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

32 3. DESIGN TECHNIQUES FOR A SIDE COUPLED LINAC
a closed formula, while the viceversa is. In other words, given a resistance,
inductance <strong>and</strong> capacitance of a lumped resonant circuit, the
geometry of the related cavity is not uniquely determined.
The shape of cavities of multi-cell coupled structure is almost fixed:
the longitudinal dimensions are related to the particles velocity in order
to have synchronism, <strong>and</strong> one tries to have them as small as possible
in order to stack as much cavities as possible. Moreover, the shapes
are rounded to reduce the wall currents path <strong>and</strong> then to maximize the
quality factor. Useful advises <strong>and</strong> procedure to design cavities shape
can be found in [12, 16]. An hard point in the design could be the
definition of the tuners shape <strong>and</strong> position, because one wants then
with a large range of intervention, but with a linear behavior <strong>and</strong> these
two requirements are normally in contrast.
In this section, after a short introduction to numerical computer
codes that are necessary for the design of a general-shape cavity, we
deal with the specific example of the single cavities design for LIBO
project.
3.1. Numeric codes. The numeric computer codes are used in
the design of cavities for linear accelerators because the analytical calculations
can be used only with simple geometries, as the so called
pill-box, which are not useful for real applications.
These numerical programs are used to optimize the shape of the
cavity, given overall dimensions, in order to get the best values for the
requested resonant frequency, field pattern <strong>and</strong> quality factor. Most
known <strong>and</strong> used computer programs for such a calculations are:
• Superfish 3 is a frequency domain 2-dimensional (2D) simulator
which uses a finite elements algorithm. From the practical
point of view, after the preparation of a file with the geometry
of the structure, one can obtain the resonant frequency for
every resonant mode of the cavity, the quality factor <strong>and</strong> the
shunt impedance <strong>and</strong> other useful parameters. The program
has lots of internal macro dedicated to the calculations of parameters
useful in the accelerator cavities design as the power
dissipated on each wall of the cavity. Other useful results given
are the resonant frequency variations for a unit displacement
of all the walls of which the cavity is composed.
• MAFIA 4 (MAxwell’s equations using a Finite Integration Algorithm)
is a 3-dimensional code either in the time <strong>and</strong> the
frequency domain. It has a CAD-like interface <strong>and</strong> it is a
powerful general purpose simulator. The later versions have
also the relevant possibility of calculation with small losses in
the walls.
3 See also the site www.lanl.gov for more information.
4 See also the site www.cst.de for more information.