Field analysis of a dielectric-loaded rectangular waveguide accelerating structure. Page: 1 of 3
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FIELD ANALYSIS OF A DIELECTRIC-LOADED RECTANGULAR
WAVEGUIDE ACCELERATING STRUCTURE
Liling Xiao, Wei Gai and Xiang Sun
Argonne National Laboratory, Argonne, IL 60439, USA
In this paper, we present a detailed analysis of the
modes of a dielectric-loaded rectangular waveguide
accelerating structure. In general, the acceleration field
in a synchronous acceleration mode is non-uniform in
the two transverse dimensions. However, we could use
an array of these structures rotated alternatively by 90
degrees to get a focusing-defocusing force
continuously as a simple FODO lattice, while
maintaining uniform energy gain. The expressions of
characteristic parameters such as R/Q, group velocity
and attenuation constant are given. The longitudinal
wake field experienced by a relativistic charged
particle beam in the structure is also presented. These
analytical results are also compared with numerical
calculations using the MAFIA code suite
demonstrating the validity of our analytic approach.
The possible applications of millimeter-wave
dielectric waveguide accelerating structures to high
energy accelerator have received much attention [1-6].
This class of accelerating structures can produce a high
accelerating gradient and can easily be fabricated. Any
dielectric slow wave structure can support travelling-
wave luminal accelerating modes. In order to avoid
breakdown of the structure at higher accelerating
fields, it is desirable to operate accelerating structures
at higher frequencies , such as at W-Band.
However, while higher frequency cylindrical structures
would yield higher accelerating fields and shunt
impedances, but the available energy per unit length
for beam acceleration is limited. Therefore, simply
scaling cylindrical geometry structures to higher
frequencies may not lead to a higher luminosity
accelerator. Tuning and fabricating small cylindrical
structure is also becoming difficulty. It was pointed
out by  that transverse wakefield and space charge
force would be smaller than the axis symmetric
Fig.1. Dielectric-loaded rectangular guide (a), the
half cross section (b)
In this paper, we study a slab type dielectric structure
as shown in Fig.1 using a normal mode analysis. The
electromagnteic properties of a planar dielectric lined
waveguide had been analysed for an idealised case
(w--oc) in  and . Wakefields were calculated in
. In this paper we calculate 3-D field distributions
for a rectangular partially filled dielectric waveguide,
and we give an exact solution for all the field
components in terms of LSM (longitudinal section
magnetic) and LSE (longitudinal section electric)
modes using a mode matching method. This analysis
provides a basis for studying the properties of this
structure as an accelerator. We also present a
wakefield calculation using the field analysis results.
2 FIELD COMPONENTS
The normal modes in dielectric-loaded guides are
LSM and LSE modes  that have no H or E
components normal to the dielectric interface. This
corresponds to assuming the transverse direction to the
interface normal vector to be the direction of
The general structure considered here is limited to
the case of two H-plane slabs placed symmetrically.
We also only analyse these modes with the longitudinal
electric components at the central point since any other
modes will not couple to the beam. It implies that the
central plane in the y-z view is a magnetic wall, so that
only a half section with two subregions is needed for
the analysis (shown in Fig. 1(b)). In each region, the
fields for LSM/LSE modes derive from the
electric/magnetic Hertzian potential and satisfy the
boundary conditions at the interface between dielectric
Due to the limited space, only the results for LSMmn
modes are given here. The electric-type Hertzian
potential function *e is
' A sin (x+-)sinkyoe) -, 0<y<a
B sin-(x+-)cosk (b-y)-e'6', a<y<b
k z0 2 - (r ky =k fl) -n,
2(1 _e ek2 -(---)2,
where k=2-f/c is the propagation constant in free
The field components for LSMmn modes derive from
*e and are given by
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Xiao, L.; Gai, W. & Sun, X. Field analysis of a dielectric-loaded rectangular waveguide accelerating structure., article, July 16, 2001; Illinois. (digital.library.unt.edu/ark:/67531/metadc723231/m1/1/: accessed October 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.