Theory, Design and Tests on a Prototype Module of a Compact ...

1. GLOBAL PARAMETERS OF THE ACCELERATOR 25
structure; then we continue with the analysis of a cavities chain, coming
to the properties of the single cavities <strong>and</strong> the last sections are devoted
to their design. Particular emphasis is on the design of the coupling
mechanism for the feeding of the structure through a waveguide in the
last section. It is apparent that the various steps have a reciprocal
feedback <strong>and</strong> are not completely close each other, but in any case they
give a way to follow.
Finally, it is worth noting that we lead with a procedure that was
not completely followed during the design of first LIBO module, because
of problem of time <strong>and</strong> of feasibility of proposed solutions. This
is normal because we remember that the first LIBO module was a
proof of principle <strong>and</strong> then it was thought golden plated. In this sense,
we hope that the procedure presented will be a first attempt to have
a methodology easy to transfer to an industrial construction of these
type of structure instead.
1. Global Parameters of the Accelerator
An accelerator for hadrontherapy needs low production costs <strong>and</strong>
not large overall dimensions of the structure. Both points are necessary
for a feasible installation in medical centers <strong>and</strong> hospitals. The second
point can be satisfied if the cavity are small in dimensions <strong>and</strong> stacked
as much as possible. Furthermore, if these cavities let easily flow the
power, it is possible to use a single alimentation for a large amount
of cavities. In reality, the type, the entry energy, <strong>and</strong> the velocity of
particles suggest the type of the structure with a good efficiency to use.
In our case, protons <strong>and</strong> 60 MeV beam entry energy suggest exactly a
multi-cell coupled structure.
The choice of the frequency <strong>and</strong> of the total length of a normalconducting
structure comes applying the Kilpatrick criterion [16, 26,
27] which states the maximum value for the electric field in each cavity
before breakdowns <strong>and</strong> sparking occur. The Kilpatrick results were
expressed in a convenient formula given as
f = 1.64E 2 Ke −8.5/EK , (3.1)
where f is the frequency in MHz <strong>and</strong> EK is in MV/m <strong>and</strong> it is said the
Kilpatrick limit. The behaviour of formula (3.1) is shown in figure 3.3.
The Kilpatrick criterion is based on experimental results, <strong>and</strong> nowadays
it is considered conservative; the formula is still used, except that the
actual peak surface field is expressed as ES = bEK, where b is known
as the bravery factor <strong>and</strong> it is chosen in a range from 1.0 to 2.0.
Let us enter now in the details of the first LIBO module; the large
availability of low cost power klystrons at 3 GHz could be a good reason
to choose that frequency. The correspondent Kilpatrick limit is around
47 MV/m. After that, one has to consider: