text: A cyclotron is a type of circular particle accelerator in which negatively or positively charged particles accelerate outwards from the centre of the cyclotron along a spiral path up to energies of several MeV. There are various types of cyclotrons. In isochronous cyclotrons, the particle beam runs each successive cycle or cycle fraction of the spiral path in the same time. A synchrocyclotron is a special type of cyclotron, in which the frequency of the driving RF electric field varies to compensate for relativistic effects as the particles' velocity approaches the speed of light. This is in contrast to the isochronous cyclotrons, where this frequency is constant. Cyclotrons are used in various fields, for example in nuclear physics, in medical treatment such as proton-therapy, or in radio pharmacology.
  A cyclotron comprises several elements including an injection system, a radiofrequency (RF) accelerating system for accelerating the charged particles, a magnetic system for guiding the accelerated particles along a precise path, an extraction system for collecting the thus accelerated particles, and a vacuum system for creating and maintaining a vacuum in the cyclotron. Superconducting cyclotrons require a cryocooling system for maintaining the superconducting elements thereof at their superconducting temperatures.
  An injection system introduces a particle beam with a relatively low initial velocity into an acceleration gap at or near the centre of the cyclotron. The RF accelerating system sequentially and repetitively accelerates this particle beam, guided outwards along a spiral path within the acceleration gap by a magnetic field generated by the magnetic system.
  The magnetic system generates a magnetic field that guides and focuses the beam of charged particles along the spiral path until reaching its target energy, Ei. The magnetic field is generated in the gap defined between two field shaping units by two solenoid main coils wound around these field shaping units, which can be magnet poles or superconducting coils separated from one another by the acceleration gap.
  The main coils are enclosed within a flux return, which restricts the magnetic field within the cyclotron. Vacuum is extracted at least within the acceleration gap. Any one of the field shaping units and flux return can be made of magnetic materials, such as iron or low carbon steel, or can consist of coils activated by electrical energy. The coils, as well as the main coils can be made of superconducting materials. In this case, the superconducting coils are cooled below their critical temperature. Cryocoolers can be used to cool the superconducting components of a cyclotron below their critical temperature which can be of the order of between 2 and 10 K, typically around 4 K for low temperature superconductors (LTS) and of the order of between 20 and 75 K for high temperature superconductors (HTS).
  When the particle beam reaches its target energy, the extraction system extracts it from the cyclotron at a point of extraction and guides it towards an extraction channel (cf. FIG. 2). Several extraction systems exist and are known to a person of ordinary skill in the art.
  In the present disclosure the extraction system creates oscillations of the particles with respect to the equilibrium orbit to drive the particles out of the cyclotron. A so-called “regenerative” beam extraction system steers the last accelerated orbit towards the extraction channel of the accelerator by locally generating a perturbation of the main magnetic field. A magnetic field bump of magnitude ΔBz, can be created over an azimuthal interval, φb, inducing a radial oscillation responsible for a shift, Δy, of the centre of the orbit. For a first harmonic field perturbation the magnitude of the shift is proportional to the amplitude of the first harmonic field perturbation. As illustrated in FIG. 2, the orbit center is shifted in the direction of the perturbation by a distance Δy. The shift eventually leads the particles out of the cyclotron through the extraction channel (cf. FIG. 2).
  Iron bars with a well-defined azimuthal and radial extension (called “regenerator”) are often used to generate a magnetic field bump. For example, U.S. Pat. No. 8,581,525 and WO2013098089 describe iron based regenerators. An iron generated field bump can have a maximal magnetic field gradient, dBz/dr, in the radial direction of the order of up to about 80 T/m. One drawback with iron based regenerators includes that the magnitude of the magnetic field bump cannot be varied easily, and certainly not during operation of the cyclotron. This is a drawback when a same cyclotron is used to extract particles at different energies.
  Like magnet poles, iron based regenerators can be replaced by coils, in particular by superconducting coils which can generate higher magnetic fields. The use of coils allows the magnitude, ΔBz, of the field bump to be varied independently of the magnitude of the main magnetic field, Bz. As shown in FIG. 1(b), however, a magnetic field bump generated by superconducting bump coils is substantially broader than a field bump produced by an iron based regenerator and the resulting maximal magnetic field gradient of the order of 20 T/m is too low to create an optimal perturbation. Without wishing to be bound by any theory, this can at least partly be explained as follows. Superconducting bump coils are cooled to very low temperatures, below their critical temperature (for example temperatures close to liquid helium, for low temperature superconductors) and maintained in a vacuum. The superconducting bump coils are therefore encapsulated inside a cooled radiation shield, which is itself contained within a vacuum chamber. This nested structure requires space and moves the superconducting bump coils further away in the z-direction from the accelerator median plane, P, which increases the full width half max (FWHM) of the coil-based regenerator field bump.
  There therefore remains a need for superconducting regenerators allowing the linear variation of the magnitude, ΔBz, of the magnetic field bump with the main magnetic field, Bz, and at the same time generating an optimal perturbation for extracting a charged particle beam out of a cyclotron. The present disclosure proposes a cyclotron provided with a superconducting regenerator fulfilling the foregoing requirements. The following sections describe these and other advantages in more details.