V.V. Paramonov
Institute for Nuclear Research of the RAS, 117312, Moscow, Russia
The Drift Tube (DT) accelerating structure is very well known, developed
and widely used in existent proton linacs. Nevertheless, in the development
of new projects all time arise the problem to estimate rf parameters of the
structure for particular case given.
This paper is the first report about activity in the creation of the data
library for accelerating structures development. Basing on particularities
of codes, which were developed early in INR (CPU time to calculate in 2D
approximation one variant of the cell is several seconds with modern computer)
and later were added with the shell to change automatically cell dimensions
and tune to the frequency given, we store one time extremely large number
of variants. The ranges of the cell dimensions overlap all known and another
reasonably interesting variants of the DT structure application (both with
focusing lenses inside drift tubes and without lenses).
The main (cells dimensions, quality factor, shunt impedance, transit
time factor) and additional results (the distribution of rf losses and so on)
are stored in the file and provide the data base for further treatment.
Using the data base obtained, we can with scaling and interpolation consider
and compare, without additional calculations, rf parameters of the structure
at different frequencies and with different limitations, finding either
optimal or compromise solution for the structure.
All times in design of the accelerating structure there is the problem
to find reasonable compromise between different requirements. It may
be internal problem in the structure design - how to choose
dimensions to have effective shunt impedance 
as high as possible and
to keep electrical field at the surface 
(usually in parts of the Kilpatric limit
)
in reasonable limits.
The increasing of an aperture radius is good for beam dynamic, but leads
to the reduction in the . The manufacturing processes will be
simpler if a set of dimensions will be constant through the structure,
but it means that will be deviation from optimal parameters.
As a role, dependencies of parameters from dimensions qualitatively are known,
but, if the problem arises to have a number (to estimate "the price" of the
solution), the designer needs to do estimation or additional calculations.
To simplify the design procedure for the DTL structure, this work has been
performed.
Several years ago the set of very powerful 2D codes [1] was developed in
INR. With modern "middle power" computers, like DEC ALFA 2000, one run takes
of
order 
sec CPU time from mesh generation to physical postprosessing
with high precision of results. Later, this set of codes was added with several
simple codes to provide the system, which allows to perform automatically
the set of similar calculations.
The idea and realization of the data base are not so complicated.
The cell of the accelerating structure may be specified with several
independent parameters (for example length, aperture radius, gap ratio
and so on) and one dependent - to tune the cell for the operating frequency
given 
.
Two options of the DTL structure have been considered (Fig. 1). The first
one is a conventional DTL with the possibility to place focusing
lenses inside drift tubes. The second option has small drift tubes
without lenses and is intended for high frequency DTL application -
Bridge Coupled DTL (BCDTL) [2].
The cell of the DTL for both options is specified with six independent
parameters and the cell radius 
as dependent one. The limits of the
independent parameters in normalized type (in parts of operating
wavelength 
) are listed in Table 1.
Several steps with each parameters were done during the data base storage.
As a role, the dependencies of the structure rf parameters vrs dimensions
are smooth enough and not so many points are needed to approximate any
curve using cubic spline interpolation. It is evident, that accuracy of this
interpolation is better for larger number of points. But, if we have M
independent parameters and are going to do N steps with each parameter,
number of variants to be calculated is 
. As the results of the
compromise between accuracy of the interpolation and the total number of
variants for calculations, from 4 to 7 steps for each parameter were
chosen, depending on influence of the parameter given on the structure rf
characteristics.
It is not so difficult to develop algorithm for this work and to pass
this long routine job to computer, for which it is directly intended.
The system takes one variant, tunes it to frequency specified, stores results
and goes to next variant automatically.
The results of this job are M-dimensional arrays in direct access file.
For every variant are stored:
a) - the cell dimensions,
b) - general parameters of the structure - transit time factor T,
quality factor Q, effective shunt impedance , maximum electric
field at the surface - 
ratio, maximum magnetic
field at the surface - 
ratio.
The surface of the cell is divided in several segments. For each segment
are stored:
c) - the relative part of rf losses (with respect to losses in total cell),
d) - frequency shift due to possible displacement of this segment,
e) - maximum electric field at the segment - 
ratio.
As the particularities of the DTL structure, frequency shift and additional
rf losses in the stem together with additional
rf losses in the end wall are calculated and stored.
The data base stored is the main value of the system.
The procedure of the application is also simple. First of all,
the designer should
specify DTL option and the operating frequency. The data base will be
extracted,
scaled to the frequency specified and the available ranges of the cell
dimensions will be displayed.
of the BCDTL option for
different operating frequencies.
There is a large variety of the data base applications for the DTL design. The
simplest one is the comparison of different DTL variants. For this purpose
the designer should specify the cells dimensions under interest.
After each specification,
using standard methods of the cubic spline interpolation, dimensions of
data arrays will be reduced at 1. At the end of this procedure the values
of rf parameters, corresponding to the cell dimensions specified, will be
displayed.
For example, at Fig. 2 and Fig. 3 the plots of and
for different BCDTL operating frequencies, assuming
are shown. If the dimensions of the
drift tube are fixed, especially aperture radius, the increasing of the
operating frequency do not leads to the increasing in shunt impedance.
surface for the BCDTL option
surface for the BCDTL option
Two dimensional plots are efficient tool to provide general picture for
the DTL parameters behavior vrs cell dimensions.
For example, at Fig. 4 and Fig. 5 the surfaces of and ,
available for BCDTL option assuming 
, are plotted. Comparing these two
surfaces, one can see, that conditions to get maximum shunt impedance
practically coincide with ones to have a large 
value.
More interesting and important case of application is to find optimal
parameters with restrictions. Usually, the aperture radius is restricted from
below with the beam dynamic requirements. The maximum electric
field at the surface - should be also specified in the beginning
of the design. Then, to simplify the manufacturing process, the designer can
specify the set of another parameters, for example, cavity radius ,
lower and upper DT radii 
, and find maximum of , determining
simultaneously the deviation from global maximum (without limitation in
parameters specified for manufacturing simplification).
It is possible to consider also the segmentation of the structure into
accelerating cavities, taking into account additional rf losses. At Fig. 6
the plots of the effective shunt impedance for regular (a) BCDTL cell
( 
), average
for 6 cells BCDTL cavities taking into account rf losses in end walls (b),
in end walls and stems with radius 
(c) are shown. Additional
rf losses strongly reduce efficiency of the structure, especially for low
proton energies.
Because the code source for data base treatment is open, it can be added with any possibility proposed.
The data base for rf parameters of the DTL structure has been developed. The large number of calculations has been performed one time and stored. The application of this data base allows for the designer to work more creatively, providing him more time to choose the best solution.
The author thanks I.V. Gonin for his help in development of the data storage system and V.A. Moiseev for fruitful comments during the system application for DTL linac consideration.