A
synchrocyclotron comprises a ferromagnetic structure (4) with a pair of poles (5, 5'), which have a generally circular cross section of
radius R which are placed on either side of a mid-plane (2) and centred on a central axis (1). These poles (5, 5') are separated by a gap forming a cavity (9) having a profile substantially symmetrical with respect to the mid-plane (2). The height of this gap varies radially and the profile of the gap comprises, in succession, starting from the central axis (1): a first portion (6, 7) of
circular section with a
radius R2, which is centred on the central axis (1), the height of the gap at the centre thereof being equal to Hcentre, and which includes an annular subportion (7) in which the height of the gap progressively increases up to a maximum height Hmax at the
radius R2, and a second portion, of annular section (8), which surrounds the first portion (6, 7) and in which the height of the gap progressively decreases down to a height Hedge at the edges of the poles (5, 5'). The height Hcentre is greater than 10 cm and the ratio of the maximum height Hmax to the height Hcentre is between 1.1 and 1.5.