Suppression of propagating TE modes in the FNAL antiproton source stochastic beam cooling system Page: 2 of 5
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SUPPRESSION OF PROPAGATING TE MOOES IN THE FNAL ANTIPROTON SOURCE STOCHASTIC BEAM COOL KG SYSTEM*
Walter C. Barry
Lawranca Barkalay Laboratory
Uni vanity of California
Barkalay, California *4720
Abatract
A method of attenuating the propagation of
waveguide model in the itochattic cooling array beam pip«
to be utilized in the accumulator and dabuncher ring* of the
Fermilab antiproton aource is detcrlbad. The attenuation
method treated involves lining the vertical walls of the
beam pipes with a ferrimsgnetic material. The general
solution for propagation in a nonhomogeneously loaded
waveguide is presented along with numerical results specific
to the antiproton source beam cooling system. Also
described is a broadband, automated technique for the
simultaneous measurement of complex m and < developed
to aid in the characterization of different ferrite materials.
Permittivity and permeability data for a typical ferrite it
presented along with a discussion of the effects of these
parameters on waveguide mode attenuation in the ferrite
lined beam pipes.
Introduction
This papar addresses the problem of attenuating
the propagation of waveguide modes in the stochastic
cooling array beam pipes to be utilized in the accumulator
and debuncher rings of the FNAL P source. 1 The
rectangular geometries of both the 1-2 GHz and 2-4 GHz
array beam pipes allow propagation of the TEiq, TE20,
TE]Q and TEsq modes within the operating band of each
pipe. These waveguide modes propagate with a velocity
comparable to that of the beam and can Induce false signals
on the array pickups thereby raising the overall noise level
in the system. The method treated here for attenuating
these waveguide modes involves lining the vertical walls of
the beam pipes with a ferrimagnetlc material of complex
permittivity and permeability (c and a). The decision to
employ ferrite as the attenuating material was based on its
excellent RF attenuating properties, vacuum compatibility,
and availability.
c ■ c' - i c" k2 - i»Z p c
w " u' - i u" yt k* - P0 c0
I
II
IV
V
hi
ko
k
ko
k
ko
‘-trH
1-11-1
-c -b »a a b c
ML M4-2IM
Fig. 1. Farrits Leaded Waveguide Geometry
The goai of the analysis is to determine the attenuating
effect of the ferrite for the different modes that may be
pretent in the guide. Some ineight info the optimum
placement of the ferrite for maximum attenuation is aiao
desired. By solving the boundary value problem for the
loaded guide, the eigenvalue equations that govern the
propagation constants of the odd and even modes in the
guide can be obtained. The attenuation of a given mode is
then related to the real part of its propagation constant.
Because of the length of the analysis, only the pertinent
results, the odd and even eigenvalue equations, are
presented below. The detailed boundary value analysis may
be found in reference [2].
The eigenvalue equations presented are valid for
odd and even TE modes with no field variations with the y
coordinate. This condition is satisfied for frequencies less
than 5 GHz for both the 1-2 GHz and 2-4 GHz arrays whose
x,y dimensions are 30 cm, 3 cm and 15 cm, 3 cm
respectively. The equations are:
The general solution for propagation in a
nonhomogeneously loaded waveguide is described along with
a broadband, automated technique for simultaneously
measuring the complex c and » of a given ferrite sample.
This measurement technique was developed to characterize
accurately the electromagnetic properties of the several
different ferrites under consideration for the attenuation
application. By using the c and u data measured by this
technique in conjunction with the loaded waveguide analysis,
the attenuation of TE modes in a beam pipe lined with a
qiven ferrite could be predicted. On this basis a particular
ferrite was chosen to line a 2-4 GHz array to be installed in
tix* debuncher ring of the p source. Future experiments to
determine the effect of this loaded array on noise levels in
the debuncher are anticipated.
Mode Analysis of Loaded Beam Pipe
Figure 1 depicts the cross section of a waveguide
(beam pipe) loaded with two slabs of ferrimagnetic material
(regions 11 and IV) of thickness tg. The slabs are parallel to
the direction of propagation (z) and at a distance tj
from each vertical wall. Regions 1, III and V are assumed to
be free space while regions U and IV have complex
permittivities and permeabilities of the form:
c - c' - jc* v * v* - Jm"
m0 ft tan(pt]) [j»o a tan(2t2) + up tan(pa)]
- np[v0 ft - up tan'ttj) tan(pa)J Even nodes (1)
w0 ft tanfpt^pp f *iQ ft tan(pa) tan(it2)]
- v*»[uP tan(2.t2) - fttan(pa)J Odd nodes (2)
where:
i - -ijp2tk2-kg
k * wVp*
Complex wave number in
loaded regions
P Complex eigenvalue for a
given mode (analogous to
cutoff wave number kc
for an unloaded guide)
ti. to. a Dimensions as defined in
Fig. I
•This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy
Physics Division, U.S. Dept, of Energy, under Contract No. DE-ACQ3-76SFQ0098.
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Barry, W.C. Suppression of propagating TE modes in the FNAL antiproton source stochastic beam cooling system, report, May 1, 1985; [Berkeley,] California. (https://digital.library.unt.edu/ark:/67531/metadc1072654/m1/2/: accessed July 16, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.