TANDEM

The XTU Tandem is a two-stage electrostatic accelerator at the INFN Legnaro National Laboratories (LNL). Installed in 1981, it represented a major step forward in the development of the Laboratory’s accelerator facilities and has since played an important role in the LNL nuclear physics research programme.

The Tandem can operate as a stand-alone accelerator, delivering ion beams directly to the experimental areas, or as an injector for the superconducting ALPI linear accelerator, where the beam can be further accelerated to higher energies.

Accelerator structure

The XTU Tandem is housed in a horizontal pressure vessel filled with sulphur hexafluoride (SF₆) at a nominal pressure of about 7 atm. The gas provides the electrical insulation required to operate the accelerator at very high electrostatic potentials.

At the centre of the accelerator is the High Voltage Terminal (HVT), maintained at a positive potential. Under current operating conditions, the Tandem can be operated at terminal voltages up to approximately 14 MV.

An evacuated beam tube extends along the longitudinal axis of the accelerator and passes through the high-voltage terminal. The accelerating tubes and their supporting structure extend on both sides of the terminal, forming the two successive acceleration stages characteristic of a tandem accelerator.

The high-voltage terminal is charged by a Laddertron system.

Figure 1. Interior of the XTU Tandem pressure vessel, showing the high-voltage terminal and the accelerating column. Photo: Andrea Alessio.

Negative-ion production

A tandem accelerator requires negatively charged ions at injection.

At LNL, the Tandem injector uses a sputtering-type negative-ion source. In the source, atoms of the material to be accelerated are released from a target by sputtering and become negatively charged through interaction with cesium.

The resulting negative ions are extracted from the source, transported through the injection line and directed towards the low-energy end of the Tandem.

This negative charge state is essential to the tandem acceleration principle: it allows the ions to be attracted towards the positively charged high-voltage terminal during the first acceleration stage.

The tandem acceleration principle

Let $V_T$ be the positive voltage of the high-voltage terminal.

A singly charged negative ion, with charge $-e$, entering the accelerator at ground potential is attracted towards the terminal. During this first stage, the ion gains approximately$$\mathrm{\Delta }{E}_1=e{V}_T\mathrm{.}$$

If the terminal voltage is 14 MV, the ion therefore gains approximately 14 MeV during the first acceleration stage, in addition to its initial injection energy.

Once the ion reaches the high-voltage terminal, its charge state is changed by a stripping process.

Stripping and charge-state conversion

Inside the high-voltage terminal, the ion beam passes through a very thin carbon stripper foil.

Collisions with the carbon atoms remove electrons from the incoming negative ions. The ions therefore emerge from the stripper positively charged.

The stripping process produces a distribution of positive charge states. If the selected ion emerges with charge$$Q=+ze,$$

where $z$ is the positive integer charge state, it is repelled by the positively charged terminal and undergoes a second acceleration as it travels from the terminal back towards ground potential.

During this second stage, the ion gains approximately$$\mathrm{\Delta }{E}_2=ze{V}_T\mathrm{.}$$

The same high-voltage terminal is therefore used twice: first to attract the negative ions and then, after charge-state conversion, to repel and further accelerate the positive ions. This is the origin of the name Tandem.

Figure 2. Schematic representation of the XTU Tandem accelerator, showing the ion source, accelerating tubes, supporting column, high-voltage terminal, stripping system, Laddertron charging system, beam diagnostics, bending magnets and SF₆-filled pressure vessel.

Final beam energy

Taking into account both acceleration stages, the kinetic energy of an ion at the Tandem exit can be written approximately as$$E_{\mathrm{o}\mathrm{u}\mathrm{t}}=E_{\mathrm{i}\mathrm{n}\mathrm{j}}+e{V}_T+ze{V}_T-\mathrm{\Delta }{E}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}},$$

where:

• $E_{\mathrm{i}\mathrm{n}\mathrm{j}}$ is the kinetic energy of the ion at injection;
• $V_T$ is the terminal voltage;
• $z$ is the positive charge state after stripping;
• $e$ is the elementary charge;
• $\mathrm{\Delta }{E}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}$ represents the relatively small energy losses occurring mainly during the stripping process.

Neglecting the injection energy and the energy losses for a simplified description, the expression becomes$$\boxed{{\displaystyle E_{\mathrm{o}\mathrm{u}\mathrm{t}}\simeq (1+z)e{V}_T}}$$

This relation illustrates one of the main advantages of tandem acceleration. After stripping, the ion may have a charge state considerably higher than $+1$, so that the energy gained during the second acceleration stage can be several times larger than that gained during the first stage.

For example, for a terminal voltage of 14 MV and an ion emerging from the stripper in charge state $6+$,$$E_{\mathrm{o}\mathrm{u}\mathrm{t}}\simeq (1+6)\times 14\mathrm{M}\mathrm{e}\mathrm{V}=98\mathrm{M}\mathrm{e}\mathrm{V},$$

apart from the injection energy and energy losses.

Charge-state selection and beam transport

Because the stripping process produces several charge states, the required beam component must be selected before it is transported to the experimental areas.

Magnetic elements downstream of the accelerator are used to select the appropriate ion species and charge state according to their magnetic rigidity.

A system of dipole and quadrupole magnets then provides beam analysis, steering and focusing. Beam-diagnostic devices installed along the transport lines allow the beam properties and position to be monitored during accelerator operation.

A switching magnet directs the accelerated beam towards the selected experimental beam line or towards the ALPI accelerator.

Figure 3. Beam-transport section downstream of the Tandem. Magnetic elements and vacuum components are used for beam selection, focusing and transport. Photo: Andrea Alessio.

Tandem and ALPI

The XTU Tandem can deliver beams directly to several experimental areas at LNL or operate as an injector for ALPI (Acceleratore Lineare Per Ioni).

ALPI is a superconducting linear accelerator located adjacent to the Tandem facility. The pre-accelerated beam from the Tandem is transported to ALPI through a dedicated beam line equipped with magnetic dipoles, quadrupoles and bunching systems.

In ALPI, superconducting radio-frequency cavities provide an additional acceleration stage, allowing higher final beam energies to be reached.

Together with PIAVE, the positive-ion injector for ALPI, the Tandem and ALPI form the Tandem–ALPI–PIAVE (TAP) accelerator complex, one of the principal accelerator infrastructures for nuclear physics research at the Legnaro National Laboratories.

Ion beams and research

The Tandem provides a broad range of stable ion beams for experiments in nuclear physics, nuclear astrophysics and related fields.

Its ability to operate both independently and in combination with ALPI provides considerable flexibility in ion species, charge states and beam energies, supporting a wide range of experimental programmes at LNL.

For up-to-date information on available beams, energies and current accelerator operating conditions, users should refer to the dedicated accelerator information and PAC pages of the Legnaro National Laboratories website.