the projectile becomes more energetic, the amount of energy deposited in the foil becomes less and less.

Tandems locate the ion source outside the terminal, which means that accessing the ion source while the terminal is at high voltage is significantly less difficult, especially if the terminal is inside a gas tank. So then a cation beam from a sputtering ion source is injected from a relatively lower voltage platform towards the now improperly-named high voltage terminal, which will be positively charged by the arriving cations. Inside the terminal, the beam impinges on a thin foil (on the order of micrograms per square centimeter), often carbon or beryllium, stripping electrons from the ion beam so that they become anions. As it is difficult to make anions of more than -1 charge state, then the energy of particles emerging from a tandem is E=(q+1)V, where we have added the second acceleration potential from that cation to the positive charge state q emerging from the stripper foil; we are adding these different charge signs together because we are increasing the energy of the nucleus in each phase. In this sense, we can see clearly that a tandem can double the maximum energy of a proton beam, whose maximum charge state is merely +1, but the advantage gained by a tandem has diminishing returns as we go to higher mass, as, for example, one might easily get a 6+ charge state of a silicon beam.

It is not possible to make every element into a cation easily, so it is very rare for tandems to accelerate any noble gases heavier than helium. Mercury also is not known to be accelerated by tandems. Although it is widely remarked by those working with tandems that acceleration of heavy noble gases with a tandem is impossible, KrF- and XeF- have been successfully produced and accelerated with a tandem, although at beam currents well below the mA scale and using an ion production procedure much more complicated than is customary.[2] It is not uncommon to make compounds in order to get cations, however, and TiH2 might be extracted as TiH- and used to produce a proton beam, because these simple, and often weakly bound chemicals, will be broken apart at the terminal stripper foil. Cation ion beam production was a major subject of study for tandem accelerator application, and one can find recipes and yields for most elements in the Negative Ion Cookbook.[3] Tandems can also be operated in terminal mode, where they function like a single-ended electrostatic accelerator, which is a more common and practical way to make beams of noble gases.

The name 'tandem' originates from this dual-use of the same high voltage, although tandems may also be named in the same style of conventional electrostatic accelerators based on the method of charging the terminal.


One trick which has to be considered with electrostatic accelerators is that usually vacuum beam lines are made of steel. However, one cannot very well connect a conducting pipe of steel from the high voltage terminal to the ground. Thus, many rings of a strong glass, like Pyrex, are assembled together in such a manner that their interface is a vacuum seal, like a copper gasket; a single long glass tube could implode under vacuum or fracture supporting its own weight. Importantly for the physics, these inter-spaced conducting rings help to make a more uniform electric field along the accelerating column. This beam line of glass rings is simply supported by compression at either end of the terminal. As the glass is non-conducting, it could be supported from the ground, but such supports near the terminal could induce a discharge of the terminal, depending on the design. Sometimes the compression is not sufficient, and the entire beam line may collapse and shatter. This idea is especially important to the design of tandems, because they naturally have longer beam lines, and the beam line must run through the terminal.

Most often electrostatic accelerators are arranged in a horizontal line. However, some tandems may have a "U" shape, and in principle the beam can be turned to any direction with a magnetic dipole at the terminal. Some electrostatic accelerators are arranged vertically, where either the ion source or, in the case of a "U" shaped vertical tandem, the terminal, is at the top of a tower. A tower arrangement can be a way to save space, and also the beam line connecting to the terminal made of glass rings can take some advantage of gravity as a natural source of compression.

Confusion with Linear Accelerators[edit]

Electrostatic accelerators are often confused with linear accelerators simply because they can (but do not always) accelerate particles in a line. As we can see even early in their history, accelerators were named in some way referring to the method or type of acceleration. Terminal accelerators pre-date both linear accelerator technology and the nomenclature, so it would be confusing and incorrect to categorize them with a newer technology which is quite different. Linear accelerators use an array of oscillating electric fields, historically arranged in a line, but nothing would prevent a person from using magnets in between the columns of linear accelerators to form some other geometric shape. Oscillating field accelerators do not actually produce beams of particles, but rather packets of particles, unlike electrostatic accelerators which can have a beam current that is constant in time. Thus, the naming scheme for accelerators is based on the method of acceleration, or the physics, and not its geometry, which can be a point of confusion. In fact, it was the oscillating field design of the linear accelerator which inspired Lawrence to construct the cyclotron, which accelerates particles in a spiral, thus taking up a considerably smaller amount of space. A linear accelerator has more in common with a cyclotron than an electrostatic terminal accelerator.

Understanding the origin of the electron volt[edit]

The relation E=qV also indicates very simply why the electronvolt (ev) was invented for use in accelerator-based sciences, because if q is entered in integer units of the elementary charge and V in volts, the energy is given in eV; if we wanted to convert the energy into joules, we need to multiply by the elementary charge in Coulombs on both sides of the equation, yielding a very small number. Usually, the high voltage is quoted in MV and the beam energy then in MeV. With more sophisticated, higher energy machines, those working in particle physics are just accustomed to discussing mass and energy in units MeV or GeV, but the relationship of the accelerator state to the beam energy is not as simple as merely knowing the terminal voltage and the particle species accelerated.


  1. ^ According to William Barletta, director of UPAS, the US particle Accelerator School, per Toni Feder, in Physics Today February 2010, "Accelerator school travels university circuit", p. 20
  2. ^ Minehara, Eisuke; Abe, Shinichi; Yoshida, Tadashi; Sato, Yutaka; Kanda, Mamoru; Kobayashi, Chiaki; Hanashima, Susumu (1984). "On the production of the KrF- and XeF- Ion beams for the tandem electrostatic accelerators". Nuclear Instruments and Methods in Physics Research Section B 5: 217. Bibcode:1984NIMPB...5..217M. doi:10.1016/0168-583X(84)90513-5. 
  3. ^ Middleton, R: A Negative Ion Cookbook, University of Pennsylvania, unpublished, 1989 Online pdf